%               Time-stamp: <2000-05-14 15:54:30 whitcher>
%
%       BIBLIOGRAPHY OF WAVELET, TIME-SERIES, AND RELATED DOCUMENTS
%
%                         Brandon J Whitcher
%                       EURANDOM, P.O. Box 513
%                 5600 MB Eindhoven, The Netherlands
%                      whitcher@eurandom.tue.nl
%                http://www.eurandom.tue.nl/whitcher
%
%
%    Please don't remove this header if you copy or transfer this file.
%
%

@String{AandA =  "Astronomy and Astrophysics"}

@String{AAP =    "Annals of Applied Probability"}

@String{AASS =   "Astronomy \& Astrophysics Supplement Series"}

@String{ACHA =   "Applied and Computational Harmonic Analysis"}

@String{AG =     "Annales Geophysicae"}

@String{AML =    "Applied Mathematical Letters"}

@String{AMM =    "American Mathematical Monthly"}

@String{AMS =    "American Mathematical Society"}

@String{AnJ =    "The Astronomical Journal"}

@String{AofMS =  "The Annals of Mathematical Statistics"}

@String{AofS =   "Annals of Statistics"}

@String{ApJ =    "The Astrophysical Journal"}

@String{AS =     "Applied Statistics"}

@String{BAMathS = "Bulletin of the American Mathematical Society
                 (N.S.)"}

@String{BAMetS = "Bulletin of the American Meteorological Society"}

@String{Ber =    "Bernoulli"}

@String{BKA =    "Biometrika"}

@String{BLM =    "Boundary-Layer Meteorology"}

@String{CE =     "Computational Economics"}

@String{CG =     "Chemical Geology"}

@String{CS =     "Computational Statistics"}

@String{CSA =    "Communications in Statistics A"}

@String{CSB =    "Communications in Statistics B"}

@String{CSDA =   "Computational Statistics \& Data Analysis"}

@String{CSS =    "Computing Science and Statistics"}

@String{ECA =    "Econometrica"}

@String{ECJ3 =   "Electronics and Communications in Japan 3"}

@String{EE =     "Empirical Economics"}

@String{EI =     "Earth Interactions"}

@String{EL =     "Economics Letters"}

@String{EP =     "Environmental Pollution"}

@String{ET =     "Econometric Theory"}

@String{FS =     "Financial Stochastics"}

@String{GJI =    "Geophysical Journal International"}

@String{GJRAS =  "Geophysical Journal of the Royal Astronomical
                 Society"}

@String{GP =     "Geophysical Prospecting"}

@String{GRL =    "Geophysical Research Letters"}

@String{IEICETFECCS = "IEICE Transactions on Fundamentals of Electronics
                 Communications and Computer Science"}

@String{IEEEAPM = "IEEE Antennas and Propagation Magazine"}

@String{IEEECSE = "IEEE Computational Science and Engineering"}

@String{IEEEP =  "IEEE Proceedings"}

@String{IEEES =  "IEEE Spectrum"}

@String{IEEESPL = "IEEE Signal Processing Letters"}

@String{IEEESPM = "IEEE Signal Processing Magazine"}

@String{IEEESPS = "IEEE Signal Processing Society"}

@String{IEEETAC = "IEEE Transactions on Automatic Control"}

@String{IEEETAE = "IEEE Transactions on Audio and Electroacoustics"}

@String{IEEETAES = "IEEE Transactions on Aerospace and Electronic
                 Systems"}

@String{IEEETASSP = "IEEE Transactions on Acoustics, Speech, and Signal
                 Processing"}

@String{IEEETC = "IEEE Transactions on Communications"}

@String{IEEETCS = "IEEE Transactions on Circuits and Systems"}

@String{IEEETCS2 = "IEEE Transactions on Circuits and Systems--II"}

@String{IEEETGRS = "IEEE Transactions on Geoscience and Remote Sensing"}

@String{IEEETIM = "IEEE Transactions on Instrumentation and
                 Measurement"}

@String{IEEETIP = "IEEE Transactions on Image Processing"}

@String{IEEETIT = "IEEE Transactions on Information Theory"}

@String{IEEETMI = "IEEE Transactions on Medical Imaging"}

@String{IEEETPAMI = "IEEE Transactions on Pattern Analysis and Machine
                 Intelligence"}

@String{IEEETSP = "IEEE Transactions on Signal Processing"}

@String{IJC =    "International Journal of Climatology"}

@String{IJE =    "International Journal of Electronics"}

@String{IJF =    "International Journal of Forecasting"}

@String{JAcSA =  "Journal of the Acoustical Society of America"}

@String{JAM =    "Journal of Applied Meteorology"}

@String{JAOT =   "Journal of Atmospheric and Oceanic Technology"}

@String{JAS =    "Journal of Atmospheric Science"}

@String{JASA =   "Journal of the American Statistical Association"}

@String{JASS =   "Journal of Applied Statistical Science"}

@String{JAT =    "Journal of Approximation Theory"}

@String{JBES =   "Journal of Business and Economic Statistics"}

@String{JC =     "Journal of Climate"}

@String{JCGS =   "Journal of Computational and Graphical Statistics"}

@String{JCty =   "Journal of Climatology"}

@String{JEcol =  "Journal of Ecology"}

@String{JEcon =  "Journal of Econometrics"}

@String{JEDC =   "Journal of Economic Dynamics and Control"}

@String{JETE =   "Journal of Economic Theory and Econometrics"}

@String{JF =     "Journal of Forecasting"}

@String{JFAA =   "Journal of Fourier Analysis and Applications"}

@String{JFM =    "Journal of Fluid Mechanics"}

@String{JGR =    "Journal of Geophysical Research"}

@String{JGRA =   "Journal of Geophysical Research -- Atmospheres"}

@String{JISS =   "Journal of the Italian Statistical Society"}

@String{JMP =    "Journal of Mathematical Physics"}

@String{JMS =    "Journal of the Meteorological Society"}

@String{JNS =    "Journal of Nonparametric Statistics"}

@String{JPA =    "Journal of Physics A"}

@String{JPO =    "Journal of Physical Oceanography"}

@String{JRSSA =  "Journal of the Royal Statistical Society A"}

@String{JRSSB =  "Journal of the Royal Statistical Society B"}

@String{JSCS =   "Journal of Statistical Computation and Simulation"}

@String{JTSA =   "Journal of Time Series Analysis"}

@String{JVA =    "Journal of Vibration and Acoustics"}

@String{JVCIR =  "Journal of Visual Communication and Image
                 Representation"}

@String{KKA =    "Kybernetika"}

@String{MCM =    "Mathematical and Computer Modelling"}

@String{MKA =    "Metrika"}

@String{MWR =    "Monthly Weather Review"}

@String{NJ =     "New Jersey"}

@String{NY =     "New York"}

@String{OE =     "Optical Engineering"}

@String{PEM =    "Probability Engineering Mechanics"}

@String{PIEEE =  "Proceedings of the IEEE"}

@String{PR =     "Pattern Recognition"}

@String{PRE =    "Physical Review E"}

@String{PRL =    "Physical Review Letters"}

@String{PRSLA =  "Proceedings of the Royal Society of London, Series A"}

@String{PTRSLA = "Philosophical Transactions of the Royal Society of
                 London A"}

@String{QJRMS =  "Quarterly Journal of the Royal Meteorological
                 Society"}

@String{RES =    "Review of Economic Studies"}

@String{SC =     "Statistics and Computing"}

@String{SD =     "San Diego"}

@String{SF =     "San Francisco"}

@String{SIAM =   "Society for Industrial and Applied Mathematics"}

@String{SIAMJMA = "SIAM Journal of Mathematical Analysis"}

@String{SIAMJSC = "SIAM Journal of Scientific Computing"}

@String{SIAMJSSC = "SIAM Journal on Scientific and Statistical
                 Computing"}

@String{SiG =    "Surveys in Geophysics"}

@String{SINUM =  "SIAM Journal of Numerical Analysis"}

@String{SIREV =  "SIAM Review"}

@String{SJS =    "Scandanavian Journal of Statistics"}

@String{SN =     "Statistica Neerlandica"}

@String{SNDE =   "Studies in Nonlinear Dynamics and Economics"}

@String{SP =     "Signal Processing"}

@String{SPIE =   "The International Society for Optical Engineering"}

@String{SPL =    "Statistics \& Probability Letters"}

@String{SPTA =   "Stochastic Processes and Their Applications"}

@String{SS =     "Statistical Science"}

@String{SSin =   "Statistica Sinica"}

@String{TAS =    "The American Statistician"}

@String{TECH =   "Technometrics"}

@String{TIEICEA = "Transactions of the Institute of Electronics,
                 Information and Communication Engineers A"}

@String{TPIA =   "Theory of Probability and Its Applications"}

@String{WRR =    "Water Resources Research"}

%%%%%----------%%%%%----------%%%%%----------%%%%%----------%%%%%

@Article{abr-ben:adaptive,
  title =        "Adaptive thresholding of wavelet coefficients",
  author =       "Felix Abramovich and Y. Benjamini",
  journal =      CSDA,
  volume =       "22",
  pages =        "351--361",
  year =         "1996",
  url =          "http://www.math.tau.ac.il/~felix/ltx/JCSDA.ps.gz",
  email =        "felix@math.tau.ac.il",
}

@InCollection{abr-ben:thresholding,
  title =        "Thresholding of wavelet coefficients as multiple
                 hypotheses testing procedure",
  author =       "Felix Abramovich and Y. Benjamini",
  pages =        "5--14",
  crossref =     "ant-opp:wavelets",
  url =          "http://www.math.tau.ac.il/~felix/Papers.html",
  email =        "felix@math.tau.ac.il",
}

@Unpublished{abr-etal:scaling,
  title =        "Wavelets for the analysis, estimation and synthesis of
                 scaling data",
  author =       "P. Abry and P. Flandrin and M. S. Taqqu and D.
                 Veitch",
  year =         "1998",
  note =         "preprint",
  url =          "http://www.serc.rmit.edu.au/~darryl/wwbook.ps",
}

@Article{abr-fla:initial,
  title =        "{O}n the initialization of the discrete wavelet
                 transform algorithm",
  author =       "P. Abry and P. Flandrin",
  journal =      IEEESPL,
  volume =       "1",
  number =       "2",
  year =         "1994",
  pages =        "32--34",
  abstract =     "The authors show that making use of the discrete
                 wavelet transform to analyse data implies performing a
                 preliminary initialization of the fast pyramidal
                 algorithm. An approximation enabling easy performance
                 of such an initialization is proposed.",
  keywords =     "initialization. discrete wavelet transform algorithm.
                 fast pyramidal algorithm. performance.",
}

@InProceedings{abr-gon-fla:based,
  title =        "Wavelet-based spectral analysis of $1/f$ processes",
  author =       "P. Abry and P. Gon\c{c}alv{\`e}s and P. Flandrin",
  booktitle =    "Proceedings of the IEEE International Conference on
                 Acoustics, Speech, and Signal Processing",
  volume =       "3",
  year =         "1993",
  pages =        "237--240",
  note =         "Minneapolis, MN, USA",
  keywords =     "1/f processes, time-scale-based spectral estimation,
                 matched tilings, time-frequency plane, probability
                 density function, discrete wavelet scheme, minimum
                 variance estimator, weighted least-squares",
  abstract =     "The authors attempt to show how and why a
                 time-scale-based spectral estimation naturally suits
                 the nature of $1/f$ processes, characterized by a power
                 spectral density proportional to $|\nu|^{-\alpha}$.
                 They show that a time-scale approach allows an unbiased
                 estimation of the spectral exponent alpha and interpret
                 this result in terms of matched tilings of the
                 time-frequency plane. They derive explicitly the
                 probability density function of the estimated value of
                 $\alpha$. From this analysis, they find that there
                 exists an optimum number of scales to use in a discrete
                 wavelet scheme for obtaining a minimum variance
                 estimator and that an improved procedure can be
                 designed by making use of weighted least-squares in the
                 estimation.",
}

@InProceedings{abr-gon-fla:spectrum,
  title =        "Wavelets, spectrum analysis and 1/f processes",
  author =       "P. Abry and P. Gon\c{c}alv{\`e}s and P. Flandrin",
  pages =        "15--29",
  crossref =     "ant-opp:wavelets",
  abstract =     "The purpose of this paper is to evidence why
                 wavelet-based estimators are naturally matched to the
                 spectrum analysis of $1/f$ processes. It is shown how
                 the revisiting of classical spectral estimators from a
                 time-frequency perspective allows to define different
                 wavelet-based generalizations which are proved to be
                 statistically and computationally efficient.
                 Discretization issues (in time and scale) are discussed
                 in some detail, theoretical claims are supported by
                 numerical experiments and the importance of the
                 proposed approach in turbulence studies is
                 underlined.",
}

@Unpublished{abr-sap-sil:bayesian,
  title =        "Wavelet thresholding via a {B}ayesian approach",
  author =       "Felix Abramovich and T. Sapatinas and Bernard
                 Silverman",
  year =         "1996",
  note =         "Submitted",
  url =          "http://www.math.tau.ac.il/~felix/ltx/Bayes.ps.gz",
  email =        "felix@math.tau.ac.il",
}

@Article{abr-sel:synthesis,
  title =        "The wavelet-based synthesis for fractional {B}rownian
                 motion - {P}roposed by {F}. {S}ellan and {Y}. {M}eyer:
                 {R}emarks and fast implementation",
  author =       "P. Abry and F. Sellan",
  journal =      ACHA,
  volume =       "3",
  number =       "4",
  pages =        "377--383",
  year =         "1996",
}

@Article{abr-sil:inverse,
  title =        "Wavelet decomposition approaches to statistical
                 inverse problems",
  author =       "F. Abramovich and B. W. Silverman",
  journal =      BKA,
  volume =       "85",
  number =       "1",
  pages =        "115--129",
  year =         "1998",
  keywords =     "exact risk analysis. near-minimax estimation. singular
                 value decomposition. spatially adaptive estimation.
                 statistical linear inverse problem. vaguelette.
                 wavelet.",
  abstract =     "A wide variety of scientific settings involve indirect
                 noisy measurements where one faces a linear inverse
                 problem in the presence of noise. Primary interest is
                 in some function f(t) but data are accessible only
                 about some linear transform corrupted by noise; The
                 usual linear methods for such inverse problems do not
                 perform satisfactorily when f(t) is spatially
                 inhomogeneous. One existing nonlinear alternative is
                 the wavelet-vaguelette decomposition method, based on
                 the expansion of the unknown f(t) in wavelet series. In
                 the vaguelette- wavelet decomposition method proposed
                 here, the observed data are expanded directly in
                 wavelet series. The performances of various methods are
                 compared through exact risk calculations, in the
                 context of the estimation of the derivative of a
                 function observed subject to noise. A result is proved
                 demonstrating that, with a suitable universal threshold
                 somewhat larger than that used for standard denoising
                 problems, both the wavelet-based approaches have an
                 ideal spatial adaptivity property.",
}

@Article{abr-vei-fla:revisiting,
  title =        "Long Range Dependence: {R}evisiting Aggregation with
                 Wavelets",
  author =       "Patrice Abry and Darryl Veitch and Patrick Flandrin",
  journal =      JTSA,
  volume =       "19",
  number =       "3",
  pages =        "253--266",
  year =         "1998",
  url =          "http://www.serc.rmit.edu.au/~darryl/A2.ps",
  keywords =     "long-range dependence, self-similarity, aggregation,
                 multiresolution analysis, wavelet transform, parameter
                 estimation",
  abstract =     "The aggregation procedure is a natural way to analyse
                 signals which exhibit long-range dependent features and
                 has been used as a basis for estimation of the Hurst
                 parameter, H. In this paper it is shown how aggregation
                 can be naturally rephrased within the wavelet transform
                 framework, being directly related to approximations of
                 the signal in the sense of a Haar-multiresolution
                 analysis. A natural wavelet based generalisation to
                 traditional aggregation is then proposed:
                 ``a-aggregation''. It is shown that a-aggregation
                 cannot lead to good estimators of H, and so a new kind
                 of aggregation, ``d-aggregation'', is defined, which is
                 related to the details rather than the approximations
                 of a multiresolution analysis. An estimator of H based
                 on d-aggregation has excellent statistical and
                 computational properties, whilst preserving the spirit
                 of aggregation. The estimator is applied to
                 telecommunications network data.",
}

@Article{abr-vei:traffic,
  title =        "Wavelet analysis of long-range-dependent traffic",
  author =       "P. Abry and D. Veitch",
  journal =      IEEETIT,
  volume =       "44",
  number =       "1",
  pages =        "2--15",
  year =         "1998",
  url =          "http://www.serc.rmit.edu.au/~darryl/A1.ps",
  keywords =     "Hurst parameter long-range dependence packet traffic
                 parameter estimation stationarity telecommunications
                 networks time-scale analysis wavelet decomposition",
  abstract =     "A wavelet-based tool for the analysis of long-range
                 dependence and a related semi-parametric estimator of
                 the Hurst parameter is introduced, The estimator is
                 shown to be unbiased under very general conditions, and
                 efficient under Gaussian assumptions. It can be
                 implemented very efficiently allowing the direct
                 analysis of very large data sets, and is highly robust
                 against the presence of deterministic trends, as wed as
                 allowing their detection and identification.
                 Statistical, computational, and numerical comparisons
                 are made against traditional estimators including that
                 of Whittle. The estimator is used to perform a thorough
                 analysis of the long-range dependence in Ethernet
                 traffic traces, New features are found with important
                 implications for the choice of valid models for
                 performance evaluation, A study of mono versus
                 multifractality is also performed, and a preliminary
                 study of the stationarity with respect to the Hurst
                 parameter and deterministic trends.",
}

@Book{ack:real-time,
  title =        "Real-Time Signal Processing: Design and Implementation
                 of Signal Processing Systems",
  booktitle =    "Real-Time Signal Processing: Design and Implementation
                 of Signal Processing Systems",
  author =       "John G. Ackenhusen",
  publisher =    "Prentice Hall",
  address =      "Upper Saddle River, NJ",
  year =         "1999",
  pages =        "461",
}

@TechReport{agu:evaluating,
  title =        "Wavelet and Autoregressive Decompositions for
                 Evaluating Frequency Compositions in Time Series",
  author =       "Omar Aguilar",
  institution =  "Institute of Statisics and Decision Sciences, Duke
                 University",
  year =         "1996",
  note =         "Discussion Paper 96-22",
  url =          "ftp://ftp.isds.duke.edu/pub/WorkingPapers/96-22.ps",
}

@InProceedings{al-li:application,
  title =        "Application of shift-invariant wavelet transform to
                 video coding",
  author =       "Mohammed A. Al-Mohimeed and Ching-Chung Li",
  pages =        "64--75",
  booktitle =    "Video Techniques and Software for Full-Service
                 Networks",
  editor =       "Tzi-cker Chiueh and Andrew G. Tescher",
  volume =       "2915",
  series =       "Proceedings of the SPIE",
  year =         "1997",
  abstract =     "The standard discrete wavelet transform lacks
                 translation invariance in 1-D signals and 2-D images.
                 The down-sampling at each coarser scale accentuates the
                 undesirable effects of the shift-variance, in
                 particular, on the motion estimation from decomposed
                 subimages in video coding. In this paper, we present a
                 study of applying the Chui-Shi shift-invariant wavelet
                 transform using 'oversampling frames' to video
                 compression. Further, we present an algorithm for
                 approximating the motion fields at different scales and
                 different frequency bands by utilizing the
                 multiresolution structure of wavelet decomposition.
                 Motion vectors at a higher resolution are predicted by
                 the motion vectors at a lower resolution through a
                 proper scaling. Experimental results on a salesman
                 video sequence show that the use of the 2-D
                 oversampling algorithm of a biorthogonal spline wavelet
                 has reduced the required number of motion vectors while
                 maintaining an acceptable prediction error when
                 compared to the classical block matching technique
                 using the standard wavelet transform. The proposed
                 approach will advance the video compression methodology
                 for applications to HDTV and video conferencing.",
}

@Book{ald-uns:medicine,
  title =        "Wavelets in Medicine and Biology",
  booktitle =    "Wavelets in Medicine and Biology",
  author =       "Akram Aldroubi and Michael Unser",
  publisher =    "CRC Press Inc.",
  address =      "Boca Raton",
  pages =        "608",
  year =         "1996",
  ISBN =         "0-8493-9483-X",
  url =          "http://www.crcpress.com/prods/9483.htm",
  abstract =     "Considerable attention from the international
                 scientific community is currently focused on the wide
                 ranging applications of wavelets. For the first time,
                 the field's leading experts have come together to
                 produce a complete guide to wavelet transform
                 applications in medicine and biology. Wavelets in
                 Medicine and Biology provides accessible, detailed, and
                 comprehensive guidelines for all those interested in
                 learning about wavelets and their applications to
                 biomedical problems. The book consists of four main
                 sections: Theory and Implementation of Wavelet
                 Transforms, Wavelets in Medical Imaging and Tomography,
                 Wavelets and Biomedical Signal Processing, Wavelets and
                 Mathematical Models in Biology. The introductory
                 material is written for non-experts and includes basic
                 discussions of the theoretical and practical
                 foundations of wavelet methods. The background and
                 introduction is followed by contributions from the most
                 prominent researchers in the field, giving the reader a
                 complete survey of the use of wavelets in biomedical
                 engineering. An international perspective is provided
                 throughout the book, with contributions from experts
                 from Germany, France, America, Belgium, Holland,
                 Turkey, and Switzerland.",
}

@TechReport{all-tet:checking,
  title =        "Checking for Model Consistency in Optimal
                 Fingerprinting",
  author =       "M. R. Allen and S. F. B. Tett",
  number =       "RAL-TR-97-040",
  institution =  "Council for the Central Laboratory of the Research
                 Councils",
  year =         "1997",
}

@Article{and-tre:trends,
  title =        "Using Wavelets to Detect Trends",
  author =       "Edgar L. Andreas and George Trevi{\~n}o",
  journal =      JAOT,
  volume =       "14",
  number =       "3",
  year =         "1997",
  pages =        "554--564",
  abstract =     "Wavelets are a new class of basis functions that are
                 finding wide use for analyzing and interpreting time
                 series data. This paper describes a new use for
                 wavelets--identifying trends in time series. The
                 general signal considered has a quadratic trend. The
                 inverted Haar wavelet and the elephant wavelet,
                 respectively, provide estimates of the first-order and
                 second-order coefficients in the trend polynomial.
                 Unlike usual wavelet applications, however, this
                 analysis requires only one wavelet dilation scale L,
                 where L is the total length of the time series. Error
                 analysis shows that wavelet trend detection is roughly
                 half as accurate as least squares trend detection when
                 accuracy is evaluated in terms of the mean-square error
                 in estimates of the first-order and second-order trend
                 coefficients. But wavelet detection is more than twice
                 as efficient as least squares detection in the sense
                 that it requires fewer than half the number of
                 floating-point operations of least squares regression
                 to yield the three coefficients of the quadratic trend
                 polynomial. This paper demonstrates wavelet trend
                 detection using artificial data and then various
                 turbulence data collected in the atmospheric surface
                 layer, and last, provides guidelines on when linear and
                 quadratic trends are ``significant'' enough to require
                 removal from a time series.",
}

@Article{and:magnitude,
  title =        "A Wavelet Magnitude Analysis Theorem",
  author =       "James C. Anderson",
  journal =      IEEETSP,
  volume =       "41",
  number =       "12",
  year =         "1993",
  pages =        "3541--3543",
  abstract =     "Wavelet transform is the constant-Q special case of
                 the generalized short time Fourier transform (GSTFT),
                 and is useful for wavelet analysis. Scalograms are
                 analyzed using specific types of filter/detector banks.
                 GSTFT results are universally applicable to wavelet
                 theory and are useful tools for scalogram sampling for
                 computation and data reduction functions.",
}

@Article{ans-gui-kai:lagrange,
  title =        "Wavelet Construction Using Lagrange Halfband Filters",
  author =       "R. Ansari and C. Guillemot and J. F. Kaiser",
  journal =      IEEETCS,
  volume =       "38",
  number =       "9",
  year =         "1991",
  pages =        "1116--1118",
  abstract =     "Using the approach described by M.J.T. Smith and T.P.
                 Barnwell (1986) for obtaining exact-reconstruction
                 filter banks, the authors present conjugate-quadrature
                 and linear-phase solutions for two-channel filter banks
                 using Lagrange halfband filters. It is shown that the
                 wavelet solutions obtained by I. Daubechies (1988)
                 under certain regularity conditions are the same as the
                 conjugate-quadrature solutions derived from Lagrange
                 halfband filters using the above approach. The
                 linear-phase solution that is described provides
                 filters with simple coefficients.",
}

@Article{ant-gij-gre:model,
  title =        "Model selection using wavelet decomposition and
                 applications",
  author =       "A. Antoniadis and I. Gijbels and G. Gr{\'e}goire",
  journal =      BKA,
  volume =       "84",
  number =       "4",
  pages =        "751--763",
  year =         "1997",
  keywords =     "consistency hypothesis testing minimum description
                 length criterion model selection nonparametric
                 regression wavelet decomposition",
  abstract =     "In this paper we discuss how to use wavelet
                 decompositions to select a regression model. The
                 methodology relies on a minimum description length
                 criterion which is used to determine the number of
                 nonzero coefficients in the vector of wavelet
                 coefficients. Consistency properties of the selection
                 rule are established and simulation studies reveal
                 information on the distribution of the minimum
                 description length selector. We then apply the
                 selection rule to specific problems, including testing
                 for pure white noise. The power of this test is
                 investigated via simulation studies and the selection
                 criterion is also applied to testing for no effect in
                 nonparametric regression.",
  email =        "Anestis.Antoniadis@imag.fr, gijbels@stat.ucl.ac.be,
                 Gerard.Gregoire@imag.fr",
}

@Article{ant-gij-mac:hazard,
  title =        "Nonparametric estimation for the location of a
                 change-point in an otherwise smooth hazard function
                 under random censoring",
  author =       "A. Antoniadis and I. Gijbels and B. MacGibbon",
  journal =      SJS,
  pages =        "???--???",
  year =         "2000",
  url =          "http://www.stat.ucl.ac.be/dp/dp98/dp9820.ps",
}

@Article{ant-gre-mck:curve,
  title =        "Wavelet Methods for Curve Estimation",
  author =       "A. Antoniadis and G. Gr{\'e}goire and I. W. McKeague",
  journal =      JASA,
  volume =       "89",
  number =       "428",
  pages =        "1340--1353",
  year =         "1994",
  keywords =     "Nonparametric regression",
}

@Article{ant-gre-nas:density,
  title =        "Density and hazard rate estimation for right censored
                 data using wavelet methods",
  author =       "Anestis Antoniadis and G{\'e}rard Gr{\'e}goire and Guy
                 P. Nason",
  journal =      JRSSB,
  volume =       "61",
  number =       "1",
  year =         "1999",
  pages =        "63--84",
  url =          "http://www.stats.bris.ac.uk:81/pub/reports/Wavelets/whf03.ps.gz",
  keywords =     "hazard rate survival data wavelet estimation",
  abstract =     "This paper describes a wavelet method for the
                 estimation of density and hazard rate functions from
                 randomly right-censored data. We adopt a nonparametric
                 approach in assuming that the density and hazard rate
                 have no specific parametric form. The method is based
                 on dividing the time axis into a dyadic number of
                 intervals and then counting the number of events within
                 each interval. The number of events and the survival
                 function of the observations are then separately
                 smoothed over time via linear wavelet smoothers, and
                 then the hazard rate function estimators are obtained
                 by taking the ratio. We prove that the estimators have
                 pointwise and global mean-square consistency, obtain
                 the best possible asymptotic mean integrated squared
                 error convergence rate and are also asymptotically
                 normally distributed. We also describe simulation
                 experiments that show that these estimators are
                 reasonably reliable in practice. The method is
                 illustrated with two real examples. The first uses
                 survival time data for patients with liver metastases
                 from a colorectal primary tumour without other distant
                 metastases. The second is concerned with times of
                 unemployment for women and the wavelet estimate,
                 through its flexibility, provides a new and interesting
                 interpretation.",
}

@TechReport{ant-gij:abrupt,
  title =        "Detecting abrupt changes by wavelet methods",
  author =       "Anestis Antoniadis and Ir{\`e}ne Gijbels",
  number =       "9716",
  institution =  "Institute de Statistique, Universit{\'e} Catholique de
                 Louvain",
  year =         "1997",
  url =          "http://www.stat.ucl.ac.be/dp/dp97/dp9716.ps",
  note =         "submitted to the {\em J. Nonpar. Stat.}",
}

@Article{ant-gus:wavelets,
  title =        "Wavelets and stochastic processes",
  author =       "I. Antoniou and K. Gustafson",
  journal =      "Mathematics and Computers in Simulation",
  volume =       "49",
  number =       "1-2",
  year =         "1999",
  pages =        "81--104",
  abstract =     "Wavelets are known to have intimate connections to
                 several other parts of mathematics, notably phase-space
                 analysis of signal processing, reproducing kernel
                 Hilbert spaces, coherent states in quantum mechanics,
                 spline approximation theory, windowed Fourier
                 transforms, and filter banks. Here, we establish and
                 survey a new connection, namely to stochastic
                 processes. Key to this link are the Kolmogorov systems
                 of ergodic theory.",
}

@Article{ant-pha:irregular,
  title =        "Wavelet regression for random or irregular design",
  author =       "Anestis Antoniadis and Dinh Tuan Pham",
  journal =      CSDA,
  volume =       "28",
  number =       "4",
  year =         "1998",
  pages =        "353--369",
  abstract =     "In this paper, wavelet regression estimators are
                 introduced, both in the random and the irregular design
                 cases and without the restriction that the sample size
                 be a power of two. A fast computational algorithm for
                 approximating the empirical counterpart of the scaling
                 and wavelet coefficients is developed. The convergence
                 rate of the estimator is established. The method is
                 illustrated by some simulations and by a real
                 example.",
}

@InCollection{ant:change-point,
  title =        "Wavelet estimators for change-point regression
                 models",
  author =       "Anestis Antoniadis",
  booktitle =    "Spline Functions and the Theory of Wavelets",
  editor =       "Serge Dubuc and Gilles Deslauriers",
  volume =       "18",
  series =       "CRM Proceedings \& Lecture Notes",
  publisher =    "American Mathematical Society",
  year =         "1999",
  pages =        "335--346",
  description =  "This work is based on a series of thematic workshops
                 on the theory of wavelets and the theory of splines.
                 Important applications are included. The volume is
                 divided into four parts: Spline Functions, Theory of
                 Wavelets, Wavelets in Physics, and Splines and Wavelets
                 in Statistics. Part one presents the broad spectrum of
                 current research in the theory and applications of
                 spline functions. Theory ranges from classical
                 univariate spline approximation to an abstract
                 framework for multivariate spline interpolation.
                 Applications include scattered-data interpolation,
                 differential equations and various techniques in CAGD.
                 Part two considers two developments in subdivision
                 schemes; one for uniform regularity and the other for
                 irregular situations. The latter includes construction
                 of multidimensional wavelet bases and determination of
                 bases with a given time frequency localization. In part
                 three, the multifractal formalism is extended to
                 fractal functions involving oscillating singularites.
                 There is a review of a method of quantization of
                 classical systems based on the theory of coherent
                 states. Wavelets are applied in the domains of atomic,
                 molecular and condensed-matter physics. In part four,
                 ways in which wavelets can be used to solve important
                 function estimation problems in statistics are shown.
                 Different wavelet estimators are proposed in the
                 following distinct cases: functions with
                 discontinuities, errors that are no longer Gaussian,
                 wavelet estimation with robustness, and error
                 distribution that is no longer stationary. Some of the
                 contributions in this volume are current research
                 results not previously available in monograph form. The
                 volume features many applications and interesting new
                 theoretical developments. Readers will find powerful
                 methods for studying irregularities in mathematics,
                 physics, and statistics.",
}

@Article{ant:review,
  title =        "Wavelets in statistics: a review (with discussion)",
  author =       "Anestis Antoniadis",
  journal =      JISS,
  volume =       "6",
  number =       "2",
  year =         "1999",
  pages =        "???--???",
}

@Article{arf:subdiurnal,
  title =        "On subdiurnal effects in earth rotation",
  author =       "K. Arfa-Kaboodvand and E. Groten",
  journal =      "Studia Geophysica et Geodaetica",
  volume =       "43",
  number =       "3",
  pages =        "275--283",
  year =         "1999",
}

@TechReport{ari-vid:scalograms,
  title =        "On Wavelet Scalograms and Their Applications in
                 Economic Time Series",
  author =       "Miguel A. {Ari\~{n}o} and Brani Vidakovic",
  number =       "95-21",
  year =         "1995",
  institution =  "Institute of Statisics and Decision Sciences, Duke
                 University",
  url =          "ftp://ftp.isds.duke.edu/pub/Users/brani/papers/WavTS.ps",
}

@TechReport{ari:forecasting,
  title =        "Time Series Forcasts Via Wavelets: {A}n Application to
                 Car Sales in the {S}panish Market",
  author =       "Miguel A. {Ari\~{n}o}",
  number =       "95-30",
  year =         "1995",
  institution =  "Institute of Statisics and Decision Sciences, Duke
                 University",
  url =          "ftp://ftp.isds.duke.edu/pub/WorkingPapers/95-30.ps",
}

@Article{aro:two-normal,
  title =        "The probability function of the product of two
                 normally distributed variables",
  author =       "Leo A. Aroian",
  journal =      AofMS,
  volume =       "18",
  pages =        "265--271",
  year =         "1947",
}

@Article{bai-sap-pow-krz:underwater,
  title =        "Signal detection in underwater sound using wavelets",
  author =       "T. C. Bailey and T. Sapatinas and K. J. Powell and W.
                 J. Krzanowski",
  journal =      JASA,
  volume =       "93",
  pages =        "73--83",
  year =         "1998",
  url =          "http://www.stats.bris.ac.uk/~mafs/jasa98_draft.ps.gz",
  keywords =     "Multivariate density estimation; Segmentation;
                 Short-time Fourier transform; Signal detection; Signal
                 processing; Thresholding; Underwater sounds; Wavelet
                 decomposition",
  abstract =     "This article considers the use of wavelet methods in
                 relation to a common signal processing problem, that of
                 detecting transient features in sound recordings that
                 contain interference or distortion. In this particular
                 case, the data are various types of underwater sounds,
                 and the objective is to detect intermittent departures
                 (potential `signals') from the background sound
                 environment in the data (`noise'), where the latter may
                 itself be evolving and changing over time. We develop
                 an adaptive model of the background interference, using
                 recursive density estimation of the joint distribution
                 of certain summary features of its wavelet
                 decomposition. Observations considered to be outliers
                 from this density estimate at any time are then flagged
                 as potential `signals.' The performance of our method
                 is illustrated on artificial data, where a known
                 `signal' is contaminated with simulated underwater
                 `noise' using a range of different signal-to-noise
                 ratios, and a `baseline' comparison is made with
                 results obtained from a relatively unsophisticated, but
                 commonly used, time-frequency approach. A similar
                 comparison is then reported in relation to the more
                 significant problem of detecting various types of
                 dolphin sound in real conditions.",
}

@Article{bal-oli-bau:discovery,
  title =        "Discovery of the near 158 day periodicity in group
                 sunspot numbers during the eighteenth century",
  author =       "J. L. Ballester and R. Oliver and F. Baudin",
  journal =      ApJ,
  volume =       "522",
  number =       "2",
  year =         "1999",
  pages =        "L153--L156",
  abstract =     "A new record of solar activity, made by compiling the
                 daily number of sunspot groups visible on the Sun's
                 surface between 1610 and 1995, has recently been made
                 available by Hoyt and Schatten. Wavelet analysis of
                 this record shows that an episode of the periodicity
                 near 158 days occurred during the eighteenth century,
                 around the maximum of solar cycle 2, and that episodes
                 of the periodicity, much weaker than that in solar
                 cycle 2, have appeared around the maxims of solar
                 cycles 16-21 (covering the interval 1923-1986). The
                 presence of the periodicity in the group sunspot number
                 confirms that it is caused by a periodic emergence of
                 magnetic flux. On the other hand, periodogram analysis
                 allows one to compare the behavior of the periodicity
                 in both sunspot groups and sunspot areas, and the
                 results suggest that, at least during the twentieth
                 century, the periodic emergence of magnetic flux has
                 adopted two different forms. In solar cycles 16 and 17,
                 new sunspot groups were periodically formed,
                 simultaneously increasing the number of sunspot groups
                 and the total sunspot area on the Sun's surface, while
                 during solar cycles 18, 19, 20, and 21 the periodicity
                 has occurred within already formed sunspot groups,
                 increasing sunspot areas only. We point out that this
                 second type of emergence, which enhances the magnetic
                 complexity of sunspot groups, is responsible for the
                 appearance of the periodicity in high-energy solar
                 flares as detected by the Solar Maximum Mission during
                 solar cycle 21.",
}

@InProceedings{bao-erd-che:scale,
  title =        "Scale-translation filtering for wideband correlated
                 noise attenuation",
  author =       "F. Bao and N. Erdol and Z. Chen",
  pages =        "652--660",
  crossref =     "szu:wavelet2",
  abstract =     "A novel idea of scale-translation filtering based on
                 the orthonormal wavelet transform is developed and
                 demonstrated.",
  keywords =     "scale-translation filtering. wideband correlated noise
                 attenuation. orthonormal wavelet transform.",
}

@InProceedings{bao-erd:discrete,
  title =        "{O}n the discrete wavelet transform and shiftability",
  author =       "Bao. Feng and N. Erdol",
  booktitle =    "Conference Record of the Twenty-Seventh Asilomar
                 Conference on Signals, Systems and Computers",
  volume =       "2",
  editor =       "A. Singh",
  year =         "1993",
  pages =        "1442--1445",
  note =         "1-3 Nov. 1993, Pacific Grove, CA, USA",
  abstract =     "We analyze the relationship between the change that is
                 observed in the wavelet coefficients when a signal is
                 time shifted and the time and frequency distributions
                 of the wavelet functions. We address the effects of
                 shift variance and show how it can be useful.",
  keywords =     "discrete wavelet transform. wavelet coefficients. time
                 shifted signal. frequency distribution. time
                 distribution. wavelet functions. shift variance.",
}

@InProceedings{bao-erd:optimal,
  title =        "{T}he optimal wavelet transform and translation
                 invariance",
  booktitle =    "IEEE International Conference on Acoustics, Speech and
                 Signal Processing",
  volume =       "3",
  pages =        "13--16",
  year =         "1994",
  author =       "F. Bao and N. Erdol",
  note =         "19-22 April 1994, Adelaide, SA, Australia",
  abstract =     "Orthonormal wavelet representations are known to be
                 time-variant. With shifting of the input signal, the
                 energy distribution in time-scale plane also changes.
                 We define the `separability' of a wavelet function both
                 in the scale and translation domains as a measure of
                 its localization with respect to translation. We derive
                 a criterion for the optimal initial phase and then
                 develop an algorithm for its choice in the case of
                 stationary and nonstationary signals.",
  keywords =     "optimal wavelet transform. orthonormal wavelet
                 representations. input signal shifting. energy
                 distribution. wavelet function separability.
                 translation domain. scale domain. translation
                 invariance. optimal initial phase. algorithm.
                 nonstationary signals. stationary stationary signals.
                 time-frequency transform. time-variant
                 representation.",
}

@Article{bas-etal:modeling,
  title =        "Modeling and estimation of multiresolution stochastic
                 processes",
  author =       "M. Basseville and A. Benveniste and K. C. Chou and S.
                 A. Golden and R. Nikoukhah and A. S. Willsky",
  journal =      IEEETIT,
  volume =       "38",
  number =       "2",
  year =         "1992",
  pages =        "766--784",
  keywords =     "multiscale statistical signal processing, data fusion,
                 estimation, multiresolution stochastic processes, image
                 processing, wavelet transform, modeling paradigm,
                 dynamic models, multiscale stationarity, homogeneous
                 trees, covariance kernels",
  abstract =     "An overview is provided of the several components of a
                 research effort aimed at the development of a theory of
                 multiresolution stochastic modeling and associated
                 techniques for optimal multiscale statistical signal
                 and image processing. A natural framework for
                 developing such a theory is the study of stochastic
                 processes indexed by nodes on lattices or trees in
                 which different depths in the tree or lattice
                 correspond to different spatial scales in representing
                 a signal or image. In particular, it is shown how the
                 wavelet transform directly suggests such a modeling
                 paradigm. This perspective then leads directly to the
                 investigation of several classes of dynamic models and
                 related notions of multiscale stationarity in which
                 scale plays the role of a time-like variable. The
                 investigation of models on homogeneous trees is
                 emphasized. The framework examined here allows for
                 consideration, in a very natural way, of the fusion of
                 data from sensors with differing resolutions. Also,
                 thanks to the fact that wavelet transforms do an
                 excellent job of 'compressing' large classes of
                 covariance kernels, it is seen that these modeling
                 paradigms appear to have promise in a far broader
                 context than one might expect.",
}

@InProceedings{bay-bar:multiple,
  title =        "Multiple Window Time-Frequency Analysis",
  author =       "Metin Bayram and Richard G. Baraniuk",
  booktitle =    "Proceedings of the IEEE-SP International Symposium on
                 Time-Frequency and Time-Scale Analysis",
  pages =        "173--176",
  year =         "1996",
  keywords =     "multiple window time-frequency analysis robust method
                 time-varying spectrum estimation nonstationary random
                 process time-scale planes Thomson's method wavelet
                 functions statistical test chirping line components
                 stationary signals",
  abstract =     "We propose a robust method for estimating the
                 time-varying spectrum of a non-stationary random
                 process. Our approach extends Thomson's powerful
                 multiple window spectrum estimation scheme to the
                 time-frequency and time-scale planes. The method
                 refines previous extensions of Thomson's method through
                 optimally concentrated window and wavelet functions and
                 a statistical test for extracting chirping line
                 components.",
}

@TechReport{bay-bar:multiple2,
  title =        "Multiple Window Time-Varying Spectrum Estimation",
  author =       "Metin Bayram and Richard G. Baraniuk",
  institution =  "Isaac Newton Institute program on Nonlinear and
                 Nonstationary Signal Analysis",
  year =         "1999",
  abstract =     "We overview a new non-parametric method for estimating
                 the time-varying spectrum of a non-stationary random
                 process. Our method extends Thomson's powerful multiple
                 window spectrum estimation scheme to the time-frequency
                 and time-scale planes. Unlike previous extensions of
                 Thomson's method, we identify and utilize optimally
                 concentrated Hermite window and Morse wavelet functions
                 and develop a statistical test for extracting chirping
                 line components. Examples on synthetic and real-world
                 data illustrate the superior performance of the
                 technique.",
}

@Article{bel-wan:symmetric,
  title =        "Compactly supported orthogonal symmetric scaling
                 functions",
  author =       "E. Belogay and Y. Wang",
  journal =      ACHA,
  volume =       "7",
  number =       "2",
  year =         "1999",
  pages =        "137--150",
  abstract =     "Daubechies (1988, Comm. Pure Appl. Math. 41, 909-996)
                 showed that, except for the Hear function, there exist
                 no compactly supported orthogonal symmetric scaling
                 functions for the dilation q = 2. Nevertheless, such
                 scaling functions do exist for dilations q > 2 (as
                 evidenced by Chui and Lien's construction (1995, Appl.
                 Comput. Harmon. Anal. 2, 68-84) for q = 3); these
                 functions are the main object of this paper. We
                 construct new symmetric scaling functions and introduce
                 the ``Batman'' family of continuous symmetric scaling
                 functions with very small supports. We establish the
                 exact smoothness of the ```Batman'' scaling functions
                 using the joint spectral radius technique.",
}

@Book{ben-fra:wavelets,
  title =        "Wavelets: Mathematics and Applications",
  editor =       "John J. Benedetto and Michael W. Frazier",
  publisher =    "CRC Press",
  address =      "Boca Raton",
  year =         "1994",
  pages =        "575",
  loc =          "QA403.3 .W4 1994",
}

@Article{ben-hoc:fdr,
  title =        "Controlling the False Discovery Rate: {A} Practical
                 and Powerful Approach to Multiple Testing",
  author =       "Yoav Benjamini and Yosef Hochberg",
  journal =      JRSSB,
  volume =       "57",
  number =       "1",
  year =         "1995",
  pages =        "289--300",
  abstract =     "The common approach to the multiplicity problem calls
                 for controlling the familywise error rate (FWER). This
                 approach, though, has faults, and we point out a few. A
                 different approach to problems of multiple significance
                 testing is presented. It calls for controlling the
                 expected proportion of falsely rejected hypotheses the
                 false discovery rate. This error rate is equivalent to
                 the FWER when all hypotheses are true but is smaller
                 otherwise. Terefore, in problems where the control of
                 the false discovery rate rather than that of the FWER
                 is desired, there is potential for a gain in power. A
                 simple sequential Bonferroni-type procedure is proved
                 to control the false discovery rate for independent
                 test statistics, and a simulation study shows that the
                 gain in power is substantial. The use of the new
                 procedure and the appropriateness of the criterion are
                 illustrated with examples.",
  keywords =     "Bonferroni-type procedures Familywise error rate
                 Multiple-comparison procedures p-values",
}

@InProceedings{bey-etal:SAR,
  title =        "{SAR} imaging and multiresolution analysis",
  author =       "G. Beylkin and J. D. Gorman and S. Li-Fliss and M. A.
                 Ricoy",
  booktitle =    "Algorithms for Synthetic Aperture Radar Imagery II",
  series =       "Proceedings of the SPIE",
  volume =       "2487",
  year =         "1995",
  pages =        "144--152",
  keywords =     "SAR imaging multiresolution analysis synthetic
                 aperture radar image formation algorithms
                 unequally-spaced FFT USFFT algorithm complexity
                 computational cost multiresolution SAR imaging image
                 reconstruction",
  abstract =     "Many synthetic aperture radar (SAR) image formation
                 algorithms require the computation of a
                 multidimensional Fourier transform of
                 irregularly-sampled or unequally-spaced data samples.
                 We apply a recently developed algorithm, the
                 unequally-spaced FFT (USFFT) (Beylkin, 1995), to SAR
                 image formation and compare its accuracy and complexity
                 to a conventional algorithm. We find that the USFFT
                 algorithm allows comparable accuracy to traditional
                 approaches at a slightly reduced computational cost. We
                 briefly discuss extensions of the USFFT algorithm to
                 multiresolution SAR imaging.",
}

@InProceedings{bey-sai:autocorrelation,
  title =        "Wavelets, their autocorrelation functions, and
                 multiresolution representation of signals",
  author =       "Gregory Beylkin and Naoki Saito",
  booktitle =    "Intelligent Robots and Computer Vision XI: Biological,
                 Neural Net and 3-D Methods",
  series =       "Proceedings of the SPIE",
  volume =       "1826",
  year =         "1992",
  pages =        "39--50",
  keywords =     "compactly supported wavelets, autocorrelation
                 functions, multiresolution signal representation,
                 iterative interpolation schemes, dilations,
                 translations, auto-correlation shell, signal analysis",
  url =          "ftp://amath-ftp.colorado.edu/pub/wavelets/papers/spie.ps.Z",
  abstract =     "We summarize the properties of the auto-correlation
                 functions of compactly supported wavelets, their
                 connection to iterative interpolation schemes, and the
                 use of these functions for multiresolution analysis of
                 signals. We briefly describe properties of
                 representations using dilations and translations of
                 these auto-correlation functions (the auto-correlation
                 shell) which permit multiresolution analysis of
                 signals.",
}

@Article{bey:representation,
  title =        "On the representation of operators in bases of
                 compactly supported wavelets",
  author =       "G. Beylkin",
  journal =      SINUM,
  volume =       "29",
  year =         "1992",
  pages =        "1716--1740",
}

@Book{bic-dok:basic-ideas,
  title =        "Mathematical Statistics: Basic Ideas and Selected
                 Topics",
  author =       "Peter J. Bickel and Kjell A. Doksum",
  publisher =    "Holden-Day, Inc.",
  address =      SF,
  pages =        "492",
  year =         "1977",
}

@TechReport{bie-vid:adaptive,
  title =        "Time Adaptive Wavelet Denoising",
  author =       "Concha Bielza and Brani Vidakovi\'{c}",
  year =         "1996",
  institution =  "Institute of Statisics and Decision Sciences, Duke
                 University",
  url =          "ftp://ftp.isds.duke.edu/pub/Users/brani/papers/Timeadapt.ps",
}

@Article{bij-sle-rue-leg:universe,
  journal =      PIEEE,
  volume =       "84",
  number =       "4",
  year =         "1996",
  pages =        "670--679",
  title =        "{W}avelets and the study of the distant universe",
  author =       "A. Bijaoui and E. Slezak and F. Rue and E. Lega",
  abstract =     "The large-scale distribution of galaxies in the
                 Universe exhibits structures at various scales, these
                 so-called groups, clusters, and superclusters of
                 galaxies being more or less hierarchically organized. A
                 specific vision model is needed in order to detect,
                 describe, and classify each component of this
                 hierarchy. To do so rue have developed a multiscale
                 vision model based on an unfolding into a scale space
                 allowing us to detect structures of different sizes. A
                 discrete wavelet transform is done by the a trous
                 algorithm. The algorithm is implemented for
                 astronomical images and also for lists of object
                 positions, currently called catalogues in astronomical
                 literature. Some applications on astrophysical data of
                 cosmological interest are briefly described: 1)
                 inventory procedures for galaxy counts on wide-field
                 images, 2) processing of X-ray cluster images, leading
                 to the analyses of the total matter distribution, and
                 3) detection of large-scale structures from galaxy
                 counts. From the analyses of n-body simulations we show
                 that the vision model from the wavelet transform
                 provides a new statistical indicator on cosmological
                 scenarios.",
  keywords =     "transform. clusters",
}

@Unpublished{bij-sta-mur:atrous,
  title =        "Restauration des Images Multi-Echelles par
                 l'{A}lgorithme \`{a} Trous",
  author =       "Albert Bijaoui and Jean-Luc Starck and Fionn Murtagh",
  year =         "1994",
  note =         "In French",
  url =          "http://http.hq.eso.org/~fmurtagh/papers/trait-sig-94.ps",
}

@Book{bil:probability68,
  title =        "Convergence of Probability Measures",
  author =       "P. Billingsley",
  year =         "1968",
  publisher =    "John Wiley \& Sons",
  address =      NY,
}

@Article{bra-mci:climate,
  title =        "Determining climate-induced patterns using wavelet
                 analysis",
  author =       "G. A. Bradshaw and B. A. McIntosh",
  journal =      EP,
  volume =       "83",
  year =         "1994",
  pages =        "133--142",
  abstract =     "A method using wavelet analysis is introduced for the
                 purpose of identifying and isolating inferred climatic
                 components of the hydrologic record. This method
                 affords an informed procedure for choosing filter
                 dimensions for the purpose of signal decomposition.",
}

@Article{bra-spi:canopy,
  title =        "Characterizing canopy gap structure in forests using
                 wavelet analysis",
  author =       "G. A. Bradshaw and Thomas A. Spies",
  journal =      JEcol,
  volume =       "80",
  number =       "2",
  year =         "1992",
  pages =        "205--215",
  keywords =     "forest ecology, plant canopies, spatial analysis,
                 statistics",
  abstract =     "1. The wavelet transform is introduced as a technique
                 to identify spatial structure in transect data. Its
                 main advantages over other methods of spatial a nalysis
                 are its ability to preserve and display hierarchical
                 information while allowing for pattern decomposition.
                 2. Two applications are presented: simple
                 one-dimensional simulations and a set of 200-m transect
                 data of canopy opening measurements taken in 12 stands
                 dominated by Pseudotsuga menziesii ranging over three
                 developmental stages. 3. The calculation of the wavelet
                 variance, derived from the transform, facilitates
                 comparison based on dominant scale of pattern between
                 multiple datase ts such as the stands described. 4. The
                 results of the analysis indicate that while canopy
                 pattern trends follow stand development, small to
                 intermediate disturbances significantly influence
                 canopy structure.",
}

@Unpublished{bre-liu-tor:monsoon,
  title =        "Intraseasonal oscillations off Monterey, {CA}",
  author =       "L. Breaker and P. Liu and C. Torrence",
  year =         "1998",
  note =         "National Center for Atmospheric Research",
  url =          "http://www.cgd.ucar.edu/~torrence/liu/",
}

@Article{bre:heuristics,
  title =        "Heuristics of instability and stabilization in model
                 selection",
  author =       "L. Breiman",
  journal =      AofS,
  volume =       "24",
  year =         "1996",
  pages =        "2350--2383",
}

@Unpublished{bri-chi-iri-mor:markov-chain,
  title =        "Some Wavelet-Based Analyses of Markov Chain Data",
  author =       "David R. Brillinger and Chang Chiann and Rafael A.
                 Irizarry and Pedro A. Morettin",
  year =         "1998",
  note =         "Version 5.0",
}

@Article{bri-hen:multigrid,
  title =        "Wavelets and Multigrid",
  author =       "William L. Briggs and Van Emden Henson",
  journal =      SIAMJSC,
  volume =       "14",
  number =       "2",
  year =         "1993",
  pages =        "506--510",
  url =          "http://www-math.cudenver.edu/~wbriggs/psfiles/briggs_henson_93.ps",
}

@Article{bri:cumulants,
  title =        "Some Uses of Cumulants in Wavelet Analysis",
  author =       "David R. Brillinger",
  journal =      "Nonparametric Statistics",
  volume =       "6",
  year =         "1996",
  pages =        "93--114",
}

@InProceedings{bri:point-processes,
  title =        "Some Wavelet Analysis of Point Process Data",
  author =       "David R. Brillinger",
  booktitle =    "Thirty-First Asilomar Conference on Signals, Systems
                 and Computers",
  year =         "1997",
  pages =        "93--114",
}

@Article{bro:distribution,
  title =        "The Distribution Function of Positive Definite
                 Quadratic Forms in Normal Random Variables",
  author =       "Robert H. Brown",
  journal =      SIAMJSSC,
  volume =       "7",
  pages =        "689--695",
  year =         "1986",
  keywords =     "Analysis of variance; Unbalanced ANOVA design;
                 Laguerre polynomial",
}

@Article{bro:quantitative,
  title =        "Quantitative convergence assessment for {M}arkov chain
                 {M}onte {C}arlo via cusums",
  author =       "S. P. Brooks",
  journal =      SC,
  volume =       "8",
  number =       "3",
  year =         "1998",
  pages =        "267--274",
}

@Article{bru-don-gao:wavelet,
  title =        "Wavelet analysis [for signal processing]",
  author =       "Andrew Bruce and David Donoho and Hong-Ye Gao",
  journal =      IEEES,
  volume =       "33",
  number =       "10",
  year =         "1996",
  pages =        "26--35",
  abstract =     "As every engineering student knows, any signal can be
                 portrayed as an overlay of sinusoidal waveforms of
                 assorted frequencies. But while classical analysis
                 copes superbly with naturally occurring sinusoidal
                 behavior-the kind seen in speech signals-it is
                 ill-suited to representing signals with
                 discontinuities, such as the edges of features in
                 images. Latterly, another powerful concept has swept
                 applied mathematics and engineering research: wavelet
                 analysis. In contrast to a Fourier sinusoid, which
                 oscillates forever, a wavelet is localized in time-it
                 lasts for only a few cycles. Like Fourier analysis,
                 however, wavelet analysis uses an algorithm to
                 decompose a signal into simpler elements. Here, the
                 authors describe how localized waveforms are powerful
                 building blocks for signal analysis and rapid
                 prototyping-and how they are now available in software
                 toolkits.",
}

@Book{bru-gao:book,
  title =        "Applied Wavelet Analysis with {S-PLUS}",
  author =       "Andrew Bruce and Hong-Ye Gao",
  year =         "1996",
  publisher =    "Springer",
  address =      NY,
  ISBN =         "0-387-94714-0",
  url =          "http://www.springer-ny.com/catalog/np/jul96np/DATA/0-387-94714-0.html",
  abstract =     "This book introduces applied wavelet analysis through
                 the S-PLUS software system. Using a visual data
                 analysis approach, wavelet concepts are explained in a
                 way that is intuitive and easy to understand. In
                 addition to wavelets, a whole range of related signal
                 processing techniques such as wavelet packets, local
                 cosine analysis, and matching pursuits are covered.
                 Applications of wavelet analysis are illustrated,
                 including nonparametric function estimation, digital
                 image compression, and time-frequency signal analysis.
                 The book and software is intended for a broad range of
                 data analysts, scientists, and engineers. While most
                 textbooks on wavelet analysis require advanced training
                 in mathematics, this book minimizes reliance on formal
                 mathematical methods. Readers should be familiar with
                 calculus and linear algebra at the undergraduate
                 level.",
}

@Article{bru-gao:waveshrink,
  title =        "Understanding {W}ave{S}hrink: {V}ariance and Bias
                 Estimation",
  author =       "Andrew Bruce and Hong-Ye Gao",
  journal =      BKA,
  volume =       "83",
  number =       "4",
  year =         "1996",
  url =          "ftp://ftp.statsci.com/pub/gao/varbias.ps.Z",
  keywords =     "Bias and Variance Estimation; Confidence Interval;
                 Hard and Soft Shrink; Non-parametric Regression; Signal
                 De-noising; Threshold Selection; Wavelet Transform;
                 WaveShrink",
  abstract =     "Donoho and Johnstone's WaveShrink procedure has proven
                 valuable for signal de-noising and non-parametric
                 regression. WaveShrink is based on the principle of
                 shrinking wavelet coefficients towards zero to remove
                 noise. WaveShrink has very broad asymptotic
                 near-optimality properties. In this paper, we derive
                 computationally efficient formulas for computing the
                 exact bias, variance and $L_2$ risk of WaveShrink
                 estimates in finite sample situations. These formulas
                 provide a new way of understanding how WaveShrink
                 works, what its limitations are, and the pros and cons
                 of the shrinkage schemes: {\em soft} shrink vs. {\em
                 hard} shrink. It complements the tools of simulation
                 and asymptotic analysis. We use these formulas to
                 estimate the bias, the variance and the $L_2$ risk for
                 WaveShrink. Variance estimates are used to construct
                 approximate pointwise confidence intervals and applied
                 to synthetic and real examples. We also address the
                 problem of threshold selection, computing minimax
                 thresholds and ideal thresholds for both hard and soft
                 shrinkage.",
}

@Article{bru-gao-stu:subset,
  title =        "Subset-selection and ensemble methods for wavelet
                 de-noising",
  author =       "Andrew Bruce and Hong-Ye Gao and Werner Stuetzle",
  journal =      SSin,
  volume =       "9",
  number =       "1",
  year =         "1999",
  pages =        "167--182",
  keywords =     "cycle spinning model combination nonparametric
                 regression stepwise regression wavelet shrinkage",
  abstract =     "Many nonparametric regression procedures are based on
                 ``subset selection'': they choose a subset of carriers
                 from a large or even infinite set, and then determine
                 the coefficients of the chosen carriers by least
                 squares. Procedures which can be cast in this framework
                 include Projection Pursuit, Turbo, Mars, and Matching
                 Pursuit. Recently, considerable attention has been
                 given to ``ensemble estimators'' which combine least
                 squares estimates obtained from multiple subsets of
                 carriers. In the parametric regression setting, such
                 ensemble estimators have been shown to improve on the
                 accuracy of subset selection procedures in some
                 situations. In this paper we compare subset selection
                 estimators and ensemble estimators in the context of
                 wavelet de-noising. We present simulation results
                 demonstrating that a certain class of ensemble wavelet
                 estimators, based on the concept of ``cycle spinning'',
                 are significantly more accurate than subset selection
                 methods. These advantages hold even when the subset
                 selection procedures can rely on an oracle to select
                 the optimal number of carriers. We compute ideal
                 thresholds for translation invariant wavelet shrinkage
                 and investigate other approaches to ensemble wavelet
                 estimation.",
}

@Book{bur-gop-guo:book,
  title =        "Introduction to Wavelets and Wavelet Transforms: {A}
                 Primer",
  author =       "C. Sidney Burrus and Ramesh A. Gopinath and Haitao
                 Guo",
  year =         "1998",
  publisher =    "Prentice Hall",
  address =      NJ,
  ISBN =         "0-13-489600-9",
  url =          "http://www-dsp.rice.edu/wavebook",
  abstract =     "This primer presents a well balanced blend of the
                 mathematical theory underlying wavelet techniques and a
                 discussion that gives insight into why wavelets are
                 successful in signal analysis, compression, dection,
                 numerical analysis, and a wide variety of other
                 theoretical and practical applications. It fills a gap
                 in the existing wavelet literature with its unified
                 view of expansions of signals into bases and frames, as
                 well as the use of filter banks as descriptions and
                 algorithms.",
}

@Article{bur-etal:spatio,
  title =        "{A} wavelet multiresolution analysis for
                 spatio-temporal signals",
  author =       "T. J. Burns and S. K. Rogers and M. E. Oxley and D. W.
                 Ruck",
  journal =      IEEETAES,
  volume =       "32",
  number =       "2",
  year =         "1996",
  pages =        "628--649",
  abstract =     "The wavelet filters of the conventional 3D
                 multiresolution analysis possess homogeneous spatial
                 and temporal frequency characteristics which Limits
                 one's ability to match filter frequency characteristics
                 to signal frequency behavior. Also, the conventional 3D
                 multiresolution analysis employs an oct-tree
                 decomposition structure which restricts the analysis of
                 signal details to identical resolutions in space and
                 time. This paper presents a 3D wavelet multiresolution
                 analysis constructed from nonhomogeneous spatial and
                 temporal filters, and an orthogonal sub-band coding
                 scheme that decouples the spatial and temporal
                 decomposition processes.",
}

@Article{bur-wil-nas:impact,
  title =        "Impact during equine locomotion: {T}echniques for
                 measurement and analysis",
  author =       "J. F. Burn and A. M. Wilson and G. P. Nason",
  journal =      "Equine Veterinary Journal",
  volume =       "23",
  year =         "1997",
  pages =        "9--12",
}

@TechReport{bus-len:numerical,
  title =        "Numerical tests for bivariate wavelet schemes",
  author =       "R. Buschini and L. Lenarduzzi",
  number =       "IAMI 97.5",
  year =         "1997",
  institution =  "Instituto per le Applicazioni della Matematica e
                 dell'Informatica",
}

@Article{cai-bro:nonequispaced,
  title =        "Wavelet Shrinkage for Nonequispaced Samples",
  author =       "T. Tony Cai and Lawrence D. Brown",
  journal =      AofS,
  volume =       "26",
  number =       "5",
  year =         "1998",
  pages =        "1783--1799",
  url =          "http://www.stat.purdue.edu/people/tcai/paper/noneq.ps",
  keywords =     "wavelets multiresolution approximation nonparametric
                 regression minimax adaptivity piecewise Holder class",
  abstract =     "Standard wavelet shrinkage procedures for
                 nonparametric regression are restricted to equispaced
                 samples. There, data are transformed into empirical
                 wavelet coefficients and threshold rules are applied to
                 the coefficients. The estimators are obtained via the
                 inverse transform of the denoised wavelet coefficients.
                 In many applications, however, the samples are
                 nonequispaced. It can be shown that these procedures
                 would produce suboptimal estimators if they were
                 applied directly to nonequispaced samples. We propose a
                 wavelet shrinkage procedure for nonequispaced samples.
                 We show that the estimate is adaptive and near optimal.
                 For global estimation, the estimate is within a
                 logarithmic factor of the minimax risk over a wide
                 range of piecewise Holder classes, indeed with a number
                 of discontinuities that grows polynomially fast with
                 the sample size. For estimating a target function at a
                 point, the estimate is optimally adaptive to unknown
                 degree of smoothness within a constant. In addition,
                 the estimate enjoys a smoothness property: if the
                 target function is the zero function, then with
                 probability tending to 1 the estimate is also the zero
                 function.",
}

@Article{cai-hur-tsa:score,
  title =        "Score tests for heteroscedasticity in wavelet
                 regression",
  author =       "Z. W. Cai and C. M. Hurvich and C. L. Tsai",
  journal =      BKA,
  volume =       "85",
  number =       "1",
  pages =        "229--234",
  year =         "1998",
  keywords =     "de-noising. signal extraction. thresholding",
  abstract =     "We consider two Score tests for heteroscedasticity in
                 the errors of a signal;plus-noise model, where the
                 signal is estimated;by wavelet thresholding methods.
                 The error variances are assumed to depend on observed
                 covariates, through a parametric relationship of known
                 form. The tests are based on the approaches of Breusch
                 & Pagan (1979) and Koenker (1981). We establish the
                 asymptotic validity of the tests and examine their
                 performance in a simulation study. The Koenker test is
                 found to perform well, in terms of both size and
                 power.",
}

@TechReport{cai-sil:incorporating,
  title =        "Incorporating Information on Neighboring Coefficients
                 into Wavelet Estimation",
  author =       "T. Tony Cai and Bernard W. Silverman",
  institution =  "Department of Statistics, Purdue University",
  number =       "98-13",
  year =         "1998",
  url =          "http://www.stat.purdue.edu/people/tcai/NeighBlock/neighblock.ps",
}

@TechReport{cai:adaptivity,
  title =        "On Adaptivity of {B}lock{S}hrink Wavelet Estimator
                 Over {B}esov Spaces",
  author =       "T. Tony Cai",
  institution =  "Department of Statistics, Purdue University",
  number =       "97-05",
  year =         "1997",
  url =          "http://www.stat.purdue.edu/people/tcai/paper/blockbesov.ps",
}

@TechReport{cai:minimax,
  title =        "Minimax Wavelet Estimation Via Block Thresholding",
  author =       "T. Tony Cai",
  institution =  "Department of Statistics, Purdue University",
  number =       "96-41",
  year =         "1996",
  url =          "http://www.stat.purdue.edu/people/tcai/paper/blockmini.ps",
}

@Article{cam-mas:approximation,
  title =        "Wavelet approximation of deterministic and random
                 signals: convergence properties and rates",
  author =       "S. Cambanis and Elias Masry",
  journal =      IEEETIT,
  volume =       "40",
  number =       "4",
  year =         "1994",
  pages =        "1013--1029",
  keywords =     "convergence properties, convergence rates,
                 deterministic signals, wavelet approximation, signal
                 resolution, correlation function, stationary random
                 signals, nonstationary random signals, finite mean
                 energy, scale function, signal smoothness",
  abstract =     "The multiresolution decomposition of deterministic and
                 random signals and the resulting approximation at
                 increasingly finer resolution is examined.
                 Specifically, an nth-order expansion is developed for
                 the error in the wavelet approximation at resolution
                 $2^{-l}$ of deterministic and random signals. The
                 deterministic signals are assumed to have n continuous
                 derivatives, while the random signals are only assumed
                 to have a correlation function with continuous
                 nth-order derivatives off the diagonal-a very mild
                 assumption. For deterministic signals square integrable
                 over the entire real line, for stationary random
                 signals over finite intervals, and for nonstationary
                 random signals with finite mean energy over the entire
                 real line, the smoothness of the scale function can be
                 matched with the signal smoothness to substantially
                 improve the quality of the approximation. In sharp
                 contrast, this is feasible only in special cases for
                 nonstationary random signals over finite intervals and
                 for deterministic signals which are only locally square
                 integrable.",
}

@Unpublished{cap:denoised,
  title =        "Wavelet de-noised financial time series",
  author =       "Enrico Capobianco",
  year =         "1997",
  note =         "Department of Mathematical Modelling, Technical
                 University of Denmark",
  url =          "http://eivind.imm.dtu.dk/staff/enrico/duke_enrico.ps",
}

@Unpublished{cap:feature-detection,
  title =        "Feature Detection with Matching Pursuit in High
                 Frequency Nonstationary Time Series",
  author =       "Enrico Capobianco",
  year =         "1999",
  note =         "Department of Mathematical Modelling, Technical
                 University of Denmark",
  url =          "ftp://eivind.imm.dtu.dk/pub/300699a.ps.Z",
}

@Unpublished{cap:high-frequency,
  title =        "High Frequency Stock Returns Volatility: Feature
                 Extraction and Pattern Recognition via Wavelet
                 Transforms",
  author =       "Enrico Capobianco",
  year =         "1999",
  note =         "Department of Mathematical Modelling, Technical
                 University of Denmark",
}

@Unpublished{cap:volatility,
  title =        "Wavelet Transforms for the Statistical Analysis of
                 Returns Generating Stochastic Processes",
  author =       "Enrico Capobianco",
  year =         "1998",
  note =         "Department of Mathematical Modelling, Technical
                 University of Denmark",
  url =          "http://eivind.imm.dtu.dk/staff/enrico/jedc.ps.Z",
}

@Unpublished{cap:wavelets,
  title =        "Wavelets for High Frequency Financial Time Series",
  author =       "Enrico Capobianco",
  year =         "1999",
  note =         "Department of Mathematical Modelling, Technical
                 University of Denmark",
  email =        "enrico@eivind.imm.dtu.dk",
  url =          "http://eivind.imm.dtu.dk/staff/enrico/int99.ps.Z",
}

@InProceedings{car-hud:EEG-signals,
  title =        "Wavelet denoising of {EEG} signals and identification
                 of evokedresponse potentials",
  author =       "R{\'e}ne A. Carmona and Lonnie H. Hudgins",
  pages =        "91--104",
  crossref =     "lai-uns:wavelet2",
  abstract =     "The purpose of this study is to apply a recently
                 developed wavelet based de-noising filter to the
                 analysis of human electroencephalogram (EEG) signals,
                 and measure its performance. The data used contained
                 subject EEG responses to two different stimuli using
                 the `odd-ball' paradigm. Electrical signals measured at
                 standard locations on the scalp were processed to
                 detect and identify the Evoked Response Potentials
                 (ERP's). First, electrical artifacts emitting from the
                 eyes were identified and removed. Second, the mean
                 signature for each type of response was extracted and
                 used as a matched filter to define baseline detector
                 performance for the noisy data. Third, a nonlinear
                 filtering procedure based on the wavelet extrema
                 representation was used to de-noise the signals.
                 Overall detection rates for the de-noised signals were
                 then compared to the baseline performance. It was found
                 that while the filtered signals have significantly
                 lower noise than the raw signals, detector performance
                 remains comparable. We therefore conclude that all of
                 the information that is important to matched filter
                 detection is preserved by the filter. The implication
                 is that the wavelet based filter eliminates much of the
                 noise while retaining ERP's.",
}

@Book{car-hwa-tor:book,
  title =        "Practical Time-Frequency Analysis: Gabor and Wavelet
                 Transforms with an Implementation in {S}",
  booktitle =    "Practical Time-Frequency Analysis: Gabor and Wavelet
                 Transforms with an Implementation in S",
  author =       "Ren{\'e} A. Carmona and Wen L. Hwang and Brun
                 Torr{\'e}sani",
  publisher =    "Academic Press",
  address =      "San Diego",
  series =       "Wavelet Analysis and Its Applications",
  volume =       "9",
  year =         "1998",
}

@Article{car-hwa-tor:characterization,
  title =        "Characterization of Signals by the Ridges of Their
                 Wavelet Transforms",
  author =       "Ren{\'e} A. Carmona and Wen L. Hwang and Brun
                 Torr{\'e}sani",
  journal =      IEEETSP,
  volume =       "45",
  number =       "10",
  pages =        "2586--2590",
  year =         "1997",
  url =          "ftp://chelsea.princeton.edu/pub/outgoing/signal/cht1.ps",
  abstract =     "We present a couple of new algorithmic procedures for
                 the detection of ridges in the modulus of the
                 (continuous) wavelet transform of one-dimensional (1-D)
                 signals, These detection procedures are shown to be
                 robust to additive white noise, We also derive and test
                 a new reconstruction procedure, The latter uses only
                 information from the restriction of the wavelet
                 transform to a sample of points from the ridge. This
                 provides a very efficient way to code the information
                 contained in the signal.",
}

@Article{car-etal:absolute,
  title =        "Absolute optimal time-frequency basis -- a research
                 tool",
  author =       "A. C{\^a}rsteanu and V. B. Sapozhnikov and V.
                 Venugopal and E. Foufoula-Georgiou",
  journal =      JPA,
  volume =       "30",
  number =       "20",
  pages =        "7133--7146",
  year =         "1997",
  abstract =     "The paper presents a method for finding the absolute
                 best basis out of the library of bases offered by the
                 wavelet packet decomposition of a discrete signal.
                 Data-adaptive optimality is achieved with respect to an
                 objective function, e.g. minimizing entropy, and
                 concerns the choice of the Heisenberg rectangles tiling
                 the time-frequency domain over which the energy of the
                 signal is distributed. It is also shown how optimizing
                 a concave objective function is equivalent to
                 concentrating maximal energy into a few basis elements.
                 Signal- adaptive basis selection algorithms currently
                 in use do not generally find the absolute best basis,
                 and moreover have an asymmetric time-frequency
                 adaptivity-although a complete wavepacket decomposition
                 comprises a symmetric set of tilings with respect to
                 time and frequency. The higher adaptivity in frequency
                 than in time can lead to ignoring frequencies that
                 exist over short time intervals (short as compared to
                 the length of the whole signal, not to the period
                 corresponding to these frequencies). Revealing
                 short-lived frequencies to the investigator can bring
                 up important features of the studied process, such as
                 the presence of coherent ('persistent') structures in a
                 time series.",
}

@InProceedings{car:transients,
  title =        "Wavelet identification of transients in noisy time
                 series",
  author =       "Ren{\'e} A. Carmona",
  pages =        "392--400",
  crossref =     "lai:wavelet1",
  url =          "http://www.isds.duke.edu/~brani/wp/CarmonaTSTrans.ps",
  keywords =     "transients detection, wavelet identification, noisy
                 time series, signal analysis, denoising procedure,
                 wavelet transform, bootstrap, direct Monte Carlo
                 simulations, reconstruction algorithm",
  abstract =     "The detection of transients in noisy time series is an
                 important part of modern signal analysis because of the
                 importance of its civil and military applications. The
                 author presents a new denoising procedure, the output
                 of which gives a very reasonable guess for the
                 component of the input signal which was buried in
                 noise. The algorithm has two main components. The first
                 one concerns the identification of the main
                 characteristics of the noise component and of the
                 typical effects it has on the wavelet transform of the
                 input signal. This information is used to identify the
                 points in the time-scale space which cannot be extrema
                 of the wavelet transform, unless something else than
                 noise was present in the input signal. This is done by
                 bootstrap in general but direct Monte Carlo simulations
                 can be used when parametric knowledge on the
                 distribution of the noise is available. The second part
                 deals with the actual reconstruction of what is
                 believed to be the component of the input which is to
                 be identified. This part of the algorithm uses the
                 reconstruction procedure of Mallat and Zhong (1992) as
                 revised by the author (1992) the main novelty being the
                 fact that this procedure is fed with the set of points
                 in the time-scale plane which passed the trimming test
                 of the extrema of the wavelet transform. The author
                 illustrates the efficiency of the reconstruction
                 algorithm using the examples of transients used
                 previously by the author (1992).",
}

@Article{cha-ho:mra,
  title =        "Multiresolution analysis, its link to the discrete
                 parameter wavelet transform, and its initialization",
  author =       "Y. T. Chan and K. C. Ho",
  journal =      IEEETSP,
  volume =       "44",
  number =       "4",
  year =         "1996",
  pages =        "1001--1007",
  keywords =     "Filtering, Electronics, Signal processing",
  abstract =     "Two-scale wavelet equations are derived for equivalent
                 multiresolution analysis (MRA) detail parameters and
                 the discrete parameter (DP) wavelet transform
                 coefficients for a signal s(t). MRA initialization by
                 prefiltering its input signal s(n) obtains the
                 equivalence between the DP and MRA coefficients. MRA
                 gives the DP of a signal s(t) when s(n) are samples of
                 the inner product of s(t) and the scaling function. A
                 simulation example is presented to discuss the
                 prefiltering procedure's effectiveness.",
}

@TechReport{cha-lon:k-stationarity,
  title =        "{K}-stationarity and wavelets",
  author =       "Bing Cheng and Howell Tong",
  number =       "96-28",
  institution =  "Institute of Mathematics and Statistics, University of
                 Kent at Cantebury",
  year =         "1996",
  url =          "ftp://ftp.ukc.ac.uk/pub/maths/reports/1996/28/28.ps.gz",
}

@Book{cha:basics,
  title =        "Wavelet Basics",
  author =       "Y. T. Chan",
  publisher =    "Kluwer Academic Publishers",
  address =      "Boston",
  year =         "1995",
  pages =        "134",
  url =          "http://kapis.www.wkap.nl/kapis/CGI-BIN/WORLD/book.htm?0-7923-9536-0",
  keywords =     "Preface. 1. Introduction. 2. Principles of the Wavelet
                 Transform 3. Multiresolution Analysis, Wavelets and
                 Digital Filters. 4. Current Topics. References.
                 Index.",
  abstract =     "Since the study of wavelets is a relatively new area,
                 much of the research coming from mathematicians, most
                 of the literature uses terminology, concepts and proofs
                 that may, at times, be difficult and intimidating for
                 the engineer. Wavelet Basics has therefore been written
                 as an introductory book for scientists and engineers.
                 The mathematical presentation has been kept simple, the
                 concepts being presented in elaborate detail in a
                 terminology that engineers will find familiar.
                 Difficult ideas are illustrated with examples which
                 will also aid in the development of an intuitive
                 insight. Chapter 1 reviews the basics of signal
                 transformation and discusses the concepts of duals and
                 frames. Chapter 2 introduces the wavelet transform,
                 contrasts it with the short-time Fourier transform and
                 clarifies the names of the different types of wavelet
                 transforms. Chapter 3 links multiresolution analysis,
                 orthonormal wavelets and the design of digital filters.
                 Chapter 4 gives a tour d'horizon of topics of current
                 interest: wavelet packets and discrete time wavelet
                 transforms, and concludes with applications in signal
                 processing.",
}

@Article{che-don-sau:atomic,
  title =        "Atomic decomposition by basis pursuit",
  author =       "S. S. B. Chen and D. L. Donoho and M. A. Saunders",
  journal =      SIAMJSC,
  volume =       "20",
  number =       "1",
  year =         "1999",
  pages =        "33--61",
  url =          "http://epubs.siam.org/sam-bin/getfile/SISC/articles/30401.ps",
  keywords =     "overcomplete signal representation denoising
                 time-frequency analysis time-scale analysis l 1 norm
                 optimization matching pursuit wavelets wavelet packets
                 cosine packetsinterior-point methods for linear
                 programming total variation denoising multiscale
                 edges",
  abstract =     "The time-frequency and time-scale communities have
                 recently developed a large number of overcomplete
                 waveform dictionaries- stationary wavelets, wavelet
                 packets, cosine packets, chirplets, and warplets, to
                 name a few. Decomposition into overcomplete systems is
                 not unique, and several methods for decomposition have
                 been proposed, including the method of frames (MOF),
                 Matching pursuit (MP), and, for special dictionaries,
                 the best orthogonal basis (BOB). Basis Pursuit (BP) is
                 a principle for decomposing a signal into an
                 ``optimal'' superposition of dictionary elements, where
                 optimal means having the smallest l(1) norm of
                 coefficients among all such decompositions. We give
                 examples exhibiting several advantages over MOF, MP,
                 and BOB, including better sparsity and superresolution.
                 BP has interesting relations to ideas in areas as
                 diverse as ill-posed problems, in abstract harmonic
                 analysis, total variation denoising, and multiscale
                 edge denoising. BP in highly overcomplete dictionaries
                 leads to large-scale optimization problems. With
                 signals of length 8192 and a wavelet packet dictionary,
                 one gets an equivalent linear program of size 8192 by
                 212,992. Such problems can be attacked successfully
                 only because of recent advances in linear programming
                 by interior-point methods. We obtain reasonable success
                 with a primal-dual logarithmic barrier method and
                 conjugate-gradient solver.",
}

@MastersThesis{che:msthesis,
  title =        "Wavelet Analysis and Statistics of {CN} Tower Current
                 Waveforms",
  author =       "Ying Chen",
  year =         "1997",
  pages =        "93",
  school =       "Department of Electrical and Computer Engineering,
                 University of Western Ontario",
  url =          "http://www.ee.ryerson.ca:8080/~yichen/thesis",
  email =        "yichen@ee.ryerson.ca",
}

@Article{chi-kol-mcc:abws,
  title =        "Adaptive Bayesian Wavelet Shrinkage",
  author =       "Hugh A. Chipman and Eric D. Kolaczyk and Robert E.
                 McCulloch",
  journal =      JASA,
  volume =       "92",
  number =       "440",
  pages =        "1413--1421",
  year =         "1997",
  url =          "http://galton.uchicago.edu/techreports/ABWS.ps.Z",
}

@Unpublished{chi-mor:estimation,
  title =        "Estimation of Time Varying Linear Systems",
  author =       "Chang Chiann and Pedro A. Morettin",
  year =         "1999",
  note =         "University of S\~{a}o Paulo, S\~{a}o Paulo, Brazil",
  url =          "ftp://ftp.ime.usp.br/pub/morettin/lsystem.ps.Z",
}

@Article{chi-mor:stationary,
  title =        "A Wavelet Analysis for Time Series",
  author =       "Chang Chiann and Pedro A. Morettin",
  journal =      JNS,
  volume =       "10",
  number =       "1",
  year =         "1999",
  pages =        "1--46",
  email =        "pam@ime.usp.br",
  url =          "ftp://ftp.ime.usp.br/pub/morettin/wavespec.ps.Z",
  keywords =     "time series wavelets wavelet periodogram wavelet
                 spectrum wavelet transform",
  abstract =     "In this paper we develop a wavelet spectral analysis
                 for a stationary discrete process. Some basic ideas on
                 wavelets are given and the concept of wavelet spectrum
                 is introduced. Asymptotic properties of the discrete
                 wavelet transform of a sample of observed values from
                 the process are derived and the wavelet periodogram is
                 considered as an estimator of the wavelet spectrum.
                 Applications to real and simulated series are given.",
}

@InProceedings{cho-bar:interpolation,
  title =        "Interpolation and denoising of nonuniformly sampled
                 data using wavelet-domain processing",
  author =       "Hyeokho Choi and Richard Baraniuk",
  booktitle =    "Proceedings of IEEE International Conference on
                 Acoustics, Speech and Signal Processing",
  year =         "1999",
  url =          "http://www-dsp.rice.edu/publications/pub/choi99in.ps.Z",
}

@InProceedings{cho-bar:segmentation,
  title =        "Image segmentation using wavelet-domain
                 classification",
  author =       "Hyeokho Choi and Richard Baraniuk",
  pages =        "???--???",
  crossref =     "uns-ald-lai:wavelet7",
  url =          "http://www-dsp.rice.edu/publications/pub/choi99im.ps.Z",
}

@InProceedings{cho-etal:complex,
  title =        "Hidden {M}arkov tree modelling of complex wavelet
                 transforms",
  author =       "Hyeokho Choi and Justin Romberg and Richard Baraniuk
                 and Nick Kingsbury",
  booktitle =    "Proceedings of IEEE International Conference on
                 Acoustics, Speech and Signal Processing",
  year =         "2000",
  pages =        "???--???",
  url =          "http://www-dsp.rice.edu/publications/pub/choi00icassp.ps.Z",
}

@Book{chu:introduction,
  title =        "An Introduction to Wavelets",
  author =       "C. K. Chui",
  volume =       "1",
  series =       "Wavelet Analysis and its Applications",
  year =         "1992",
  publisher =    "Academic Press, Inc.",
  ISBN =         "0-12-174584-8",
  keywords =     "An Overview, Fourier Analysis, Wavelet Transforms and
                 Time-frequency Analysis, Cardinal Spline Analysis,
                 scaling functions and Wavelets, Cardinal Spline
                 Wavelets, Orthogonal Wavelets and Wavelet Packets",
  abstract =     "This is the first volume in the series WAVELET
                 ANALYSIS AND ITS APPLICATIONS. It is an introductory
                 treatise on wavelet analysis, with an emphasis on
                 spline wavelets and and time-frequency analysis. Among
                 the basic topics covered are time frequency
                 localization, intergral wavelet transforms, dyadic
                 wavelets, frames, spine wavelets, orthonormal wavelet
                 bases, and wavelet packets. Is is suitable as a
                 textbook for a beginning course on wavelet analysis and
                 is directed toward both mathematicians and engineers
                 who wish to learn about the subject.",
}

@Book{chu:theory,
  title =        "Wavelets: Theory, Algorithms, and Applications",
  editor =       "Charles K. Chui and Laura Montefusco and Luigia
                 Puccio",
  volume =       "5",
  series =       "Wavelet Analysis and its Applications",
  year =         "1994",
  publisher =    "Academic Press, Inc.",
  ISBN =         "0-12-174575-9",
  keywords =     "Multiresolution and Multilevel Analyses, Wavelet
                 Transforms, Spline-Wavelets, Other Mathematical Tools
                 for Time-Frequency Analysis, Wavelets and Fractals,
                 Numerical Methods and Algorithms, Applications",
  abstract =     "Wavelets: Theory, Algorithms, and Applications is the
                 fifth volume in the highly respected series, WAVELET
                 ANALYSIS AND ITS APPLICATIONS. This volume shows why
                 wavelet analysis has become a tool of choice in fields
                 ranging from image compression, to signal detection and
                 analysis in electrical engineering and geophysics, to
                 analysis of turbulent or intermittent processes. The 28
                 papers comprising this volume are organized into seven
                 subject areas: multiresolution analysis, wavelet
                 transforms, tools for time-frequency analysis, wavelets
                 and fractals, numerical methods and algorithms, and
                 applications. More than 135 figures supplement the
                 text.",
}

@Book{chu:tool,
  title =        "Wavelets: {A} Mathematical Tool for Signal Analysis",
  author =       "Charles K. Chui",
  series =       "SIAM Monographs on Mathematical Modeling and
                 Computation",
  year =         "1997",
  publisher =    SIAM,
  address =      "Philadelphia",
  ISBN =         "0-89871-384-6",
  abstract =     "Wavelets continue to be powerful mathematical tools
                 that can be used to solve problems for which the
                 Fourier (spectral) method does not perform well or
                 cannot handle. This book is for engineers, applied
                 mathematicians, and other scientists who want to learn
                 about using wavelets to analyze, process, and
                 synthesize images and signals. Applications are
                 described in detail and there are step-by-step
                 instructions about how to construct and apply wavelets.
                 The only mathematically rigorous monograph written by a
                 mathematician specifically for nonspecialists, it
                 describes the basic concepts of these mathematical
                 techniques, outlines the procedures for using them,
                 compares the performance of various approaches, and
                 provides information for problem solving, putting the
                 reader at the forefront of current research.",
}

@Book{chu:tutorial,
  title =        "Wavelets: {A} Tutorial in Theory and Applications",
  author =       "C. K. Chui",
  volume =       "2",
  series =       "Wavelet Analysis and its Applications",
  year =         "1992",
  publisher =    "Academic Press, Inc.",
  ISBN =         "0-12-174590-2",
  abstract =     "Wavelets: A Tutorial in Theory and Applications is the
                 second volume in the new series WAVELET ANALYSIS AND
                 ITS APPLICATIONS. As a companion to the first volume in
                 this series, this volume covers several of the most
                 important areas in wavelets, ranging from the
                 development of the basic theory such as construction
                 and analysis of wavelet bases to an introduction of
                 some of the key applictions, including Mallat's local
                 wavelet maxima technique in second generagion image
                 coding.",
}

@Proceedings{cia-cox-mon-pav:advanced,
  title =        "Advanced Mathematical Tools in Metrology",
  booktitle =    "Advanced Mathematical Tools in Metrology",
  editor =       "P. Ciarlini and M. Cox and R. Monaco and F. Pavese",
  volume =       "16",
  series =       "Advances in Mathematics for Applied Sciences",
  publisher =    "World Scientific",
  address =      "Singapore",
  year =         "1994",
  url =          "http://www.wspc.co.uk/wspc/Books/book_series.html",
  note =         "Proceedings of the International Workshop",
}

@Article{cim-etal:time-series,
  title =        "Time series analysis of geological data",
  author =       "G. Cimino and G. Del Duce and L. K. Kadonaga and G.
                 Rotundo and A. Sisani and G. Stabile and B. Tirozzi and
                 M. Whiticar",
  journal =      CG,
  volume =       "161",
  number =       "1-3",
  pages =        "253--270",
  year =         "1999",
}

@Article{cly-par-vid:multiple,
  title =        "Multiple shrinkage and subset selection in wavelets",
  author =       "M. Clyde and G. Parmigiani and B. Vidakovic",
  journal =      BKA,
  volume =       "85",
  number =       "2",
  pages =        "391--401",
  year =         "1998",
  abstract =     "This paper discusses Bayesian methods for multiple
                 shrinkage estimation in wavelets. Wavelets are used in
                 applications for data denoising, via shrinkage of the
                 coefficients towards zero, and for data compression, by
                 shrinkage and setting small coefficients to zero. We
                 approach wavelet shrinkage by using Bayesian
                 hierarchical models, assigning a positive prior
                 probability to the wavelet coefficients being zero. The
                 resulting estimator for the wavelet coefficients is a
                 multiple shrinkage estimator that exhibits a wide
                 variety of nonlinear patterns. We discuss fast
                 computational implementations, with a focus on
                 easy-to-compute analytic approximations as well as
                 importance sampling and Markov chain Monte Carlo
                 methods. Multiple shrinkage estimators prove to have
                 excellent mean squared error performance in
                 reconstructing standard test functions. We demonstrate
                 this in simulated test examples, comparing various
                 implementations of multiple shrinkage to commonly-used
                 shrinkage rules. Finally, we illustrate our approach
                 with an application to the so-called 'glint' data.",
}

@TechReport{cly-geo:empirical,
  title =        "Empirical Bayes Estimation in Wavelet Nonparametric
                 Regression",
  author =       "Merlise A. Clyde and Edward I. George",
  number =       "99--06",
  institution =  "Institute of Statistics and Decision Sciences, Duke
                 University",
  year =         "1999",
}

@Article{coh-dau-via:interval,
  title =        "Wavelets on the interval and fast wavelet transforms",
  author =       "A. Cohen and I. Daubechies and P. Vial",
  journal =      ACHA,
  volume =       "1",
  number =       "1",
  year =         "1993",
  pages =        "54--81",
  keywords =     "fast wavelet transform, orthonormal wavelet bases,
                 interval",
  abstract =     "The authors discuss several constructions of
                 orthonormal wavelet bases on the interval, and they
                 introduce a new construction that avoids some of the
                 disadvantages of earlier constructions.",
}

@Book{coh-rya:multiscale,
  title =        "Wavelets and Multiscale Signal Processing",
  author =       "A. Cohen and R. D. Ryan",
  publisher =    "Chapman \& Hall",
  year =         "1995",
  pages =        "248",
  keywords =     "Introduction. Multiresolution analysis. Introduction.
                 The continuous point of view. The discrete point of
                 view. The multivariate case. Conclusions. Wavelets and
                 conjugate quadrature filters. Introduction. The general
                 case. The finite case. Wavelets with compact support.
                 Action of the FWT on oscillating signals. The
                 regularity of scaling functions and wavelets.
                 Introduction. Regularity and oscillation. The
                 subdivision algorithms. Spectral estimates of the
                 regularity. Estimation of the Lp-Sobolev exponent.
                 Applications. Biorthogonal wavelet bases. Introduction.
                 General principles of Subband coding. Unconditional
                 biorthogonal wavelet bases. Dual filters and
                 biorthogonal Riesz bases. Examples and applications.
                 Stochastic processes. Introduction. Linear
                 approximation. Linear approximation of images.
                 Approximation and compression of real images. Piecewise
                 stationary processes. Nonlinear approximation.
                 Quasi-analytic wavelet bases. Multivariate
                 constructions. Multiscale unconditional bases.
                 Notation. References.",
  abstract =     "Since their appearance in the mid-1980s, wavelets and,
                 more generally, multiscale methods have become powerful
                 tools in mathematical analysis and in applications to
                 numerical analysis and signal processing. This book is
                 based on Ondelettes et Traitement Numerique du Signal
                 by Albert Cohen. It has been translated from French by
                 Robert D. Ryan and extensively updated by both Cohen
                 and Ryan. It studies the existing relations between
                 filter banks and wavelet decompositions and shows how
                 these relations can be exploited in the context of
                 digital signal processing. Throughout, the book
                 concentrates on the fundamentals. It begins with a
                 chapter on the concept of multiresolution analysis,
                 which contains complete proofs of the basic results.
                 The description of filter banks that are related to
                 wavelet bases is elaborated in both the orthogonal case
                 (Chapter 2), and in the biorthogonal case (Chapter 4).
                 The regularity of wavelets, how this is related to the
                 properties of the filters, and the importance of
                 regularity for the algorithms are the subjects of
                 Chapter 3. Chapter 5 looks at multiscale decomposition
                 as it applies to stochastic processing, in particular
                 to signal and image processing. Wavelets and Multiscale
                 Signal Processing will be of particular interest to
                 mathematicians working in analysis, academic and
                 research electrical engineers, and researchers who need
                 to analyse time series, in areas such as hydrodynamics,
                 aeronautics, meteorology, geophysics, statistics and
                 economics.",
}

@Article{coh-raz-mal:adaptive,
  title =        "Adaptive suppression of {W}igner interference-terms
                 using shift-invariant wavelet packet decompositions",
  author =       "Israel Cohen and Shalom Raz and David Malah",
  journal =      SP,
  volume =       "73",
  number =       "3",
  year =         "1999",
  pages =        "203--223",
  url =          "http://www.elsevier.nl/cas/tree/store/sigpro/1999/73/3/1340.pdf",
  abstract =     "The Wigner distribution (WD) possesses a number of
                 desirable mathematical properties relevant to
                 time-frequency analysis. However, the presence of
                 interference terms renders the WD of multicomponent
                 signals extremely difficult to interpret. In this work,
                 we propose adaptive suppression of interference terms
                 using the shift-invariant wavelet packet decomposition.
                 A prescribed signal is expanded on its best basis and
                 transformed into the Wigner domain. Subsequently, the
                 interference terms are eliminated by adaptively
                 thresholding the cross-WD of interactive basis
                 functions, according to their amplitudes and distance
                 in an idealized time--frequency plane. We define a
                 distance measure that weighs the Euclidean distance
                 with the local distribution of the signal. The
                 amplitude and distance thresholds control the
                 cross-term interference, the useful properties of the
                 distribution, and the computational complexity. The
                 properties of the resultant modified Wigner
                 distribution (MWD) are investigated, and its
                 performance in eliminating interference terms, while
                 still retaining high-energy resolution, is compared
                 with that of other existing approaches. It is shown
                 that the proposed MWD is directly applicable to
                 resolving multicomponent signals. Each component is
                 determined as a partial sum of basis functions over a
                 certain equivalence class in the time--frequency
                 plane.",
}

@Article{coh-raz-mal:orthonormal,
  title =        "Orthonormal shift-invariant wavelet packet
                 decomposition and representation",
  author =       "Israel Cohen and Shalom Raz and David Malah",
  journal =      SP,
  volume =       "57",
  number =       "3",
  year =         "1997",
  pages =        "251--270",
  url =          "http://www-sipl.technion.ac.il/Sipl/siltd.ps",
  keywords =     "shift-invariant best basis time frequency wavelets
                 wavelet packets algorithm translation",
  abstract =     "In this work, a shifted wavelet packet (SWP) library,
                 containing all the time shifted wavelet packet bases,
                 is defined. A corresponding shift-invariant wavelet
                 packet decomposition (SIWPD) search algorithm for a
                 best basis' is introduced. The search algorithm is
                 representable by a binary tree, in which a node
                 symbolizes an appropriate subspace of the original
                 signal. We prove that the resultant 'best basis' is
                 orthonormal and the associated expansion, characterized
                 by the lowest information cost, is shift- invariant.
                 The shift invariance stems from an additional degree of
                 freedom, generated at the decomposition stage and
                 incorporated into the search algorithm. The added
                 dimension is a relative shift between given parent node
                 and its respective children nodes. We prove that for
                 any subspace it suffices to consider one of two
                 alternative decompositions, made feasible by the SWP
                 library. These decompositions correspond to a zero
                 shift and a 2(-l) relative shift where l denotes the
                 resolution level. The optimal relative shifts, which
                 minimize the information cost, are estimated using
                 finite depth subtrees. By adjusting their depth, the
                 quadratic computational complexity associated with
                 SIWPD may be controlled at the expense of the attained
                 information cost down to O(Nlog(2)N).",
}

@Article{coh-raz-mal:translation-invariant,
  title =        "Translation-invariant denoising using the minimum
                 description length criterion",
  author =       "Israel Cohen and Shalom Raz and David Malah",
  journal =      SP,
  volume =       "75",
  number =       "3",
  year =         "1999",
  pages =        "201--223",
  url =          "http://www.elsevier.nl/cas/tree/store/sigpro/sub/1999/75/3/1380.pdf",
  keywords =     "denoising signal estimation shift-invariant wavelet
                 packet minimum description length best basis
                 time-frequency representation Wigner distribution",
  abstract =     "A translation-invariant denoising method based on the
                 minimum description length (MDL) criterion and
                 tree-structured best-basis algorithms is presented. A
                 collection of signal models is generated using an
                 extended library of orthonormal wavelet-packet bases,
                 and an additive cost function, approximately
                 representing the MDL principle, is derived. We show
                 that the minimum description length of the noisy
                 observed data is achieved by utilizing the
                 shift-invarient wavelet packet decomposition (SIWPD)
                 and thresholding the resulting coefficients. This
                 approach is extendable to local trigonometric
                 decompositions, and corresponding procedures to
                 optimize either the library of bases or the filter
                 banks used at each node of the expansion-tree are
                 described. The signal estimator is efficiently combined
                 with a modified Wigner distribution, yielding robust
                 time-frequency representations, characterized by high
                 resolution and suppressed interference-terms. The
                 proposed method is compared to alternative existing
                 methods, and its superiority is demonstrated by
                 synthetic and real data examples.",
}

@Book{coh:time-frequency,
  title =        "Time Frequency Analysis: Theory and Applications",
  author =       "Leon Cohen",
  publisher =    "Prentice Hall, Inc.",
  address =      "New Jersey",
  year =         "1994",
  pages =        "320",
  keywords =     "The Time and Frequency Description of Signals.
                 Instantaneous Frequency and the Complex Signal. The
                 Uncertainty Principle. Densities and Characteristic
                 Functions. The Need for Time-Frequency Analysis.
                 Time-Frequency Distributions: Fundamental Ideas. The
                 Short-Time Fourier Transform. The Wigner Distribution.
                 General Approach and the Kernel Method. Characteristic
                 Function Operator Method. Kernel Design for Reduced
                 Interference. Some Distributions. Further Developments.
                 Positive Distributions Satisfying the Marginals. The
                 Representation of Signals. Density of a Single
                 Variable. Joint Representations for Arbitrary
                 Variables. Scale. Joint Scale Representations",
  abstract =     "Featuring traditional coverage as well as new research
                 results that, until now, have been scattered throughout
                 the professional literature, this book brings together
                 --- in simple language --- the basic ideas and methods
                 that have been developed to study natural and man-made
                 signals whose frequency content changes with time;
                 e.g., speech, sonar and radar, optical images,
                 mechanical vibrations, acoustic signals,
                 biological/biomedical and geophysical signals. Covers
                 time analysis, frequency analysis, and scale analysis;
                 time-bandwidth relations; instantaneous frequency;
                 densities and local quantities; the short time Fourier
                 Transform; time-frequency analysis; the Wigner
                 representation; time-frequency representations;
                 computation methods; the synthesis problem;
                 spatial-spatial/frequency representations; time-scale
                 representations; operators; general joint
                 representations; stochastic signals; and higher order
                 time-frequency distributions. Illustrates each concept
                 with examples and shows how the methods have been
                 extended to other variables, such as scale.",
}

@InProceedings{coi-don:spinning,
  title =        "Time-Invariant Wavelet De-Noising",
  author =       "Ronald R. Coifman and David Donoho",
  pages =        "125--150",
  url =          "ftp://playfair.stanford.edu/pub/donoho/TIDeNoise.ps.Z",
  crossref =     "ant-opp:wavelets",
}

@InCollection{coi-etal:packets,
  author =       "Ronald R. Coifman and Yves Meyer and Stephen Quake and
                 Mladen Victor Wickerhauser",
  title =        "Signal Processing and Compression with Wavelet
                 Packets",
  pages =        "77--93",
  crossref =     "mey-roq:progress",
}

@InCollection{coi-mey-wic:analysis,
  author =       "Ronald R. Coifman and Yves Meyer and Mladen Victor
                 Wickerhauser",
  title =        "Wavelet analysis and signal processing",
  pages =        "153--178",
  crossref =     "rus-etal:wavelets",
  url =          "ftp://wuarchive.wustl.edu:/doc/techreports/wustl.edu/math/wasp.ps.Z.",
  abstract =     "This describes the use of wavelet analysis for various
                 tasks in signal processing.",
}

@InProceedings{coi-mey-wic:size,
  title =        "Size properties of wavelet packets",
  author =       "Ronald R. Coifman and Yves Meyer and Mladen Victor
                 Wickerhauser",
  pages =        "453--470",
  crossref =     "rus-etal:wavelets",
}

@Article{coi-wic:entropy-based,
  title =        "Entropy-Based Algorithms for Best Basis Selection",
  author =       "Ronald R. Coifman and Mladen Victor Wickerhauser",
  journal =      IEEETIT,
  volume =       "38",
  number =       "2",
  year =         "1992",
  pages =        "713--718",
  url =          "http://wuarchive.wustl.edu/doc/techreports/wustl.edu/math/papers/entbb.ps.Z",
  abstract =     "Adapted waveform analysis uses a library of
                 orthonormal bases and an efficiency functional to match
                 a basis to a given signal or family of signals. It
                 permits efficient compression of a variety of signals,
                 such as sound and images. The predefined libraries of
                 modulated waveforms include orthogonal wavelet-packets
                 and localized trigonometric functions, and have
                 reasonably well-controlled time-frequency localization
                 properties. The idea is to build out of the library
                 functions an orthonormal basis relative to which the
                 given signal or collection of signals has the lowest
                 information cost. The method relies heavily on the
                 remarkable orthogonality properties of the new
                 libraries: all expansions in a given library conserve
                 energy and are thus comparable. Several cost
                 functionals are useful; one of the most attractive is
                 Shannon entropy, which has a geometric interpretation
                 in this context.",
}

@Article{cor-vet:time-varying,
  title =        "Orthogonal time-varying filter banks and wavelet
                 packets",
  author =       "C. Herley and M. Vetterli",
  journal =      IEEETSP,
  volume =       "42",
  number =       "10",
  year =         "1994",
  pages =        "2650--2663",
  keywords =     "orthogonal time-varying filter banks wavelet packets
                 construction time domain description two-channel
                 orthogonal filter bank one-sided signals finite-length
                 signals optimization subband tree structures filter
                 sets iteration continuous-time bases half-line regions
                 interval regions",
  abstract =     "We consider the construction of orthogonal
                 time-varying filter banks. By examining the time domain
                 description of the two- channel orthogonal filter bank
                 the authors find it possible to construct a set of
                 orthogonal boundary filters, which allows to apply the
                 filter bank to one-sided or finite-length signals,
                 without redundancy or distortion. The method is
                 constructive and complete. There is a whole space of
                 orthogonal boundary solutions, and there is
                 considerable freedom for optimization. This may be used
                 to generate subband tree structures where the tree
                 varies over time, and to change between different
                 filter sets. The authors also show that the iteration
                 of discrete- time time-varying filter banks gives
                 continuous-time bases, just as in the stationary case.
                 This gives rise to wavelet, or wavelet packet, bases
                 for half-line and interval regions.",
}

@Article{cor:boundary,
  title =        "Boundary filters for finite-length signals and
                 time-varying filter banks",
  author =       "C. Herley",
  journal =      IEEETCS2,
  volume =       "42",
  number =       "2",
  year =         "1995",
  pages =        "102--114",
  keywords =     "finite-length signals time-varying filter banks
                 M-channel nonorthogonal case boundary filters
                 time-varying synthesis section nonorthogonal bases
                 frequency localization multirate filter banks",
  abstract =     "We examine the question of how to construct
                 time-varying filter banks in the most general M-channel
                 nonorthogonal case. We show that by associating with
                 both analysis and synthesis operators a set of boundary
                 filters, it is possible to make the analysis structure
                 vary arbitrarily in time, and yet reconstruct the input
                 with a similarly time-varying synthesis section. There
                 is no redundancy or distortion introduced. This gives a
                 solution to the problem of applying filter banks to
                 finite length signals; it suffices to apply the
                 boundary filters at the beginning and end of the signal
                 segment. This also allows the construction of
                 orthogonal and nonorthogonal bases with essentially any
                 prescribed time and frequency localization, but which,
                 nonetheless, are based on structures with efficient
                 filter bank implementations.",
}

@Article{cou-cou:wavelet-HMMs,
  title =        "Wavelet-based method for nonparametric estimation of
                 {HMM}'s",
  author =       "L. Couvreur and C. Couvreur",
  journal =      IEEESPL,
  volume =       "7",
  number =       "2",
  year =         "2000",
  pages =        "25--27",
  abstract =     "In this letter, we propose a new algorithm for
                 nonparametric estimation of hidden Markov models
                 (HMM's), The algorithm is based on a
                 ``wavelet-shrinkage'' density estimator for the
                 state-conditional probability density functions of the
                 HMM's. It operates in an iterative fashion similar to
                 that of the EM reestimation formulae used for
                 maximum-likelihood estimation of parametric HMM's. We
                 apply the resulting algorithm to simple examples and
                 show its convergence. The proposed method is also
                 compared to classical nonparametric HMM estimation
                 based on quantization of observations (``histograms'')
                 and discrete HMM's.",
}

@Article{cra:xy,
  title =        "On the frequency function of $xy$",
  author =       "Cecil C. Craig",
  journal =      AofMS,
  volume =       "7",
  pages =        "1--15",
  year =         "1936",
}

@InProceedings{cre-hew:neighbor,
  title =        "A wavelet-based method of nearest neighbor pattern
                 classification using scale sequential matching",
  author =       "C. D. Creusere and G. Hewer",
  booktitle =    "Conference Record of the Twenty-Eighth Asilomar
                 Conference on Signals, Systems and Computers",
  volume =       "2",
  editor =       "A. Singh",
  year =         "1994",
  pages =        "1123--1127",
  keywords =     "nearest neighbor pattern classification, scale
                 sequential matching. wavelet-based method.
                 post-detection radar pulses, feature extraction.
                 trained nearest neighbor codebook. pattern classifier,
                 radar pulse fingerprinting. noise, Monte Carlo
                 simulations, shift invariant classifier, undecimated
                 wavelet transform, pulse edge, wavelet coefficients",
  abstract =     "In this method of pattern classification a wavelet
                 transform is used to extract features from the input
                 signal which are then compared in a scale sequential
                 manner (from coarse to fine) to a trained nearest
                 neighbor codebook. At each scale, possible
                 classification categories are eliminated until only one
                 class is left. We apply this pattern classifier to the
                 problem of fingerprinting post-detection radar pulses
                 and analyze its performance in noise using Monte Carlo
                 simulations. To make our classifier shift invariant, we
                 process the input with an undecimated wavelet transform
                 until the pulse edge is sensed and then start
                 decimating the wavelet coefficients as appropriate to
                 each scale.",
}

@Unpublished{cro-bar:fast-exact,
  title =        "Fast, Exact Synthesis of {G}aussian and non{G}aussian
                 Long-Range Dependent Processes",
  author =       "Matthew S. Crouse and Richard G. Baraniuk",
  year =         "1999",
  note =         "submitted to {\em IEEE Trans. on Info. Theory}",
  url =          "http://www-dsp.rice.edu/publications/pub/fftMC.ps.Z",
  abstract =     "Wavelet-based statistical signal processing techniques
                 such as denoising and detection typically model the
                 wavelet coefficients as independent or jointly
                 Gaussian. These models are unrealistic for many
                 real-world signals. In this paper, we develop a new
                 framework for statistical signal processing based on
                 wavelet-domain hidden Markov models (HMMs). The
                 framework enables us to concisely model the statistical
                 dependencies and nonGaussian statistics encountered
                 with real-world signals. Wavelet-domain HMMs are
                 designed with the intrinsic properties of the wavelet
                 transform in mind and provide powerful yet tractable
                 probabilistic signal models. Efficient Expectation
                 Maximization algorithms are developed for fitting the
                 HMMs to observational signal data. The new framework is
                 suitable for a wide range of applications, including
                 signal estimation, detection, classification,
                 prediction, and even synthesis. To demonstrate the
                 utility of wavelet-domain HMMs, we develop novel
                 algorithms for signal denoising, classification, and
                 detection.",
}

@Article{cro-now-bar:hidden,
  title =        "Wavelet-Based Statistical Signal Processing Using
                 Hidden Markov Models",
  author =       "Matthew S. Crouse and Robert D. Nowak and Richard G.
                 Baraniuk",
  journal =      IEEETSP,
  volume =       "46",
  number =       "4",
  year =         "1998",
  url =          "http://www-dsp.rice.edu/publications/pub/wmarkov.ps.Z",
  abstract =     "Wavelet-based statistical signal processing techniques
                 such as denoising and detection typically model the
                 wavelet coefficients as independent or jointly
                 Gaussian. These models are unrealistic for many
                 real-world signals. In this paper, we develop a new
                 framework for statistical signal processing based on
                 wavelet-domain hidden Markov models (HMMs). The
                 framework enables us to concisely model the statistical
                 dependencies and nonGaussian statistics encountered
                 with real-world signals. Wavelet-domain HMMs are
                 designed with the intrinsic properties of the wavelet
                 transform in mind and provide powerful yet tractable
                 probabilistic signal models. Efficient Expectation
                 Maximization algorithms are developed for fitting the
                 HMMs to observational signal data. The new framework is
                 suitable for a wide range of applications, including
                 signal estimation, detection, classification,
                 prediction, and even synthesis. To demonstrate the
                 utility of wavelet-domain HMMs, we develop novel
                 algorithms for signal denoising, classification, and
                 detection.",
}

@Unpublished{dah-neu:locally,
  title =        "Locally Adaptive...",
  author =       "Rainer Dahlhaus and Michael H. Neumann",
  year =         "1999",
  note =         "StatLab Heidelberg, Institut f{\"u}r Angewandte
                 Mathematik",
  url =          "ftp://statlab.uni-heidelberg.de/pub/reports/by.series/beitrag.60.ps",
  abstract =     "We fit a class of semiparametric models to a
                 nonstationary process. This class is parametrized by a
                 mean function \mu(.) and a p-dimensional function
                 theta(.) = (theta^{(1)}(.), ..., theta^{(p)}(.))' that
                 parametrizes the time-varying spectral density
                 f_{theta(.)}(\lambda). Whereas the mean function is
                 estimated by a usual kernel estimator, each component
                 of theta(.) is estimated by a nonlinear wavelet method.
                 According to a truncated wavelet series expansion of
                 theta^{(i)}(.), we define empirical versions of the
                 corresponding wavelet coefficients by minimizing an
                 empirical version of the Kullback-Leibler distance. In
                 the main smoothing step, we perform nonlinear
                 thresholding on these coefficients, which finally
                 provides a locally adaptive estimator of
                 theta^{(i)}(.). This method is fully automatic and
                 adapts to different smoothness classes. It is shown
                 that usual rates of convergence in Besov smoothness
                 classes are attained up to a logarithmic factor.",
}

@Article{dah-new-von:nonlinear,
  title =        "Nonlinear wavelet estimation of time-varying
                 autoregressive processes",
  author =       "Rainer Dahlhaus and Michael H. Neumann and Rainer {von
                 Sachs}",
  journal =      "Bernoulli",
  volume =       "5",
  number =       "5",
  year =         "1999",
  url =          "ftp://statlab.uni-heidelberg.de/pub/reports/by.series/report.09.ps",
  abstract =     "We consider nonparametric estimation of the parameter
                 functions a(i)(.), i = 1, ..., p, of a time-varying
                 autoregressive process. Choosing an orthonormal wavelet
                 basis representation of the Functions a(i), the
                 empirical wavelet coefficients are derived from the
                 time series data as the solution of a least-squares
                 minimization problem. In order to allow the a(i) to be
                 functions of inhomogeneous regularity, we apply
                 nonlinear thresholding to the empirical coefficients
                 and obtain locally smoothed estimates of the a(i). We
                 show that the resulting estimators attain the usual
                 minimax L-2 rates up to a logarithmic factor,
                 simultaneously in a large scale of Besov classes. The
                 finite-sample behaviour of our procedure is
                 demonstrated by application to two typical simulated
                 examples.",
}

@Article{dao-fra-wil:MAR,
  title =        "Multiscale autoregressive models and wavelets",
  author =       "Khalid Daoudi and Austin B. Frakt and Alan S.
                 Willsky",
  journal =      IEEETIT,
  volume =       "45",
  number =       "3",
  year =         "1999",
  pages =        "828--845",
}

@Article{dat-hir:wavelet-based,
  title =        "Wavelet-based estimations in fractional {B}rownian
                 motion",
  author =       "C. E. {D'Attellis} and G. A. Hirchoren",
  journal =      "Latin American Applied Research",
  volume =       "29",
  number =       "3-4",
  year =         "1999",
  pages =        "221--225",
  abstract =     "Fractional Brownian motion (fBm) is used as a model of
                 1/f-type stochastic processes, an important class of
                 processes that characterize a large number of physical
                 phenomena. Since the Hurst parameter H characterizes
                 these processes, its estimation from a signal is an
                 important issue in many applications. This paper points
                 out some applications of recent results on estimations
                 of fBm, and shows a new method for estimating the Hurst
                 parameter. Since variation in H indicates changes in
                 the physical system that produces the measured signal,
                 the determination of these variations is relevant for
                 failure detection. In this paper an algorithm that
                 allows the estimation of changes in the Hurst parameter
                 is introduced. The method is based on multiresolution
                 analysis. The results obtained processing an acoustic
                 emission signal from a coating breakdown are
                 presented.",
}

@Article{dau-lag:difference1,
  title =        "Two-scale difference equations, {I}",
  author =       "Ingrid Daubechies and J. Lagarias",
  journal =      SIAMJMA,
  volume =       "22",
  year =         "1991",
  pages =        "1388--1410",
}

@Article{dau-lag:difference2,
  title =        "Two-scale difference equations. {II}. {L}ocal
                 regularity, infinite products of matrices and
                 fractals",
  author =       "Ingrid Daubechies and J. Lagarias",
  journal =      SIAMJMA,
  volume =       "23",
  year =         "1992",
  pages =        "1031--1079",
  abstract =     "We study solutions of the functional equation
                 $f(x)=\sum\sp N\sb {n=0}c\sb nf(kx-n)$, where $k\geq 2$
                 is an integer, and $\sum\sp N\sb {n=0}c\sb n=k$. Part I
                 showed [SIAM J. Math. Anal. 22 (1991), no. 5,
                 1388--1410; MR 92d:39001] that equations of this type
                 have at most one $L\sp 1$-solution up to a
                 multiplicative constant, which necessarily has compact
                 support in $[0,N/k-1]$. This paper gives a time-domain
                 representation for such a function $f(x)$ (if it
                 exists) in terms of infinite products of matrices (that
                 vary as $x$ varies). Sufficient conditions are given on
                 $\{c\sb n\}$ for a continuous nonzero $L\sp 1$-solution
                 to exist. Additional conditions sufficient to guarantee
                 $f\in C\sp r$ are also given. The infinite matrix
                 product representations are used to bound from below
                 the degree of regularity of such an $L\sp 1$-solution
                 and to estimate the Holder exponent of continuity of
                 the highest-order well-defined derivative of $f(x)$.
                 Such solutions $f(x)$ are often smoother at some points
                 than others. For certain $f(x)$ a hierarchy of fractal
                 sets in $\bold R$ corresponding to different Holder
                 exponents of continuity for $f(x)$ is described.",
}

@TechReport{dau-swe:factor,
  author =       "I. Daubechies and W. Sweldens",
  title =        "Factoring Wavelet Transforms into Lifting Steps",
  institution =  "Bell Laboratories, Lucent Technologies",
  year =         "1996",
  url =          "http://cm.bell-labs.com/who/wim/papers/factor.ps.gz",
  abstract =     "The lifting scheme is a new flexible tool for
                 constructing wavelets and wavelet transforms. In this
                 paper, we use the Euclidean algorithm to show how any
                 discrete wavelet transform or two band subband
                 transform with finite filters can be obtained with a
                 finite number of lifting steps starting from the Lazy
                 wavelet (or polyphase transform). We show a bound on
                 the number of lifting steps which is proportional to
                 the length of the filters. This factorization provides
                 an alternative for the lattice factorization, with the
                 advantage that it can also be used in the biorthogonal
                 (non-unitary) case. The lifting factorization
                 asymptotically reduces the computational complexity of
                 the transform by a factor of two and allows for wavelet
                 transforms that map integers to integers.",
}

@InCollection{dau:connection,
  title =        "Orthonormal Bases of Wavelets with Finite Support --
                 Connection with Discrete Filters",
  author =       "Ingrid Daubechies",
  pages =        "38--66",
  crossref =     "com-gro-tch:wavelets",
}

@Article{dau:orthonormal,
  title =        "Orthonormal bases of compactly supported wavelets",
  author =       "Ingrid Daubechies",
  journal =      "Communications in Pure and Applied Mathematics",
  volume =       "41",
  pages =        "909--996",
  year =         "1988",
}

@Book{dau:ten,
  title =        "Ten Lectures on Wavelets",
  author =       "Ingrid Daubechies",
  series =       "CBMS-NSF Regional Conference Series in Applied
                 Mathematics",
  volume =       "61",
  publisher =    SIAM,
  address =      "Philadelphia",
  year =         "1992",
  url =          "http://www.siam.org/catalog/mcc02/daubechi.htm",
  keywords =     "Introduction; Preliminaries and Notation; The What,
                 Why, and How of Wavelets; The Continuous Wavelet
                 Transform; Discrete Wavelet Transforms: Frames;
                 Time-Frequency Density and Orthonormal Bases;
                 Orthonormal Bases of Wavelets and Multiresolutional
                 Analysis; Orthonormal Bases of Compactly Supported
                 Wavelets; More About the Regularity of Compactly
                 Supported Wavelets; Symmetry for Compactly Supported
                 Wavelet Bases; Characterization of Functional Spaces by
                 Means of Wavelets; Generalizations and Tricks for
                 Orthonormal Wavelet Bases; References; Indexes.",
  abstract =     "Wavelets are a mathematical development that may
                 revolutionize the world of information storage and
                 retrieval according to many experts. They are a fairly
                 simple mathematical tool now being applied to the
                 compression of data--such as fingerprints, weather
                 satellite photographs, and medical x-rays--that were
                 previously thought to be impossible to condense without
                 losing crucial details. This monograph contains 10
                 lectures presented by Dr. Daubechies as the principal
                 speaker at the 1990 CBMS-NSF Conference on Wavelets and
                 Applications. The author has worked on several aspects
                 of the wavelet transform and has developed a collection
                 of wavelets that are remarkably efficient. The opening
                 chapter provides an overview of the main problems
                 presented in the book. Following chapters discuss the
                 theoretical and practical aspects of wavelet theory,
                 including wavelet transforms, orthonormal bases of
                 wavelets, and characterization of functional spaces by
                 means of wavelets. The last chapter presents several
                 topics under active research, as multidimensional
                 wavelets, wavelet packet bases, and a construction of
                 wavelets tailored to decompose functions defined in a
                 finite interval. Because of their interdisciplinary
                 origins, wavelets appeal to scientists and engineers of
                 many different backgrounds.",
}

@Article{dau:time-frequency,
  title =        "The Wavelet Transform, Time-Frequency Localization and
                 Signal Analysis",
  author =       "I. Daubechies",
  journal =      IEEETIT,
  volume =       "36",
  number =       "5",
  year =         "1990",
  pages =        "961--1005",
  abstract =     "Two different procedures for effecting a frequency
                 analysis of a time-dependent signal locally in time are
                 studied. The first procedure is the short-time or
                 windowed Fourier transform; the second is the wavelet
                 transform, in which high-frequency components are
                 studied with sharper time resolution than low-frequency
                 components. The similarities and the differences
                 between these two methods are discussed. For both
                 schemes a detailed study is made of the reconstruction
                 method and its stability as a function of the chosen
                 time-frequency density. Finally, the notion of
                 time-frequency localization is made precise, within
                 this framework, by two localization theorems.",
}

@InCollection{dau:wavelet-transform,
  title =        "The Wavelet Transform: {A} Method for Time-Frequency
                 Localization",
  author =       "Ingrid Daubechies",
  pages =        "366--417",
  crossref =     "hay:advances",
}

@Article{dav-lab-les:commodity,
  title =        "Wavelet Analysis of Commodity Price Behavior",
  author =       "Russel Davidson and Walter C. Labys and Jean-Baptiste
                 Lesourd",
  journal =      CE,
  volume =       "11",
  year =         "1998",
  pages =        "103--128",
}

@InCollection{dav-mar-wis:multifractal,
  title =        "Wavelet-based multifractal analysis of non-stationary
                 and/or intermittent geophysical signals",
  author =       "Anthony Davis and Alexander Marshak and Warren
                 Wiscombe",
  pages =        "249--298",
  crossref =     "fou-kum:geophysics",
  url =          "ftp://climate.gsfc.nasa.gov/pub/davis/Wavelets/Wavelets.text.PS.Z",
}

@Article{dav:distribution,
  title =        "The Distribution of a Linear Combination of $\chi^2$
                 Random Variables",
  author =       "Robert B. Davies",
  journal =      AS,
  volume =       "29",
  year =         "1980",
  pages =        "323--333",
  keywords =     "Quadratic form",
}

@InCollection{dav:tables,
  title =        "Tables of the Correlation Coefficient",
  author =       "F. N. David",
  booktitle =    "Biometrika Tables for Statisticians",
  editor =       "E. S. Pearson and H. O. Hartley",
  publisher =    "Cambridge University Press",
  address =      "Cambridge",
  volume =       "1",
  edition =      "3",
  year =         "1966",
}

@Article{del-gam-sal:interannual,
  title =        "Interannual signals in length of day and atmospheric
                 angular momentum",
  author =       "R. A {del Rio} and D. Gambis and D. A. Salstein",
  journal =      AG,
  volume =       "18",
  number =       "3",
  year =         "2000",
  pages =        "347--364",
  keywords =     "Meteorology and atmospheric dynamics (general
                 circulation) - Solar physics, astrophysics and
                 astronomy (celestial mechanics)",
  abstract =     "Atmospheric angular momentum (AAM) and length of day
                 (LOD) series are investigated for their characteristics
                 on interannual time scales during the half-century
                 period 1949 to 1998. During this epoch, the interannual
                 variability in LOD can be separated naturally into
                 three bands: a quasi-biennial, a triennial-quadrennial
                 and one at six-seven years. The atmosphere appears to
                 excite the first two bands, while it does not
                 contribute to the last. Considering the quasi-biennial
                 (QB) band alone, the atmosphere appears to excite most
                 of its signal in LOD, but it arises from separate
                 fluctuations with stratospheric and tropospheric
                 origin. Thus, although close in frequency,
                 stratospheric and tropospheric processes differ in
                 their amplitude and phase variability. The time shift
                 can be noted especially during the strong El Nino
                 events of 1982-83 and 1997-98 when both processes have
                 positive phase and thus combine to help produce
                 particularly strong peak in AAM and LOD. In addition,
                 we have reconfirmed the downward propagation in the
                 stratosphere and upward propagation in the troposphere
                 of AAM observed in earlier studies for other variables.
                 In the triennial-quadrennial (TQ) band, time-variable
                 spectral analyses reveal that LOD and AAM contain
                 strong variability, with periods shorter than four
                 years before 1975 and longer thereafter. This signal
                 originates mainly within the troposphere and propagates
                 upwards from the lower to the higher layers of the
                 troposphere. According to a zonal analysis, an
                 equatorial poleward mode, strongly linked to the SOI,
                 explains more than 60% of the total variability at
                 these ranges. In addition, this study also indicates
                 that an equatorward mode, originating within polar
                 latitudes, explains, on average, more than 15% of the
                 triennial-quadrennial oscillation (TQO) variability in
                 AAM, and up to 30% at certain epochs. Finally, a six
                 year period in LOD noted in earlier studies, as well as
                 in lengthier series covering much of the century, is
                 found to be absent in atmospheric excitations, and it
                 is thus likely to arise from mantle/core
                 interactions.",
}

@Article{del-jud:computation,
  journal =      JAT,
  volume =       "88",
  number =       "1",
  year =         "1997",
  pages =        "47--79",
  title =        "{O}n the computation of wavelet coefficients",
  author =       "B. Delyon and A. Juditsky",
  url =          "http://www.irisa.fr/EXTERNE/bibli/pi/pi856.html",
  abstract =     "We consider fast algorithms of wavelet decomposition
                 of a function f when discrete observations of f (supp f
                 subset of or equal to[0,1](d)) are available. The
                 properties of the algorithms are studied for three
                 types of observation design which for $d=1$ can be
                 described as follows: the regular design, when the
                 observations $f(xi)$ are taken on the regular grid
                 $x(i)=i/N$, $i=1, ..., N$; the case of a jittered
                 regular grid, when it is only known that for all 1 less
                 than or equal to i less than or equal to $N$, $i/N$
                 less than or equal to $x(i)&lt;i+1)/N$; and the random
                 design case; in which $x(i), i=1, ..., N$, are
                 independent and identically distributed random
                 variables on [0,1]. We show that these algorithms are
                 in a certain sense efficient when the accuracy of the
                 approximation is concerned. The proposed algorithms are
                 computationally straightforward; the whole effort to
                 compute the decomposition is order $N$ for the sample
                 size $N$.",
}

@InCollection{del-jud:estimation,
  title =        "Estimating Wavelet Coefficients",
  author =       "Bernard Delyon and Anatoli Juditsky",
  pages =        "151--168",
  crossref =     "ant-opp:wavelets",
  email =        "iouditsk@irisa.fr",
}

@Article{del-wei:M-band,
  title =        "{\em M}-band wavepacket-based transient signal
                 detector using a translation-invariant wavelet
                 transform",
  author =       "Stephen del Marco and John Weiss",
  journal =      OE,
  volume =       "33",
  number =       "7",
  year =         "1994",
  pages =        "2175--2182",
  abstract =     "This paper develops a two-dimensional M-band
                 translation-invariant wavelet transform (2-D MTI). Use
                 of the MTI overcomes the shift-variance of the wavelet
                 transform by applying a cost function over M shifts of
                 the input signal. The new transform is proven to be
                 translation-invariant. Use of M-band wavelets enables a
                 finer frequency partitioning and greater energy
                 compaction in the transform representation. Examples
                 are presented which show that the translation-invariant
                 transforms provide superior energy concentration
                 compared to the corresponding nominal wavelet
                 transforms. Examples are also presented comparing the
                 energy concentration capability of M-band wavelets and
                 the modulated lapped transform (MLT). We explored the
                 MTI as a tool for image processing by using it to
                 represent several different images.",
}

@Article{del-wei:improved,
  title =        "Improved transient signal detection using a
                 wavepacket-based detector with an extended
                 translation-invariant wavelet transform",
  author =       "Stephen del Marco and John Weiss",
  journal =      IEEETSP,
  volume =       "45",
  number =       "4",
  year =         "1997",
  pages =        "841--850",
  url =          "http://www.tiac.net/users/nurit/ETI/ETI.html",
  abstract =     "This paper presents the theory of M-band, extended
                 translation-invariant (ETI) wavelet transforms. The ETI
                 generalizes the translation-invariant wavelet transform
                 of Weiss. It is shown that iteration of the ETI, in a
                 tree structure, provides a signal decomposition into an
                 orthonormal wavepacket basis, Other properties such as
                 translation invariance and invertibility of the
                 transform are proven, The theory is then applied to
                 transient signal detection through development of a
                 family of translation-invariant wavepacket-based
                 detectors. This family of detectors provides improved
                 performance over previously defined wavepacket-based
                 detectors, A performance analysis is conducted. ROC
                 curves generated by Monte-Carlo simulation are
                 presented, indicating detector performance, Detector
                 performance is demonstrated to be independent of the
                 signal translation.",
  keywords =     "compactly supported wavelets, representation,
                 algorithms",
}

@TechReport{der-lou-war:arbitrary,
  title =        "Multiresolution Analysis for Sufaces of Arbitrary
                 Topological Type",
  author =       "Tony D. DeRose and Michael Lounsbery and Joe Warren",
  institution =  "Department of Computer Science and Engineering,
                 University of Washington",
  number =       "93-10-05",
  year =         "1993",
}

@Article{dij-maz-bag:reciprocal,
  title =        "Reciprocal processes on a tree-modeling and estimation
                 issues",
  author =       "R. W. Dijkerman and R. R. Mazumdar and A. Bagchi",
  journal =      IEEETAC,
  volume =       "40",
  number =       "2",
  year =         "1995",
  pages =        "330--335",
  keywords =     "reciprocal processes, estimation issues,
                 multiresolution decomposition methods, discrete wavelet
                 transformation, truncated N-ary trees, nearest neighbor
                 models, recursive description, autoregressive
                 processes, zero-valued boundary values, smoothing
                 equations",
  abstract =     "Motivated by multiresolution decomposition methods
                 such as the discrete wavelet transformation, the
                 authors introduce reciprocal processes on truncated
                 N-ary trees. The authors discuss the relationship
                 between such processes and nearest neighbor models. The
                 authors show that they can derive a recursive
                 description of the process, and that all reciprocal
                 processes on N-ary trees reduce to autoregressive
                 processes in the case of zero-valued boundary values at
                 the bottom of the tree, corresponding to truncation of
                 the tree. The authors then study the smoothing
                 equations associated with such models.",
}

@Article{dij-maz:correlation,
  title =        "On the correlation structure of the wavelet
                 coefficients of fractional {B}rownian motion",
  author =       "R. W. Dijkerman and R. R. Mazumdar",
  journal =      IEEETIT,
  volume =       "40",
  number =       "5",
  year =         "1994",
  pages =        "1609--1612",
  keywords =     "correlation structure, wavelet coefficients,
                 fractional Brownian motion, normalized correlation,
                 decay",
  abstract =     "Shows that the interdependence of the discrete wavelet
                 coefficients of fractional Brownian motion, defined by
                 normalized correlation, decays exponentially fast
                 across scales and hyperbolically fast along time.",
}

@Article{dij-maz:representation,
  title =        "Wavelet representations of stochastic processes and
                 multiresolution stochastic models",
  author =       "R. W. Dijkerman and R. R. Mazumdar",
  journal =      IEEETSP,
  volume =       "42",
  number =       "7",
  year =         "1994",
  pages =        "1640--1652",
  keywords =     "stochastic processes, multiresolution stochastic
                 models, deterministic signal analysis, wavelet
                 representations, wavelet bases, time domain,
                 correlation structure, discrete wavelet coefficients,
                 correlation decay, trees, time process, approximations,
                 wavelet transform, decorrelation",
  abstract =     "Deterministic signal analysis in a multiresolution
                 framework through the use of wavelets has been
                 extensively studied very successfully in recent years.
                 In the context of stochastic processes, the use of
                 wavelet bases has not yet been fully investigated. We
                 use compactly supported wavelets to obtain
                 multiresolution representations of stochastic processes
                 with paths in L/sup 2/ defined in the time domain. We
                 derive the correlation structure of the discrete
                 wavelet coefficients of a stochastic process and give
                 new results on how and when to obtain strong decay in
                 correlation along time as well as across scales. We
                 study the relation between the wavelet representation
                 of a stochastic process and multiresolution stochastic
                 models on trees proposed by Basseville et al. (see IEEE
                 Trans. Inform. Theory, vol.38, p.766-784, Mar. 1992).
                 We propose multiresolution stochastic models of the
                 discrete wavelet coefficients as approximations to the
                 original time process. These models are simple due to
                 the strong decorrelation of the wavelet transform.
                 Experiments show that these models significantly
                 improve the approximation in comparison with the often
                 used assumption that the wavelet coefficients are
                 completely uncorrelated.",
}

@Article{don-joh-ker-pic:asymptopia,
  title =        "Wavelet Shrinkage: Asymptopia? (with discussion)",
  author =       "David L. Donoho and Iain M. Johnstone and G{\'e}rard
                 Kerkyacharian and Dominique Picard",
  journal =      JRSSB,
  volume =       "57",
  number =       "2",
  year =         "1995",
  pages =        "301--369",
  url =          "http://playfair.Stanford.EDU/reports/donoho/asymp.ps.Z",
  abstract =     "Much recent effort has sought asymptotically minimax
                 methods for recovering infinite dimensional objects -
                 curves, densities, spectral densities, images - from
                 noisy data. A now rich and complex body of work
                 develops nearly or exactly minimax estimators for an
                 array of interesting problems. Unfortunately, the
                 results have rarely moved into practice, for a variety
                 of reasons - among them being similarity to known
                 methods, computational intractability and lack of
                 spatial adaptivity. We discuss a method for curve
                 estimation based on n noisy data: translate the
                 empirical wavelet coefficients towards the origin by an
                 amount [sq.root](2 log n) [sigma]/[sq.root]n. The
                 proposal differs from those in current use, is
                 computationally practical and is spatially adaptive; it
                 thus avoids several of the previous objections.
                 Further, the method is nearly minimax both for a wide
                 variety of loss functions - pointwise error, global
                 error measured in Lp-norms, pointwise and global errors
                 in estimation of derivatives - and for a wide range of
                 smoothness classes, including standard H{\"o}lder and
                 Sobolev classes, and bounded variation. This is a much
                 broader near optimality than anything previously
                 proposed: we draw loose parallels with near optimality
                 in robustness and also with the broad near
                 eigenfunction properties of wavelets themselves.
                 Finally, the theory underlying the method is
                 interesting, as it exploits a correspondence between
                 statistical questions and questions of optimal recovery
                 and information-based complexity.",
  keywords =     "Adaptive estimation Besov spaces Density estimation
                 Minimax estimation Nonparametric regression Optimal
                 recovery Spatial adaptation Wavelet orthonormal bases",
}

@Article{don-joh:adapting,
  title =        "Adapting to unknown smoothness by wavelet shrinkage",
  author =       "David L. Donoho and Iain M. Johnstone",
  journal =      JASA,
  volume =       "90",
  year =         "1995",
  pages =        "1200--1224",
  url =          "http://playfair.Stanford.EDU/reports/donoho/isaws.ps.Z",
}

@Article{don-joh:asymptotic,
  title =        "Asymptotic minimaxity of wavelet estimators with
                 sampled data",
  author =       "David L. Donoho and Iain M. Johnstone",
  journal =      SSin,
  volume =       "9",
  number =       "1",
  year =         "1999",
  pages =        "1--32",
  keywords =     "Besov spaces bounded operators between Besov spaces
                 Minimax estimation thresholding wavelet transforms of
                 sampled data wavelets white noise equivalence",
  abstract =     "Donoho and Johnstone (1998) studied a setting where
                 data were obtained in the continuum white noise model
                 and shop;ed that scalar nonlinearities applied to
                 wavelet coefficients gave estimators which were
                 asymptotically minimax over Besov balls. They claimed
                 that this implied similar asymptotic minimaxity results
                 in the sampled-data model. In this paper we carefully
                 develop and fully prove this implication. Our results
                 are based on a careful definition of an empirical
                 wavelet transform and precise bounds on the discrepancy
                 between empirical wavelet coefficients and the
                 theoretical wavelet coefficients.",
}

@Article{don-joh:ideal,
  title =        "Ideal spatial adaptation by wavelet shrinkage",
  author =       "David L. Donoho and Iain M. Johnstone",
  journal =      BKA,
  volume =       "81",
  number =       "3",
  year =         "1994",
  pages =        "425--455",
  url =          "http://playfair.Stanford.EDU/reports/donoho/ausws.ps.Z",
}

@Article{don-joh:minimax,
  title =        "Minimax estimation via wavelet shrinkage",
  author =       "David L. Donoho and Iain M. Johnstone",
  journal =      AofS,
  volume =       "26",
  number =       "3",
  year =         "1998",
  pages =        "879--921",
  url =          "http://playfair.Stanford.EDU/reports/donoho/mews.ps.Z",
  keywords =     "minimax decision theory minimax Bayes estimation Besov
                 Holder Sobolev Triebel spaces nonlinear estimation
                 white noise model nonparametric regression orthonormal
                 bases of compactly supported wavelets renormalization
                 white noise approximation",
  abstract =     "We attempt to recover an unknown function from noisy,
                 sampled data. Using orthonormal bases of compactly
                 supported wavelets, we develop a nonlinear method which
                 works in the wavelet domain by simple nonlinear
                 shrinkage of the empirical wavelet coefficient. The
                 shrinkage can be tuned to be nearly minimax over any
                 member of a wide range of Triebel- and Besov-type
                 smoothness constraints and asymptotically minimax over
                 Besov bodies with p less than or equal to q. Linear
                 estimates cannot achieve even the minimax rates over
                 Triebel and Besov classes with p < 2, so the method can
                 significantly outperform every linear method (e.g.,
                 kernel, smoothing spline, sieve) in a minimax sense.
                 Variants of our method based on simple threshold
                 nonlinear estimators are nearly minimax. Our method
                 possesses the interpretation of spatial adaptivity; it
                 reconstructs using a kernel which may vary in shape and
                 bandwidth from point to point, depending on the data.
                 Least favorable distributions for certain of the
                 Triebel and Besov scales generate objects with sparse
                 wavelet transforms. Many real objects have similarly
                 sparse transforms, which suggests that these minimax
                 results are relevant for practical problems. Sequels to
                 this paper, which was first drafted in November 1990,
                 discuss practical implementation, spatial adaptation
                 properties, universal near minimaxity and applications
                 to inverse problems.",
}

@Article{don-joh:neo-classical,
  title =        "Neo-classical minimax problems, thresholding and
                 adaptive function estimation",
  author =       "David L. Donoho and Iain M. Johnstone",
  journal =      Ber,
  volume =       "2",
  number =       "1",
  year =         "1996",
  pages =        "39--62",
  abstract =     "We study the problem of estimating &theta; from data
                 Y&126;N(&theta;, &sigma;2) under squared-error loss. We
                 define three new scalar minimax problems in which the
                 risk is weighted by the size of &theta;. Simple
                 thresholding gives asymptotically minimax estimates in
                 all three problems. We indicate the relationships of
                 the new problems to each other and to two other
                 neo-classical problems: the problems of the bounded
                 normal mean and of the risk-constrained normal mean.
                 Via the wavelet transform, these results have
                 implications for adaptive function estimation in two
                 settings: estimating functions of unknown type and
                 degree of smoothness in a global l2 norm; and
                 estimating a function of unknown degree of local
                 H{\"o}lder smoothness at a fixed point. In the latter
                 setting, the scalar minimax results imply: Lepskii's
                 results that it is not possible fully toadapt the
                 unknown degree of smoothness without incurring a
                 performance cost; and that simple thresholding of the
                 empirical wavelet transform gives an estimate of a
                 function at a fixed point which is, to within
                 constants, optimally adaptive to unknown degree of
                 smoothness.",
  keywords =     "adaptive estimation; lp balls; minimax estimation;
                 weak lp balls",
}

@Unpublished{don-mal-von:covariances,
  title =        "Estimating Covariances of Locally Stationary
                 Processes: Rates of Convergence of Best Basis Methods",
  author =       "David L. Donoho and Steph{\'a}ne Mallat and Rainer
                 {von Sachs}",
  year =         "1997",
  note =         "Unpublished",
}

@TechReport{don:interpolating,
  title =        "Interpolating Wavelet Transforms",
  author =       "David L. Donoho",
  year =         "1992",
  institution =  "Technical Report 408, Department of Statistics,
                 Stanford University",
  url =          "http://playfair.Stanford.EDU/reports/donoho/interpol.ps.Z",
}

@InProceedings{don:nonlinear,
  title =        "Nonlinear Wavelet Methods for Recovery of Signals,
                 Densities, and Spectra from Indirect and Noisy Data",
  author =       "David L. Donoho",
  booktitle =    "Proceedings of Symposia in Applied Mathematics",
  organization = AMS,
  volume =       "47",
  year =         "1993",
  pages =        "173--205",
  url =          "http://playfair.Stanford.EDU/reports/donoho/ShortCourseFigs.epsf.shar.Z",
  abstract =     "Wavelet methods for the recovery of objects from noisy
                 and incomplete data are described. The common themes:
                 (a) the new methods use nonlinear operations in the
                 wavelet domain; (b) they accomplish tasks which are not
                 possible by traditional linear/Fourier approaches to
                 such problems. An attempt is made to indicate the
                 heuristic principles, theoretical foundations and
                 possible application areas for these methods, i.e.
                 wavelet de-noising, wavelet approaches to linear
                 inverse problems, wavelet packet de-noising, segmented
                 multiresolutions, and nonlinear multi-resolutions.",
}

@InCollection{don:smooth,
  author =       "David L. Donoho",
  title =        "Smooth Wavelet Decompositions with Blocky Coefficient
                 Kernels",
  pages =        "1--43",
  url =          "http://playfair.Stanford.EDU/reports/donoho/blocky.ps.Z",
  crossref =     "sch-web:recent",
}

@Article{don:soft,
  title =        "De-noising by Soft-Thresholding",
  author =       "David L. Donoho",
  journal =      IEEETIT,
  volume =       "41",
  number =       "3",
  year =         "1995",
  pages =        "613--627",
  url =          "http://playfair.Stanford.EDU/reports/donoho/denoiserelease3.ps.Z",
  keywords =     "soft-thresholding, de-noising, reconstruction, unknown
                 function, noisy data, standard Gaussian random
                 variables, wavelet domain, empirical wavelet
                 coefficients, estimator, probability, smoothness
                 measures, statistical inference, optimal recovery
                 model",
  abstract =     "Donoho and Johnstone (1994) proposed a method for
                 reconstructing an unknown function f on (0,1) from
                 noisy data d/sub i/=f(t/sub i/)+ sigma z/sub i/, i=0,
                 ..., n-1,t/sub i/=i/n, where the z/sub i/ are
                 independent and identically distributed standard
                 Gaussian random variables. The reconstruction f*/sub n/
                 is defined in the wavelet domain by translating all the
                 empirical wavelet coefficients of d toward 0 by an
                 amount sigma . square root (2log (n)/n). The authors
                 prove two results about this type of estimator.
                 (Smooth): with high probability f*/sub n/ is at least
                 as smooth as f, in any of a wide variety of smoothness
                 measures. (Adapt): the estimator comes nearly as close
                 in mean square to f as any measurable estimator can
                 come, uniformly over balls in each of two broad scales
                 of smoothness classes. These two properties are
                 unprecedented in several ways. The present proof of
                 these results develops new facts about abstract
                 statistical inference and its connection with an
                 optimal recovery model.",
}

@Article{dor:least-asymmetric,
  title =        "On the least asymmetric wavelets",
  author =       "Milo\v{s} L. Doroslova\v{c}ki",
  journal =      IEEETSP,
  volume =       "46",
  number =       "4",
  year =         "1998",
  pages =        "1125--1130",
  keywords =     "least asymmetric wavelets scaling functions second
                 moment wavelet-generating discrete-time filter
                 uncertainty relation discrete-time signals asymmetry
                 measures signal processing transfer function phase
                 nonlinearities minimisation",
  abstract =     "The asymmetry of Daubechies' (1988, 1992) scaling
                 functions and wavelets can be diminished by minimizing
                 a special second moment in time for the
                 wavelet-generating discrete-time filter. The moment is
                 involved in an uncertainty relation for discrete-time
                 signals. Other measures of asymmetry are addressed as
                 well, and corresponding results are compared.",
}

@Article{dow-sil:multiple,
  title =        "The discrete multiple wavelet transform and
                 thresholding methods",
  author =       "T. R. Downie and B. W. Silverman",
  journal =      IEEETSP,
  volume =       "46",
  number =       "9",
  year =         "1998",
  pages =        "2558--2562",
  url =          "http://www.stats.bris.ac.uk/~bernard/threshmwave3.ps.gz",
}

@Article{dro-kat:new,
  title =        "New filter banks and more regular wavelets",
  author =       "Karim Drouiche and Djalil Kateb",
  journal =      IEEETSP,
  volume =       "47",
  number =       "8",
  year =         "1999",
  pages =        "2220--2227",
}

@Article{duf-mil:prior,
  title =        "Statistical signal restoration with $1/f$ wavelet
                 domain prior models",
  author =       "R. M. Dufour and E. L. Miller",
  journal =      SP,
  volume =       "78",
  number =       "3",
  year =         "1999",
  pages =        "289--307",
  email =        "rdufour@cdsp.neu.edu,elmiller@ece.neu.edu",
}

@InProceedings{dut:algorithm,
  title =        "An Implementation of the ``algorithme {\`a} trous'' to
                 Compute the Wavelet Transform",
  author =       "P. Dutilleux",
  pages =        "298--304",
  crossref =     "com-gro-tch:wavelets",
}

@Unpublished{edw:discrete,
  title =        "Discrete Wavelet Transforms: Theory and
                 Implementation",
  author =       "Tim Edwards",
  note =         "Deptartment of Statistics, Stanford University",
  year =         "1991",
  email =        "tim@sinh.stanford.edu",
  abstract =     "This includes a brief introduction to wavelets in
                 general and the discrete wavelet transform in
                 particular, covering a number of implementation issues
                 that are often missed in the literature. A hardware
                 implementation on a commercially available DSP system
                 is described along with a program listing to show how
                 such an implementation can be simulated.",
}

@Article{efr-mor:stein,
  title =        "Data Analysis Using {S}tein's Estimator and Its
                 Generalizations",
  author =       "Bradley Efron and Carl Morris",
  journal =      JASA,
  volume =       "70",
  number =       "350",
  year =         "1975",
  pages =        "311--319",
}

@Article{efr:overcome,
  title =        "How to overcome the curse of long-memory errors",
  author =       "S. Efromovich",
  journal =      IEEETIT,
  volume =       "45",
  number =       "5",
  year =         "1999",
  pages =        "1735--1741",
  author =       "allows one to overcome this curse {Long-memory errors
                 dramatically slow down the convergence of minimax risks
                 in a fixed design nonparametric regression. The problem
                 becomes even more complicated for the case of adaptive
                 estimation. This defines the curse of long-memory
                 errors. I show that using a random design, instead of a
                 fixed one} and make familiar data-driven estimators
                 robust. Moreover, the result holds for a wide class of
                 nonstationary errors with bounded moments (including
                 bounded deterministic errors). Possible extensions are
                 discussed.",
}

@Article{efr:quasi-linear,
  title =        "Quasi-linear wavelet estimation",
  author =       "S. Efromovich",
  journal =      JASA,
  volume =       "94",
  number =       "445",
  year =         "1999",
  pages =        "189--204",
  keywords =     "adaptation asymptotic besov space data compression
                 filtering monotone function Monte Carlo nonparametric
                 regression rate optimality sharp optimality small
                 sample",
  abstract =     "The main paradigm of the modern wavelet theory of
                 spatial adaptation formulated by Donoho and Johnstone
                 is that there is a divergence between the linear
                 minimax adaptation theory and the heuristic guiding
                 algorithm development that leads to the necessity of
                 using strongly nonlinear adaptive thresholded methods.
                 On the other hand, it is well known that linear
                 adaptive estimates are the best whenever an estimated
                 function is smooth. Is it possible to suggest a
                 quasi-linear wavelet estimate, by adding to a linear
                 adaptive estimate a minimal number of nonlinear terms
                 on finest scales, that offers advantages of linear
                 adaptive estimates and at the same time matches
                 asymptotic properties of strongly nonlinear procedures
                 like the benchmark SureShrink? The answer is ``yes,''
                 and we discuss quasi-linear estimation both
                 theoretically and via a Monte Carlo study. In
                 particular, I show that, asymptotically, a quasi-linear
                 procedure not only matches properties of SureShrink
                 over the Besov scale, but also allows us to relax
                 familiar assumptions and solve a long standing problem
                 of rate and sharp optimal estimation of monotone
                 functions. For the case of small sample sizes and
                 functions that contain spiky/jumps parts and smooth
                 parts, a quasi-linear estimate performs exceptionally
                 well in terms of visual aesthetic appeal,
                 approximation, and data compression.",
}

@InProceedings{erd-bao-che:interpolation,
  title =        "Wavelet Interpolation: {F}rom Orthonomal To The
                 Oversampled Wavelet Transform",
  author =       "Nurgun Erdol and Feng Bao and Zajing Chen",
  booktitle =    "International Conference on Acoustics, Speech, and
                 Signal Processing",
  volume =       "2",
  pages =        "1093--1096",
  year =         "1995",
  note =         "9-12 May 1995, Detroit, MI, USA",
  keywords =     "oversampled wavelet transform. wavelet interpolation.
                 orthonormal wavelet transform. signal representation.
                 aliasing. decimation stage. signal resolution. signal
                 processing. wideband correlation processing. time
                 alignment sensitivity. nonorthogonal wavelet transform.
                 redundancy. wavelet transform coefficients. feature
                 extraction. filter banks.",
  abstract =     "The orthonormal wavelet transform is an efficient way
                 for signal representation since there is no redundancy
                 in its expression, but due to aliasing in the
                 decimation stage it lacks the often desired property of
                 shift invariance. On the other hand, the oversampled or
                 nonorthogonal wavelet offers a finer resolution in
                 translation; thus reducing the effect of shift of
                 origin, it becomes more robust to changes in the
                 initial phase of the signal. In some areas of signal
                 processing, such as wideband correlation processing,
                 sensitivity to time alignment necessitates the use of
                 the nonorthogonal wavelet transform. The price paid for
                 the advantage of robustness to shifting is the
                 introduction of redundancy in the expression. In many
                 applications, both of these two properties are needed
                 in different stages of signal processing. Thus there is
                 a need to know the conditions under which the redundant
                 and nonorthonormal wavelet transform coefficients can
                 be derived from the orthonormal wavelet transform
                 coefficients. The answer provides us with a convenient
                 way to switch between these two forms: the orthonormal
                 wavelet for efficient expression, and the nonorthogonal
                 one whenever it is necessary for feature extraction.",
}

@InProceedings{erd-bao:use,
  title =        "{U}se of shift variance of the wavelet transform for
                 signal detection",
  booktitle =    "Sixth IEEE Digital Signal Processing Workshop",
  year =         "1994",
  author =       "N. Erdol and Bao. Feng",
  note =         "2-5 Oct. 1994, Yosemite National Park, CA, USA",
  abstract =     "Characterizes signals according to the degree with
                 which a time shift affects their wavelet series
                 coefficients and develops a measure called the `shift
                 index' to quantify that effect. The authors argue that
                 the shift index can be used to locate, separate and
                 cluster and/or detect pulse like signals with random
                 arrival times. Examples are given to verify the
                 established theory.",
  keywords =     "wavelet transform. signal detection. shift variance.
                 time shift. wavelet series coefficients. shift index.
                 pulse like signals. random arrival times.",
}

@Article{esk-etal:seperating,
  title =        "Separating different scales of motion in time series
                 of meteorological variables",
  author =       "Robert E. Eskridge and Jia-Yeong Ku and S. Trivikrama
                 Rao and P. Steven Porter and Igor G. Zurbenko",
  journal =      BAMetS,
  volume =       "78",
  number =       "7",
  year =         "1997",
  pages =        "1473--1484",
  abstract =     "The removal of synoptic and seasonal signals from time
                 series of meteorological variables leaves datasets
                 amenable to the study of trends, climate change, and
                 the reasons for such trends and changes. In this paper,
                 four techniques for separating different scales of
                 motion are examined and their effectiveness compared.
                 These techniques are PEST, anomalies, wavelet
                 transform, and the Kolmogorov-Zurbenko (KZ) filter. It
                 is shown that PEST and anomalies do not cleanly
                 separate the synoptic and seasonal signals from the
                 data as well as the other two methods. The KZ filter
                 method is shown to have the same level of accuracy as
                 the wavelet transform method. However, the KZ filter
                 method can be applied to datasets with missing
                 observations and is much easier to use than the wavelet
                 transform method.",
}

@Article{fan-hal-mar-pat:adaptation,
  title =        "Adaptation to high spatial inhomogeneity using wavelet
                 methods",
  author =       "J. Q. Fan and P. Hall and M. A. Martin and P. Patil",
  journal =      SSin,
  volume =       "9",
  number =       "1",
  year =         "1999",
  pages =        "85--102",
  keywords =     "convergence rate. fine-scale. local adaptivity.
                 resolution. wavelet",
  abstract =     "Many of the signals to which waselet methods are
                 applied, including those encountered in simulation
                 experiments, are essentially smooth but contain a small
                 number of high-frequency episodes such as spikes. In
                 principle it is possible to employ a different amount
                 of smoothing at different spatial locations, but in the
                 context of wavelets this is so awkward to implement
                 that it is not really practicable. Instead, it is
                 attractive to select the primary resolution level (or
                 smoothing parameter) so as to give good performance for
                 smooth parts of the signal. While this is readily
                 accomplished using a cross-validation argument., it is
                 unclear whether it has a deleterious impact on
                 performance at high-frequency episodes. In this paper
                 we show that it does not. We derive upper and lower
                 bounds to pointwise rates of convergence for functions
                 whose `spikiness' increases with sample size. (This
                 allows us to model contexts where wavelet methods have
                 to work hard to recover high-frequency events.) We show
                 that, in order to achieve optimal rates of convergence,
                 it is necessary for the primary resolution level of the
                 empirical wavelet transform to vary with location,
                 sometimes extensively. nevertheless, the convergence
                 rate penalty incurred through using a non-varying
                 resolution level, chosen to provide good performance
                 for coarse-scale features, equals a factor that is less
                 than the logarithm of sample size.",
}

@Article{fan-hal-mar-pat:local,
  journal =      JASA,
  volume =       "91",
  number =       "433",
  year =         "1996",
  pages =        "258--266",
  title =        "{O}n local smoothing of nonparametric curve
                 estimators",
  author =       "J. Q. Fan and P. Hall and M. A. Martin and P. Patil",
  abstract =     "We develop new local versions of familiar smoothing
                 methods; such as cross-validation and smoothed
                 cross-validation, in the contexts of density estimation
                 and regression. These new methods are locally adaptive
                 in the sense that they capture smooth local
                 fluctuations in the curve by using smoothly varying
                 bandwidths that change as the character of the curve
                 changes. Moreover, the new methods are accurate, easy
                 to apply, and computationally expedient.",
  keywords =     "density-estimation. bandwidth choice.
                 cross-validation.",
}

@Article{fan-lin:curves,
  title =        "Test of significance when data are curves",
  author =       "J. Q. Fan and S. K. Lin",
  journal =      JASA,
  volume =       "93",
  number =       "443",
  year =         "1998",
  pages =        "1007--1021",
  keywords =     "adaptive analysis of variance adaptive Neyman rest
                 functional data repeated measurements thresholding
                 wavelets",
  abstract =     "With modern technology, massive data can easily be
                 collected in a form of multiple sets of curves. New
                 statistical challenge includes testing whether there is
                 any statistically significant difference among these
                 sets of curves. In this article we propose some new
                 tests for comparing two groups of curves based on the
                 adaptive Neyman test and the wavelet thresholding
                 techniques introduced earlier by Fan. We demonstrate
                 that these tests inherit the properties outlined by Fan
                 and that they are simple and powerful for detecting
                 differences between two sets of curves. We then further
                 generalize the idea to compare multiple sets of curves,
                 resulting in an adaptive high-dimensional analysis of
                 variance, called HANOVA. These newly developed
                 techniques are illustrated by using a dataset on pizza
                 commercials where observations are curves and an
                 analysis of cornea topography in ophthalmology where
                 images of individuals are observed. A simulation
                 example is also presented to illustrate the power of
                 the adaptive Neyman test.",
}

@Article{fan:test,
  journal =      JASA,
  volume =       "91",
  number =       "434",
  year =         "1996",
  pages =        "674--688",
  title =        "{T}est of significance based on wavelet thresholding
                 and {N}eyman's truncation",
  author =       "J. Q. Fan",
  abstract =     "Traditional nonparametric tests, such as the
                 Kolomogorov-Smirnov test and the Cramer-Von Mises test,
                 are based on the empirical distribution functions.
                 Although these tests possess root-n consistency, they
                 effectively use only information contained in the low
                 frequencies. This leads to low power in detecting fine
                 features such as sharp and short aberrants as well as
                 global features such as high-frequency alternations.
                 The drawback can be repaired via smoothing-based test
                 statistics. In this article we propose two such kind of
                 test statistics based on the wavelet thresholding and
                 the Neyman truncation. We provide extensive evidence to
                 demonstrate that the proposed tests have higher power
                 in detecting sharp peaks and high frequency
                 alternations, while maintaining the same capability in
                 detecting smooth alternative densities as the
                 traditional tests. Similar conclusions can be made for
                 two-sample nonparametric tests of distribution
                 functions. In that case, the traditional linear rank
                 tests such as the Wilcoxon test and the Fisher-Yates
                 test have low power in detecting two nearby densities
                 where one has local features or contains high-frequency
                 components, because these procedures are essentially
                 testing the uniform distribution based on the sample
                 mean of rank statistics. In contrast, the proposed
                 tests use more fully the sampling information and have
                 better ability in detecting subtle features.",
  keywords =     "adaptive Neyman test. goodness-of-fit.
                 hard-thresholding parameter. soft-thresholding
                 parameter. two-sample test. wavelet thresholding.",
}

@InProceedings{far-bro:applications,
  title =        "Applications of Time-Frequency and Time-Scale
                 Transforms to Ultra-Wideband Radar Transient Signal
                 Detection",
  author =       "Monique P. Fargues and William A. Brooks",
  booktitle =    "Advanced Signal Processing Algorithms, Architectures,
                 and Implementations IV",
  editor =       "Franklin T. Luk",
  volume =       "2027",
  organization = SPIE,
  year =         "1993",
  pages =        "180--193",
  address =      "San Diego, California",
  abstract =     "Compared to conventional radars, ultra-wideband (UWB)
                 radars are characterized by very large bandwidth and
                 fine range resolution. Potential applications of this
                 type of radar include terrain mapping, and target
                 identification/classification. In this paper we use a
                 non- stationary approach and analyze UWB radar data
                 using time- frequency and time-scale transformations.
                 The time-frequency transformations considered are the
                 Short-Time Fourier Transform (STFT), the Wigner-Ville
                 Distribution (WD), the Instantaneous Power Spectrum
                 (IPS), and the ZAM transform. Two discrete
                 implementations of the Wavelet Transform (DWT) are also
                 investigated: the decimated A-trous algorithm proposed
                 by Holschneider et al, which uses non-orthogonal
                 wavelets; and the Mallat algorithm, which employs
                 orthogonal wavelets. The transients under study are UWB
                 radar returns from a boat (with and without corner
                 reflector) in the presence of sea clutter, multipath,
                 and radio frequency interferences (RFI). Results show
                 that all time-frequency and time-scale transforms
                 clearly detect the transient radar returns
                 corresponding to the boat with a corner reflector.
                 However, as the radar cross section of the target
                 decreases (boat without a corner reflector), results
                 change drastically as the RFI component dominates the
                 signal. Simulations show that the Instantaneous Power
                 Spectrum may be better adapted for localizing the
                 transient among the time-frequency techniques studied.
                 The decimated A-trous algorithm has the best time
                 resolution of the techniques studied as the return
                 appears better localized in the scalogram.",
}

@Proceedings{far-hun-vas:wavelets,
  title =        "Wavelets, fractals, and Fourier transforms",
  booktitle =    "Wavelets, fractals, and Fourier transforms",
  editor =       "M. Farge and Julian C. R. Hunt and J. C Vassilicos",
  volume =       "43",
  series =       "Institute of Mathematics and Its Applications
                 conference series",
  year =         "1993",
  publisher =    "Clarendon Press",
  address =      NY,
  keywords =     "Wavelets, Mathematics, Fractals, Fourier
                 transformations",
  loc =          "QA403.3 .W39 1993",
  note =         "Based on the proceedings of a conference on wavelets,
                 fractals, and Fourier transforms held at Newnham
                 College, Cambridge in December 1990",
}

@Article{far-kev-per-goi:turbulence,
  journal =      PIEEE,
  volume =       "84",
  number =       "4",
  year =         "1996",
  pages =        "639--669",
  title =        "{W}avelets and turbulence",
  author =       "M. Farge and N. Kevlahan and V. Perrier and U.
                 Goirand",
  abstract =     "We have used wavelet transform techniques to analyze,
                 model, and compute turbulent flows. The theory and open
                 questions encountered in turbulence are presented The
                 wavelet-based techniques that we have applied to
                 turbulence problems are explained and the main results
                 obtained are summarized.",
  keywords =     "partial-differential equations. two-dimensional
                 turbulence. statistical equilibrium states.
                 negative-temperature states. fully-developed
                 turbulence. perfect fluid-dynamics. reynolds-number.
                 isotropic turbulence. numerical-solution.
                 kinetic-equations",
}

@Article{far:AS256,
  title =        "The Distribution of a Quadratic Form in Normal
                 Variables",
  author =       "R. W. Farebrother",
  journal =      AS,
  volume =       "39",
  number =       "2",
  pages =        "294--309",
  year =         "1990",
  keywords =     "Imhof procedure; Koerts-Ambrose algorithm; Linear
                 combination of chi-squared variables",
}

@Article{far:eigenvalue,
  title =        "Eigenvalue-{F}ree Methods for Computing the
                 Distribution of a Quadratic Form in Normal Variables",
  author =       "R. W. Farebrother",
  journal =      "Statistische Hefte",
  volume =       "26",
  pages =        "287--302",
  year =         "1985",
}

@Article{far:wavelets,
  title =        "Wavelet transforms and their applications to
                 turbulence",
  author =       "M. Farge",
  journal =      "Annual Review of Fluid Mechanics",
  volume =       "24",
  year =         "1992",
  pages =        "395--457",
}

@InProceedings{fer-per-swe:spie96,
  title =        "{LIFTPACK}: {A} software package for wavelet
                 transforms using lifting",
  author =       "G. Fern\'{a}ndez and S. Periaswamy and Wim Sweldens",
  crossref =     "uns-ald-lai:wavelet4",
  url =          "http://cm.bell-labs.com/who/wim/papers/spi96.ps",
  abstract =     "We present LIFTPACK: A software package written in C
                 for fast calculation of 2D biorthogonal wavelet
                 transforms using the lifting scheme. The lifting scheme
                 is a new approach for the construction of biorthogonal
                 wavelets entirely in the spatial domain, i.e.,
                 independent of the Fourier Transform. Constructing
                 wavelets using lifting consists of three simple phases:
                 the first step or Lazy wavelet splits the data into two
                 subsets, even and odd, the second step calculates the
                 wavelet coefficients (high pass) as the failure to
                 predict the odd set based on the even, and finally the
                 third step updates the even set using the wavelet
                 coefficients to compute the scaling function
                 coefficients (low pass). The predict phase ensures
                 polynomial cancelation in the high pass (vanishing
                 moments of the dual wavelet) and the update phase
                 ensures preservation of moments in the low pass
                 (vanishing moments of the primal wavelet). By varying
                 the order, an entire family of transforms can be built.
                 The lifting scheme ensures fast calculation of the
                 forward and inverse wavelet transforms that only
                 involve FIR filters. The transform works for images of
                 arbitrary size with correct treatment of the
                 boundaries. Also, all computations can be done
                 in-place.",
}

@Article{fis:frequency,
  title =        "Frequency distribution of the values of the
                 correlation coefficient in samples from an indefinitely
                 large population",
  author =       "R. A. Fisher",
  journal =      BKA,
  volume =       "10",
  year =         "1915",
  pages =        "507--521",
}

@Article{fis:tests,
  title =        "Tests of significance in harmonic analysis",
  author =       "R. A. Fisher",
  journal =      PRSLA,
  volume =       "125",
  year =         "1929",
  pages =        "54--59",
}

@InCollection{fla-gon:from,
  title =        "From Wavelets to Time-Scale Energy Distributions",
  author =       "P. Flandrin and P. Gon\c{c}lav{\`e}s",
  pages =        "309--334",
  crossref =     "sch-web:recent",
}

@Article{fla:brownian,
  title =        "Wavelet Analysis and Synthesis of Fractional
                 {B}rownian Motion",
  author =       "Patrick Flandrin",
  journal =      IEEETIT,
  volume =       "38",
  number =       "2",
  year =         "1992",
  pages =        "910--917",
  abstract =     "Fractional Brownian motion (FBM) offers a convenient
                 modeling for nonstationary stochastic processes with
                 long-term dependencies and 1/f-type spectral behavior
                 over wide ranges of frequencies. Statistical
                 self-similarity is an essential feature of FBM and
                 makes natural the use of wavelets for both its analysis
                 and its synthesis. A detailed second-order analysis is
                 carried out for wavelet coefficients of FBM. It reveals
                 a stationary structure at each scale and a power-law
                 behavior of the coefficients' variance from which the
                 fractal dimension of FBM can be estimated. Conditions
                 for using orthonormal wavelet decompositions as
                 approximate whitening filters are discussed,
                 consequences of discretization are considered, and some
                 connections between the wavelet point of view and
                 previous approaches based on length measurements
                 (analysis) or dyadic interpolation (synthesis) are
                 briefly pointed out.",
}

@Article{fos:unevenly,
  title =        "Wavelets for Period Analysis of Unevenly Sampled Time
                 Series",
  author =       "Grant Foster",
  journal =      AnJ,
  volume =       "112",
  number =       "4",
  year =         "1996",
  pages =        "1709--1729",
  email =        "gfoster@aavso.org",
}

@InProceedings{fou:blocking,
  title =        "Wavelet analysis of observed geopotential and wind:
                 {B}locking and local energy coupling across scales",
  author =       "Aim\'{e} Fournier",
  crossref =     "uns-ald-lai:wavelet4",
  email =        "fournier@cloudy.geology.yale.edu",
  abstract =     "Atmospheric blocking during three unusual winter
                 months is studied by multiresolution analysis and a
                 wavelet based adaptation of traditional Fourier series
                 based energetics. We demonstrate that blocking, in part
                 a large and localized meteorological phenomenon, is
                 largely described by just the largest scale part of the
                 multiresolution analysis. New forms of the transfer
                 functions of kinetic energy with the mean and eddy
                 parts of the atmospheric circulation are introduced.
                 These quantify the spatially localized conversion of
                 energy between scales. A new accounting method for
                 wavelet indexed transfers permits the introduction of a
                 physically meaningful localized scale flux function.
                 These techniques are applied to the data, and some
                 support is found for the hypothesis that blocking is
                 partially maintained by an inverse cascade.",
}

@Unpublished{fou:introduction,
  title =        "An introduction to orthonormal wavelet analysis with
                 shift invariance: {A}pplication to observed
                 atmospheric-blocking spatial structure",
  author =       "Aim\'{e} Fournier",
  year =         "1999",
  note =         "Submitted to the {\em Journal of the Atmospheric
                 Sciences}",
  abstract =     "Orthonormal wavelet analysis (OWA) is a special form
                 of wavelet analysis which is especially suitable for
                 analyzing spatial structures, such as atmospheric
                 fields. For this purpose, OWA is more efficient and
                 accurate than the nonorthogonal wavelet analysis (NWA)
                 which has been introduced to the meteorological
                 community in recent years, and which is more suitable
                 for ``making time series sing.'' Since NWA is strictly
                 correct only for infinite domains, OWA must be derived
                 from NWA by use of appropriate boundary conditions, in
                 this case, by periodization of OWA on an infinite
                 domain. OWA is not translation invariant, unlike NWA.
                 Two remedies are to use all possible translations,
                 known as the Stationary Wavelet Transform, or else to
                 use a `best' translation, known as the Best Shift OWA.
                 OWA is a generalization of Fourier series, and the
                 associated multiresolution analysis (MRA) is a
                 generalization of Reynolds averaging. Like these,
                 OWA/MRA on discrete and continuous domains satisfy
                 analogous identities arithmetically exactly, unlike
                 NWA. OWA/MRA is more efficient than Fourier series for
                 analyzing nearly-singular synthetic functions, and also
                 sequences of observed geopotential height maps which
                 contain atmospheric blocking. Close to or more than 90%
                 of the spatial variance of latitude-band averaged
                 geopotential height, averaged over five different
                 blocking events, is reconstructed by only two wavelets
                 using best shift. This is comparable to EOF analysis,
                 but is much faster and less data-dependent. All of the
                 basic OWA programs are freely available for MATLAB (R),
                 in the package WaveLab (c).",
}

@InProceedings{fou:lower,
  title =        "Wavelet representation of lower-atmospheric long
                 nonlinear wave dynamics, governed by the
                 {B}enjamin-{D}avis-{O}no-{B}urgers equation",
  author =       "Aim\'{e} Fournier",
  crossref =     "szu:wavelet2",
  pages =        "672--681",
}

@InProceedings{fou:simulated,
  title =        "Wavelet multiresolution analysis of numerically
                 simulated 3{D} radiative convection",
  author =       "Aim\'{e} Fournier",
  pages =        "642--653",
  crossref =     "szu:wavelet3",
  email =        "fournier@cloudy.geology.yale.edu",
  abstract =     "A wavelet multiresolution analysis is performed on
                 atmospheric fields simulated by a multilevel
                 3-dimensional atmospheric boundary layer model. Wavelet
                 cospectra of the vertical wind and potential
                 temperature are calculated and compared with radial
                 Fourier cospectra. The former indicate most of the
                 field variance to have horizontal scales roughly equal
                 to the vertical scale, as should be the case for
                 convectively driven turbulence. Fourier spectra exhibit
                 a -3 power law, suggesting that the statistics may
                 depend only on a quantity with units of time.
                 Observations of time-and scale-dependent structures
                 suggest certain physical mechanisms at work. The
                 multiresolution analysis analogue of turbulent energy
                 equations are formulated. This framework supports the
                 proposed physical mechanisms.",
}

@Article{fri-gro-tch:gaps,
  title =        "Wavelet analysis of signals with gaps",
  author =       "P. Frick and A. Grossmann and P. Tchamitchian",
  journal =      JMP,
  volume =       "39",
  number =       "8",
  year =         "1998",
  pages =        "4091--4107",
  abstract =     "A recently introduced algorithm [Frick et al.,
                 Astrophys. J. 483, 426 (1997)] of spectral analysis of
                 data with gaps via a modified continuous wavelet
                 transform is developed and studied. This algorithm is
                 based on a family of functions called ``gapped
                 wavelets'' which fulfill the admissibility condition on
                 the gapped support. The wavelet family is characterized
                 by an additional parameter which should be calculated
                 for every scale and position. Three theorems concerning
                 the properties of gapped wavelet transform are
                 formulated and proved. They affirm the global stability
                 of the algorithm as well as its stability in both
                 limits of large and small scales. These results are
                 illustrated by some numerical examples, which show that
                 the algorithm really attenuates the artifacts coming
                 from gaps (and/or boundaries), and is particularly
                 efficient at small and large scales.",
}

@InProceedings{gag:numerical-results,
  title =        "Wavelet filtering of speckle noise -- some numerical
                 results",
  author =       "Langis Gagnon",
  booktitle =    "Proceedings of the Conference Vision Interface",
  year =         "1999",
  pages =        "???--???",
  email =        "langis.gagnon@crim.ca",
  url =          "http://www.crm.umontreal.ca/~lgagnon/articles/vi99.pdf",
}

@Article{gal-hut:terrain,
  title =        "Scale dependence in terrain analysis",
  author =       "J. C. Gallant and M. F. Hutchinson",
  journal =      "Mathematics and Computers in Simulation",
  volume =       "43",
  number =       "3--6",
  month =        mar,
  year =         "1997",
  pages =        "313--321",
  keywords =     "elevation",
  abstract =     "Topographic attributes computed from digital elevation
                 models are dependent on the resolution of the elevation
                 data from which they are computed. A regular
                 rectangular grid is not an ideal representation of
                 topographic surfaces for the study of scale effects.
                 Spectral and wavelet techniques are obvious
                 alternatives but have several deficiencies,
                 particularly in their use of oscillatory basis
                 functions. The positive wavelet representation has very
                 attractive properties of localisation and feature
                 representation. Preliminary application to
                 one-dimensional topographic data (profiles) yields
                 useful results, including the identification of changes
                 in topographic structure with scale. Extension to
                 two-dimensional analysis will allow quantification of
                 characteristic shapes, scales and orientations in the
                 landscape.",
}

@Article{gam:wavelet,
  title =        "Wavelet transform analysis of the length of the day
                 and {E}l-{N}i{\~n}o/{S}outhern {O}scillation variations
                 at intraseasonal and interannual time scales",
  author =       "D. Gambis",
  journal =      AG,
  volume =       "10",
  year =         "1992",
  pages =        "429--437",
}

@Article{gao-bru:firm,
  title =        "{W}ave{S}hrink with Firm Shrinkage",
  author =       "Hong-Ye Gao and Andrew Bruce",
  journal =      SSin,
  volume =       "7",
  number =       "4",
  year =         "1997",
  pages =        "855--874",
  url =          "ftp://ftp.statsci.com/pub/gao/firm.ps.Z",
  keywords =     "Bias Estimation; Confidence Interval; Firm Shrinkage;
                 Minimax Thresholds; Non-parametric Regression; Signal
                 De-noising; Trend Estimation; Variance Estimation;
                 Wavelet Transform; WaveShrink",
  abstract =     "Donoho and Johnstone's WaveShrink procedure has proven
                 valuable for signal de-noising and non-parametric
                 regression. WaveShrink has very broad asymptotic
                 near-optimality properties. In this paper, we introduce
                 a new shrinkage scheme, {\em firm}, which generalizes
                 the hard and soft shrinkage proposed by Donoho and
                 Johnstone. We derive minimax thresholds and provide
                 formulas for computing the pointwise variance, bias,
                 and risk for WaveShrink with firm shrinkage. We study
                 the properties of the shrinkage functions, and
                 demonstrate that firm shrinkage offers advantages over
                 both hard shrinkage (uniformly smaller risk and less
                 sensitivity to small perturbations in the data) and
                 soft shrinkage (smaller bias and overall $L_2$ risk).
                 Software is provided to reproduce all results in this
                 paper.",
}

@Article{gao-li:coherent,
  journal =      JAM,
  volume =       "32",
  number =       "11",
  year =         "1993",
  pages =        "1717--1725",
  title =        "{W}avelet analysis of coherent structures at the
                 atmosphere-forest interface",
  author =       "W. Gao and BL. Li",
  abstract =     "Wavelet studies were used for the turbulent data
                 obtained inside and over a deciduous forest to
                 investigate spatial and scale properties of a coherent
                 structure in the area. Discrete warm and cool centers
                 are linked to organized updrafts and downdrafts. Their
                 patterns are alike, but the magnitudes vary at various
                 heights. Temperature structures over the canopy possess
                 a shorter duration, but the rate of reduction in the
                 time scale with increasing height seems proportional to
                 the rise in mean wind speed.",
}

@Article{gao:choice,
  title =        "Choice of Thresholds for Wavelet Shrinkage Estimate of
                 the Spectrum",
  author =       "Hong-Ye Gao",
  journal =      JTSA,
  volume =       "18",
  number =       "3",
  year =         "1997",
  pages =        "231--251",
  url =          "ftp://ftp.mathsoft.com/pub/wavelets/wavethresh.ps",
  keywords =     "Log Spectrum Estimation; Orthogonal Wavelet
                 Transformation; Shrinkage Estimator",
  abstract =     "We study the problem of estimating the log spectrum of
                 a stationary Gaussian time series by thresholding the
                 empirical wavelet coefficients. We propose the use of
                 thresholds $t_{j,n}$ depending on sample size n,
                 wavelet basis and resolution level j. At fine
                 resolution levels (j=1, 2,...), we propose \[ t_{j,n} =
                 A_j\log n, \] where $A_j$ are level-dependent constants
                 and at coarse levels (j>>1), \[ t_{j,n} =
                 \frac{\pi}{\sqrt{3}}\sqrt{\log n}. \] The purpose of
                 this thresholding level is to make the reconstructed
                 log-spectrum as nearly noise-free as possible. In
                 addition to being pleasant from a visual point of view,
                 the noise-free character leads to attractive
                 theoretical properties over a wide range of smoothness
                 assumptions. Previous proposals set much smaller
                 thresholds and did not enjoy these properties.",
}

@Article{gao:garrote,
  title =        "Wavelet Shrinkage DeNoising Using Non-Negative
                 Garrote",
  author =       "Hong-Ye Gao",
  journal =      JCGS,
  volume =       "7",
  number =       "4",
  year =         "1998",
  pages =        "469--488",
  url =          "http://www.amstat.org/publications/jcgs/pdf_98/Gao.pdf",
  keywords =     "Cycle-Spinning; Minimax Threshold; Non-negative
                 Garrote; Nonparametric Regression; Shrinkage Functions;
                 Stein's Unbiased Risk Estimate (SURE); Wavelet
                 Transform",
  abstract =     "In this paper, we combine Donoho and Johnstone's
                 Wavelet Shrinkage denoising technique (known as
                 WaveShrink) with Breiman's non-negative garrote. We
                 show that the non-negative garrote shrinkage estimate
                 enjoys the same asymptotic convergence rate as the hard
                 and the soft shrinkage estimates. For finite sample
                 simulations, non-negative garrote performs better
                 (smaller mean-square-error) than both hard and soft,
                 and comparable to the firm shrinkage. We derive the
                 minimax thresholds for the non-negative garrote. We
                 study the threshold selection procedure based on
                 Stein's Unbiased Risk Estimate (SURE) for both
                 non-negative garrote and soft shrinkages. We propose a
                 new threshold selection procedure based on combining
                 Coifman and Donoho's cycle-spinning and SURE. We call
                 our new procedure SPINSURE. We use examples to show
                 that SPINSURE is more stable than SURE: smaller
                 standard deviation and smaller range.",
}

@Unpublished{gao:heteroscedastic,
  title =        "Wavelet Shrinkage Estimates For Heteroscedastic
                 Regression Models",
  author =       "Hong-Ye Gao",
  note =         "Statistical Sciences Division, MathSoft, Inc",
  year =         "1997",
  url =          "ftp://ftp.statsci.com/pub/gao/wsshd.ps.Z",
  keywords =     "Heteroscedasticity; Nonparametric Regression; Running
                 MAD; Wavelet Transform; Variance Estimation.",
  abstract =     "We extend Donoho and Johnstone's wavelet shrinkage
                 smoothing technique (known as WaveShrink) to handle
                 data with heteroscedastic noise. We first show that if
                 the noise variances are known, WaveShrink estimate
                 achieves the same near-optimal convergence rate as in
                 the white noise case. We then propose a procedure for
                 estimating the noise variances. Our procedure is based
                 on applying running MAD (Median Absolute Deviation from
                 the median) to the non-decimated finest level wavelet
                 coefficients. We apply our technique to various
                 numerical examples.",
}

@Unpublished{gao:isontonic,
  title =        "Wavelets and Isotonic Regression",
  author =       "Hong-Ye Gao",
  note =         "Statistical Sciences Division, MathSoft, Inc",
  year =         "199?",
  url =          "ftp://ftp.statsci.com/pub/gao/isotonic.ps.Z",
  keywords =     "Grenander Estimator; Isotonic Regression; Monotone
                 Curve; Orthogonal Wavelet Transformation; Shrinkage
                 Estimator",
  abstract =     "Consider the following isotonic regression model: \[
                 y_i = f(t_i) + z_i\] where $f$ is only known to be a
                 decreasing function and $\{z_i\}$ are iid Gaussian with
                 mean zero and variance $\sigma^2$. We propose a simple
                 thresholding procedure based on the fact that the
                 wavelet coefficients for $f$, under Haar basis, are
                 non-negative. We show that our estimator is competitive
                 with the Grenander estimator both theoretically and
                 numerically (in the sense of mean-square-error).",
}

@Unpublished{gao:selection,
  title =        "Threshold Selection in {W}ave{S}hrink",
  author =       "Hong-Ye Gao",
  note =         "Statistical Sciences Division, MathSoft, Inc",
  year =         "1997",
  url =          "ftp://ftp.statsci.com/pub/gao/threshold.ps.Z",
  keywords =     "Cycle-Spinning; Minimax Threshold; Non-negative
                 Garrote; Nonparametric Regression; Shrinkage Functions;
                 Stein's Unbiased Risk Estimate (SURE); Wavelet
                 Transform; WaveShrink",
  abstract =     "Donoho and Johnstone's wavelet shrinkage denoising
                 technique (known as WaveShrink) consists three steps:
                 (1) transform data into wavelet domain; (2) shrink the
                 wavelet coefficients; and (3) transform the shrunk
                 coefficients back. The choice of shrinkage function and
                 thresholds in step (2) plays an important role for
                 WaveShrink both theoretically and in practice. In this
                 paper, we discuss the issue of threshold selection in
                 WaveShrink. We first review the threshold selection
                 procedure based minimax thresholds and Stein's Unbiased
                 Risk Estimate (SURE). We then propose a new threshold
                 selection procedure based on combining Coifman and
                 Donoho's cycle-spinning and SURE. We call our new
                 procedure SPINSURE. We use examples to show that
                 SPINSURE is numerically more stable than SURE: smaller
                 standard deviation and smaller range. Various
                 comparisons with the ideal and minimax thresholds are
                 also presented.",
}

@Unpublished{gao:spectral,
  title =        "Spectral Density Estimation via Wavelet Shrinkage",
  author =       "Hong-Ye Gao",
  note =         "Statistical Sciences Division, MathSoft, Inc",
  year =         "1996",
  url =          "ftp://ftp.statsci.com/pub/gao/spec.ps.Z",
  keywords =     "Non-Gaussian Model; Periodized Meyer Wavelets;
                 Shrinkage Estimator; Spectral Density Estimation;
                 Wavelet Transform",
  abstract =     "We study the problem of estimating the spectral
                 density of a stationary Gaussian time series. We use an
                 orthogonal wavelet system whose members are periodic
                 functions and have a finite number of non-zero Fourier
                 coefficients -- periodized Meyer wavelets. We apply
                 shrinkage rules to the empirical wavelet coefficients.
                 We show that estimates based on thresholds $t_{j,n} =
                 \lm_j\log n$ for certain $\lm_j$, with $n$ the sample
                 size, have near-optimal $L_2$ convergence rates, over
                 any Besov class in a wide range. In some cases, which
                 includes the Bump Algebra, wavelet shrinkage procedures
                 significantly outperform classical linear procedures,
                 such as window methods and AR approximation methods.",
}

@PhdThesis{gao:thesis,
  title =        "Wavelet Estimation of Spectral Densities in Time
                 Series Analysis",
  author =       "Hong-Ye Gao",
  school =       "University of California, Berkeley",
  year =         "1993",
}

@Unpublished{gen-sel-whi:differentiating,
  title =        "Differentiating intraday seasonalities through wavelet
                 multi-scaling",
  author =       "R. Gen\c{c}ay and F. Sel\c{c}uk and B. Whitcher",
  year =         "1999",
  note =         "submitted",
}

@Unpublished{gen-sel-whi:high-frequency,
  title =        "Wavelet Scale Analysis of High-Frequency Foreign
                 Exchange Rates",
  author =       "R. Gen\c{c}ay and F. Sel\c{c}uk and B. Whitcher",
  year =         "2000",
  note =         "submitted",
}

@Article{ger-har-mas:fractal,
  title =        "Fractal functions and wavelet expansions based on
                 several scaling functions",
  author =       "Jeffrey S. Geronimo and Douglas P. Hardin and Peter R.
                 Massopust",
  journal =      JAT,
  volume =       "78",
  number =       "3",
  year =         "1994",
  pages =        "373--401",
}

@InProceedings{gil-wil-fel:visualizing,
  title =        "Visualizing multifractal scaling behavior: {A} simple
                 coloring heuristic",
  author =       "A. C. Gilbert and W. Willinger and A. Feldman",
  booktitle =    "Conference Record of The Thirty-Second Asilomar
                 Conference on Signals, Systems and Computers",
  volume =       "1",
  year =         "1998",
  pages =        "715--722",
  email =        "agilbert@research.att.com, walter@research.att.com,
                 anja@research.att.com",
  url =          "http://www.research.att.com/~agilbert/ps.files/asilomar98.ps.Z",
}

@Article{gil:trend,
  title =        "Testing for the onset of trend, using wavelets",
  author =       "Scott D. Gilbert",
  journal =      JTSA,
  volume =       "20",
  number =       "5",
  year =         "1999",
  pages =        "513--526",
}

@InCollection{gof:wavelets,
  title =        "Wavelets in macroeconomics: {A}n introduction",
  author =       "W. L. Goffe",
  booktitle =    "Computational Techniques for Econometrics and Economic
                 Analysis",
  editor =       "D. A. Belsley",
  publisher =    "Kluwar Academic Publishers",
  address =      "Dordrecht",
  series =       "Advances in Computational Economics",
  volume =       "3",
  year =         "1993",
  pages =        "???--???",
}

@InProceedings{gon-abr:multiple-window,
  title =        "Multiple-window wavelet transform and local scaling
                 exponent estimation",
  author =       "P. Gon\c{c}alv{\`e}s and P. Abry",
  booktitle =    "Proceedings of the IEEE International Conference on
                 Acoustics, Speech, and Signal Processing",
  volume =       "4",
  year =         "1997",
  pages =        "3433--3436",
  email =        "paulo.goncalves@inria.fr, pabry@physique.ens-lyon.fr",
  abstract =     "We propose here a multiple-window wavelet transform
                 for the purpose of identifying non-stationary
                 self-similar structures in random processes and
                 estimating the time-varying scaling exponent H(t) that
                 controls the local regularity and correlation of the
                 process. More specifically, our final aim is to be able
                 to track even rapidly varying trajectories (t,H(t)).
                 The solution described here combines analysis obtained
                 from scalograms computed with a set of multi-windows
                 designed so as to satysfy to a decorrelation condition.
                 We derive here the statistics for the estimate of H(t),
                 compare it against numerical simulations and show that
                 we obtain a substantial reduction of variance in
                 estimation, without introducing bias.",
}

@InCollection{gon-fla:bilinear,
  title =        "Bilinear Time-Scale Analysis Applied to Local Scaling
                 Exponents Estimation",
  author =       "P. Gon\c{c}alv{\`e}s and P. Flandrin",
  pages =        "271--276",
  crossref =     "mey-roq:progress",
}

@InProceedings{gon-fla:scaling,
  title =        "Scaling exponents estimation from time-scale energy
                 distributions",
  author =       "P. Gon\c{c}alv{\`e}s and P. Flandrin",
  booktitle =    "Proceedings of the IEEE International Conference on
                 Acoustics, Speech, and Signal Processing",
  volume =       "5",
  year =         "1992",
  pages =        "157--160",
}

@Unpublished{gon-etal:financial,
  title =        "The Wavelet Transform for Filtering Financial Data
                 Streams",
  author =       "Zheng Gonghui and Jean-Luc Stark and Jonathan Campbell
                 and Fionn Murtagh",
  year =         "1998",
  note =         "Submitted to {\em Journal of Computational
                 Intelligence in Finance}",
}

@InProceedings{gon-rie-bar:simple,
  title =        "Simple Statistical Analysis of Wavelet-based
                 Multifractal Spectrum Estimation",
  author =       "P. Gon\c{c}alv{\`e}s and R. H. Riedi and R. G.
                 Baraniuk",
  booktitle =    "Conference Record of The Thirty-Second Asilomar
                 Conference on Signals, Systems and Computers",
  volume =       "?",
  year =         "1998",
  pages =        "???--???",
  url =          "http://www-dsp.rice.edu/~riedi/cv_frame.html",
  abstract =     "The multifractal spectrum characterizes the scaling
                 and singularity structures of signals and proves useful
                 in numerous applications, from network traffic analysis
                 to turbulence. Of great concern is the estimation of
                 the spectrum from a finite data record. In this paper,
                 we derive asymptotic expressions for the bias and
                 variance of a wavelet-based estimator for a fractional
                 Brownian motion (fBm) process. Numerous numerical
                 simulations demonstrate the accuracy and utility of our
                 results.",
}

@Article{gou-auv-bag:dwarfs,
  title =        "Wavelet Analysis of Pulsating White Dwarfs",
  author =       "M. J. Goupil and M. Auvergne and A. Baglin",
  journal =      AandA,
  volume =       "250",
  number =       "1",
  year =         "1991",
  pages =        "89--98",
  abstract =     "Parts of light curves of two variable white dwarfs,
                 Giclas 191-16 (BR Cam) and PG 1351+489 (EM UMa), are
                 investigated by means of a wavelet analysis. This
                 time-frequency analysis decomposes the light curves
                 into their different oscillating components whose
                 temporal behaviors are then individually studied. In
                 addition to an oscillation of large amplitude, small
                 amplitude oscillations are thereby clearly emphasized
                 for both stars. Amplitude variations are found for most
                 detected oscillations with periods of modulation as
                 long or greater than the time intervals of the
                 corresponding runs. A wavelet analysis of a comparison
                 star gives the quality of the night in localizing
                 perturbative atmospheric events.",
}

@Article{gra:introduction,
  title =        "An introduction to wavelets",
  author =       "Amara Graps",
  journal =      IEEECSE,
  volume =       "2",
  number =       "2",
  year =         "1995",
  pages =        "50--61",
  url =          "ftp://ftp.best.com/pub/agraps/papers/IEEEwavelet.ps.gz",
  keywords =     "wavelets, scale-based analysis, mathematical
                 requirements, data represention, packet techniques,
                 applications, data analysis, discretely sampled
                 time-series data",
  abstract =     "Wavelets were developed independently by
                 mathematicians, quantum physicists, electrical
                 engineers and geologists, but collaborations among
                 these fields during the last decade have led to new and
                 varied applications. What are wavelets, and why might
                 they be useful to you? The fundamental idea behind
                 wavelets is to analyze according to scale. Indeed, some
                 researchers feel that using wavelets means adopting a
                 whole new mind-set or perspective in processing data.
                 Wavelets are functions that satisfy certain
                 mathematical requirements and are used in representing
                 data or other functions. Most of the basic wavelet
                 theory has now been done. The mathematics have been
                 worked out in excruciating detail, and wavelet theory
                 is now in the refinement stage. This involves
                 generalizing and extending wavelets, such as in
                 extending wavelet packet techniques. The future of
                 wavelets lies in the as-yet uncharted territory of
                 applications. Wavelet techniques have not been
                 thoroughly worked out in such applications as practical
                 data analysis, where, for example, discretely sampled
                 time-series data might need to be analyzed. Such
                 applications offer exciting avenues for exploration.",
}

@Article{gre-gie-lip:invariance,
  title =        "Translational invariance in turbulent cascade models",
  author =       "M. Greiner and J. Giesemann and P. Lipa",
  journal =      PRE,
  volume =       "56",
  number =       "4",
  year =         "1997",
  pages =        "4263--4274",
  url =          "http://ojps.aip.org/journal_cgi/getabs?KEY=PLEEE8&cvips=PLEEE8000056000004004263000001&gifs=No",
  keywords =     "fully-developed turbulence hydrodynamic turbulence
                 exact resummations wavelet correlations",
  abstract =     "Due to the underlying hierarchical structure, spatial
                 correlation functions calculated from multiplicative
                 cascade models are not translationally invariant. A
                 scheme is presented that restores translational
                 invariance by averaging over the experimentally unknown
                 spatial location of cascade realizations with respect
                 to the observation window. The impact of this scheme on
                 multiplier distributions for the energy dissipation
                 field in fully developed turbulence is analyzed; only
                 the experimental multiplier distribution is found to be
                 invariant under a wide range of scales.",
}

@Article{gre-ros:fast,
  title =        "A fast wavelet-based Karhunen-Loeve transform",
  author =       "I. R. Greenshields and J. A. Rosiene",
  journal =      PR,
  volume =       "31",
  number =       "7",
  year =         "1998",
  pages =        "839--845",
  abstract =     "The paper describes the role of the standard wavelet
                 decomposition in computing a fast Karhunen-Loeve
                 transform. The standard wavelet decomposition (which we
                 show is different from the conventional wavelet
                 transform) leads to a highly sparse and simply
                 structured transformed version of the correlation
                 matrix which can be easily subsetted (with little loss
                 of Frobenius norm). The eigenstructure of this smaller
                 matrix can be efficiently computed using standard
                 algorithms such as QL. Finally, we provide an example
                 of the use of the efficient transform by classifying a
                 219-channel AVIRIS image with respect to its
                 eigensystem.",
}

@InCollection{gre:cross-validation,
  title =        "Wavelet basis selection for regression by
                 cross-validation",
  author =       "Seth A. Greenblatt",
  booktitle =    "Computational Approaches to Economic Problems",
  editor =       "H. M. Amman and B. Rustem and A. B. Whinston",
  publisher =    "Kluwar Academic Publishers",
  address =      "Dordrecht",
  series =       "Advances in Computational Economics",
  volume =       "6",
  year =         "1997",
  pages =        "39--55",
}

@InCollection{gre:outlier,
  title =        "Wavelets in econometrics: {A}n application to outlier
                 testing",
  author =       "Seth A. Greenblatt",
  booktitle =    "Computational Economic Systems: Models, Methods \&
                 Econometrics",
  editor =       "M. Gilli",
  publisher =    "Kluwar Academic Publishers",
  address =      "Dordrecht",
  series =       "Advances in Computational Economics",
  volume =       "5",
  year =         "1996",
  pages =        "139--160",
}

@InProceedings{gro-kro-mar:reading,
  title =        "Reading and understanding continuous wavelet
                 transforms",
  author =       "A. Grossmann and R. Kronland-Martinet and J. Morlet",
  pages =        "2--20",
  crossref =     "com-gro-tch:wavelets",
  keywords =     "wavelets",
  abstract =     "An introduction to continuous wavelet transforms and a
                 description of the representation methods that have
                 evolved. Also discusses the influence of the choice of
                 the wavelet in the interpretation of wavelet
                 transforms.",
}

@Article{gro-mor:hardy,
  title =        "Decomposition of {H}ardy Functions into Square
                 Integrable Wavelets of Constant Shape",
  author =       "A. Grossmann and J. Morlet",
  journal =      SIAMJMA,
  volume =       "15",
  number =       "4",
  year =         "1984",
  pages =        "723--736",
}

@Article{gru-wal:seismic,
  title =        "{C}haracterizing seismic time series using the
                 discrete wavelet transform",
  author =       "H. J. Grubb and A. T. Walden",
  journal =      GP,
  volume =       "45",
  number =       "2",
  year =         "1997",
  pages =        "183--205",
  abstract =     "The discrete wavelet transform (DWT) has potential as
                 a tool for supplying discriminatory attributes with
                 which to characterize or cluster groups of seismic
                 traces in reservoir studies. The wavelet transform has
                 the great advantage over the Fourier transform in being
                 able to better localize changes. The multiscale nature
                 and structure of the DWT leads to a method of display
                 which highlights this and allows comparison of changes
                 in the transform with changing data. Many different
                 sorts of wavelet exist and it is found that the quality
                 of reconstruction of a seismic trace segment, using
                 some of the coefficients, is dependent on the choice of
                 wavelet, which leads us to consider choosing a wavelet
                 under a 'best reconstruction' criterion. Location
                 shifts, time zero uncertainties, are also shown to
                 affect the transform, as do truncations, resampling,
                 etc. Using real data, examples of utilizing the DWT
                 coefficients as attributes for whole trace segments or
                 fractional trace segments are given. Provided the DWT
                 is applied consistently, for example with a fixed
                 wavelet, and non-truncated data, the transform produces
                 useful results. Care must be exercised if it is applied
                 to data of different lengths. However, as the algorithm
                 is refined and improved in the future, the DWT should
                 prove increasingly useful.",
  keywords =     "projection pursuit, sampling theory, propagation,
                 signal",
}

@MastersThesis{guo:msthesis,
  title =        "Theory and Applications of the Shift-Invariant,
                 Time-Varying and Undercimated Wavelet Transforms",
  author =       "Haitao Guo",
  year =         "1995",
  pages =        "144",
  school =       "Electrical and Computer Engineering Department, Rice
                 University",
  url =          "http://www-dsp.rice.edu/~harry/paper/ms.ps.Z",
  email =        "harry@ece.rice.edu",
  abstract =     "In this thesis, we generalize the classical discrete
                 wavelet transform, and construct wavelet transforms
                 that are shift-invariant, time-varying, undecimated,
                 and signal dependent. The result is a set of powerful
                 and efficient algorithms suitable for a wide variety of
                 signal processing tasks, e.g., data compression, signal
                 analysis, noise reduction, statistical estimation, and
                 detection. These algorithms are comparable and often
                 superior to traditional methods. In this sense, we put
                 wavelets in action.",
}

@Article{haa:haar,
  title =        "Zur {T}heorie der orthogonalen {F}unktionensysteme",
  author =       "Alfred Haar",
  journal =      "Mathematische Annalen",
  volume =       "69",
  pages =        "331--371",
  year =         "1910",
  note =         "In German",
}

@Article{hal-ker-pic:block,
  title =        "Block threshold rules for curve estimation using
                 kernel and wavelet methods",
  author =       "P. Hall and G. Kerkyacharian and D. Picard",
  journal =      AofS,
  volume =       "26",
  number =       "3",
  year =         "1998",
  pages =        "922--942",
  keywords =     "adaptivity bias convergence rate density estimation
                 minimax nonparametric regression smoothing parameter
                 variance",
  abstract =     "Motivated by recently developed threshold rules for
                 wavelet estimators, we suggest threshold methods for
                 general kernel density estimators, including those of
                 classical Rosenblatt-Parzen type. Thresholding makes
                 kernel methods competitive in terms of their adaptivity
                 to a wide variety of aberrations in complex signals. It
                 is argued that term-by-term thresholding does not
                 always produce optimal performance, since individual
                 coefficients cannot be estimated sufficiently
                 accurately for reliable decisions to be made.
                 Therefore, we suggest grouping coefficients into blocks
                 and making simultaneous threshold decisions about all
                 coefficients within a given block. It is argued that
                 block thresholding has a number of advantages,
                 including that it produces adaptive estimators which
                 achieve minimax-optimal convergence rates without the
                 logarithmic penalty that is sometimes associated with
                 term-by-term thresholding. More than this, the
                 convergence rates are achieved over large classes of
                 functions with discontinuities, indeed with a number of
                 discontinuities that diverges polynomially fast with
                 sample size. These results are also established for
                 block thresholded wavelet estimators, which, although
                 they can be interpreted within the kernel framework,
                 are often most conveniently constructed in a slightly
                 different way.",
}

@Article{hal-ker-pic:minimax,
  title =        "On the minimax optimality of block thresholded wavelet
                 estimators",
  author =       "P. Hall and G. Kerkyacharian and D. Picard",
  journal =      SSin,
  volume =       "9",
  number =       "1",
  year =         "1999",
  pages =        "33--49",
  keywords =     "Besov space. chirp function. convergence rate. Doppler
                 function. mean squared error. nonparametric regression.
                 smoothing parameter",
  abstract =     "Block thresholding methods have been proposed by Hall,
                 Kerkyacharian and Picard (1995) as a means of obtaining
                 increased adaptivity when estimating a function using
                 wavelet methods. For example, it has been shown that
                 block thresholding reduces mean squared error by
                 rendering the estimator more adaptive to relatively
                 subtle, local changes in curvature, of the type that
                 local bandwidth choice is designed to accommodate in
                 traditional kernel methods. In this paper we show that
                 block thresholding also provides extensive adaptivity
                 to many varieties of aberration, including those of
                 chirp and Doppler type. Indeed, in a wide variety of
                 function classes, block thresholding methods possess
                 minimax-optimal convergence rates, and in particular
                 enjoy those rates without the extraneous logarithmic
                 penalties that are usually suffered by term-by-term
                 thresholding methods.",
}

@Article{hal-mck-tur:performance,
  title =        "Performance of wavelet methods for functions with many
                 discontinuities",
  author =       "Peter Hall and Ian McKay and Berwin Turlach",
  journal =      AofS,
  volume =       "24",
  number =       "6",
  year =         "1996",
  pages =        "???--???",
}

@TechReport{hal-nas:non-integer,
  title =        "On Choosing a Non-integer Resolution Level when Using
                 Wavelet Methods",
  author =       "Peter Hall and Guy P. Nason",
  year =         "1996",
  institution =  "Centre for Mathematics and its Applications,
                 Australian National University",
}

@Article{hal-pat:effect,
  title =        "Effect of Thresholding Rules on Performance of
                 Wavelet-Based Curve Estimators",
  author =       "Peter Hall and Prakash Patil",
  journal =      SSin,
  volume =       "6",
  year =         "1996",
  pages =        "331--345",
}

@Article{hal-pat:methods,
  title =        "On wavelet methods for estimating smooth functions",
  author =       "Peter Hall and Prakash Patil",
  journal =      Ber,
  volume =       "1",
  number =       "1",
  year =         "1995",
  pages =        "41--58",
  abstract =     "Without assuming any prior knowledge of wavelet
                 methods, we develop theory describing their performance
                 as estimators of smooth functions. The linear part of
                 the wavelet estimator is discussed by analogy with
                 classical kernel methods. Concise formulae are
                 developed for its bias, variance and mean square error.
                 These quantities oscillate somewhat erratically on a
                 wavelength that is equivalent to the bandwidth,
                 reflecting the irregular numerical fluctuations that
                 are observed in practice. Nevertheless, the
                 contributions of these oscillations to mean integrated
                 square error tend to dampen one another out, even over
                 very small intervals, with the result that mean
                 integrated square error properties of linear wavelet
                 methods are much closer to those of kernel methods than
                 is perhaps reasonable, given the local behaviour. We
                 illustrate the adaptive qualities of the nonlinear
                 component of a wavelet estimator by describing its
                 performance when the target function is smooth but has
                 high-frequency oscillations. It is shown that the
                 nonlinear component automatically adapts to changing
                 local conditions, to the extent of achieving (except
                 for a logarithmic factor) the same convergence rate as
                 the optimal linear estimator, but without a need to
                 adjust the underlying bandwidth. This makes explicitly
                 clear the way in which the linear part of the estimator
                 takes care of the &lsquo;average&rsquo; characteristics
                 of the unknown curve, while the nonlinear part corrects
                 for more erratic fluctuations, in a manner which is
                 virtually independent of the construction of the linear
                 part.",
  keywords =     "convergence rate density estimation differentiability
                 dilation equation kernel method nonparametric curve
                 estimation orthogonal series regression scaling
                 function smoothness wavelet",
}

@Article{hal-pat:smoothing,
  journal =      JRSSB,
  volume =       "58",
  number =       "2",
  year =         "1996",
  pages =        "361--377",
  title =        "{O}n the choice of smoothing parameter, threshold and
                 truncation in nonparametric regression by non-linear
                 wavelet methods",
  author =       "P. Hall and P. Patil",
  abstract =     "Concise asymptotic theory is developed for non-linear
                 wavelet estimators of regression means, in the context
                 of general error distributions, general designs,
                 general normalizations in the case of stochastic
                 design, and non-structural assumptions about the mean.
                 The influence of the tail weight of the error
                 distribution is addressed in the setting of choosing
                 threshold and truncation parameters. Mainly, the tail
                 weight is described in an extremely simple way, by a
                 moment condition; previous work on this topic has
                 generally imposed the much more stringent assumption
                 that the error distribution be normal. Different
                 approaches to correction for stochastic design are
                 suggested. These include conventional kernel estimation
                 of the design density, in which case the interaction
                 between the smoothing parameters of the non-linear
                 wavelet estimator and the linear kernel method is
                 described.",
}

@Article{hal-pen-ker-pic:block,
  journal =      SC,
  volume =       "7",
  number =       "2",
  year =         "1997",
  pages =        "115--124",
  title =        "Numerical performance of block thresholded wavelet
                 estimators",
  author =       "Peter Hall and Spiridon Penev and G{\'e}rard
                 Kerkyacharian and Dominique Picard",
  keywords =     "Adaptivity bias density estimation mean squared error
                 non-parametric regression smoothing parameter
                 variance",
  abstract =     "Usually, methods for thresholding wavelet estimators
                 are implemented term by term, with empirical
                 coefficients included or excluded depending on whether
                 their absolute values exceed a level that reflects
                 plausible moderate deviations of the noise. We argue
                 that performance may be improved by pooling
                 coefficients into groups and thresholding them
                 together. This procedure exploits the information that
                 coefficients convey about the sizes of their
                 neighbours. In the present paper we show that in the
                 context of moderate to low signal-to-noise ratios, this
                 `block thresholding' approach does indeed improve
                 performance, by allowing greater adaptivity and
                 reducing mean squared error. Block thresholded
                 estimators are less biased than term-by-term
                 thresholded ones, and so react more rapidly to sudden
                 changes in the frequency of the underlying signal. They
                 also suffer less from spurious aberrations of Gibbs
                 type, produced by excessive bias. On the other hand,
                 they are more susceptible to spurious features produced
                 by noise, and are more sensitive to selection of the
                 truncation parameter.",
}

@TechReport{hal-tur:competitors,
  title =        "Convolution and Interpolation: {C}ompetitors with
                 Local Polynomial Smoothing",
  author =       "Peter Hall and Berwin A. Turlach",
  institution =  "Centre for Mathematics and its Applications,
                 Australian National University",
  number =       "SRR95-037",
  year =         "1995",
  email =        "berwin@alphasun.anu.edu.au",
  abstract =     "Local polynomial smoothing enjoys a variety of very
                 attractive features. It is often viewed as superior to
                 convolution and interpolation methods, which offer
                 greater numerical stability but inferior theoretical
                 performance. In this paper we show that modifications
                 to convolution and interpolation techniques produce
                 effective competitors with local polynomial smoothing,
                 enjoying similar bias, variance and mean squared error
                 properties but without the downside of numerical
                 instability. The methods suggested here may be employed
                 as the basis for empirical wavelet transforms of
                 ungridded data.",
}

@Article{hal-tur:enhancing,
  title =        "Enhancing Convolution and Interpolation Methods for
                 Nonparametric Regression",
  author =       "Peter Hall and Berwin A. Turlach",
  journal =      BKA,
  volume =       "84",
  number =       "4",
  year =         "1997",
  pages =        "779--790",
  email =        "halstat@fac.anu.edu.au,berwin.turlach@anu.edu.au",
}

@Book{har-etal:wavelets,
  title =        "Wavelets, Approximation, and Statisticsl
                 Applications",
  author =       "Wolfgang H{\"a}rdle and Gerard Kerkyacharian and
                 Dominique Picard and Alexander Tsybokov",
  booktitle =    "Wavelets, Approximation, and Statisticsl
                 Applications",
  series =       "Lecture Notes in Statistics",
  volume =       "129",
  publisher =    "Springer-Verlag",
  address =      "New York",
  pages =        "265",
  year =         "1998",
}

@Article{hen-etal:invest,
  title =        "Investigating the Nonlinear Dynamics of Cellular
                 Motion in the Inner Ear Using the Short-Time {F}ourier
                 and Continuous Wavelet Transforms",
  author =       "Conor Heneghan and Shyam Khanna and {\AA}ke Flock and
                 Mats Ulfendahl and Lou Brundin and Malvin C. Teich",
  journal =      IEEETSP,
  volume =       "42",
  number =       "12",
  year =         "1994",
  pages =        "3335--3352",
  abstract =     "The short-time Fourier transform (STFT) and the
                 continuous wavelet transform (CWT) are used to analyze
                 the time course of cellular motion in the inner ear.
                 The velocity responses of individual outer hair cells
                 and Hensen's cells to sinusoidal and amplitude
                 modulated (AM) acoustical signals applied at the ear
                 canal display characteristics typical of nonlinear
                 systems, including the generation of harmonic and
                 half-harmonic components. The STFT proves to be
                 valuable for following the time course of the frequency
                 components generated using sinusoidal and ARM input
                 signals. The CWT is also useful for analyzing these
                 signals; however, it is generally not as effective as
                 the STFT when octave-band-based CWT's are used. For the
                 transient response, the spectrogram (which is the
                 squared magnitude of the STFT) and the
                 octave-band-based scalogram (which is the squared
                 magnitude of the CWT) prove equally valuable, and the
                 authors have used both to study the responses of these
                 cells to step-onset tones of different frequencies.
                 Such analyses reveal information about the preferred
                 vibration frequencies of cells in the inner ear and are
                 useful for deciding among alternative mathematical
                 models of nonlinear cellular dynamics. A modified
                 Duffing oscillator model yields results that bear some
                 similarity to the data.",
}

@Article{her-vet:time-varying,
  title =        "Orthogonal Time-Varying Filter Banks and Wavelet
                 Packets",
  author =       "Cormac Herley and Martin Vetterli",
  journal =      IEEETSP,
  volume =       "42",
  number =       "10",
  year =         "1994",
  pages =        "2650--2663",
}

@Book{her-wei:first,
  title =        "A First Course on Wavelets",
  author =       "Eugenio Hern\'{a}ndez and Guido Weiss",
  publisher =    "CRC Press Inc.",
  address =      "Boca Raton",
  pages =        "512",
  year =         "1996",
  url =          "http://www.crcpress.com/prods/8274.htm",
  abstract =     "Wavelet theory had its origin in quantum field theory,
                 signal analysis, and function space theory. In these
                 areas wavelet-like algorithms replace the classical
                 Fourier-type expansion of a function. This unique new
                 book is an excellent introduction to the basic
                 properties of wavelets, from background math to
                 powerful applications. The authors provide elementary
                 methods for constructing wavelets, and illustrate
                 several new classes of wavelets. The text begins with a
                 description of local sine and cosine bases that have
                 been shown to be very effective in applications. Very
                 little mathematical background is needed to follow this
                 material. A complete treatment of band-limited wavelets
                 follows. These are characterized by some elementary
                 equations, allowing the authors to introduce many new
                 wavelets. Next, the idea of multiresolution analysis
                 (MRA) is developed, and the authors include simplified
                 presentations of previous studies, particularly for
                 compactly supported wavelets. Some of the topics
                 treated include: Several bases generated by a single
                 function via translations and dilations;
                 Multiresolution analysis, compactly supported wavelets,
                 and spline wavelets; Band-limited wavelets;
                 Unconditionality of wavelet bases; Characterizations of
                 many of the principal objects in the theory of
                 wavelets, such as low-pass filters and scaling
                 functions. The authors also present the basic
                 philosophy that all orthonormal wavelets are completely
                 characterized by two simple equations, and that most
                 properties and constructions of wavelets can be
                 developed using these two equations. Material related
                 to applications is provided, and constructions of
                 splines wavelets are presented. Mathematicians,
                 engineers, physicists, and anyone with a mathematical
                 background will find this to be an important text for
                 furthering their studies on wavelets.",
}

@Article{her:boundary,
  title =        "Boundary Filters for Finite-Length Signals and
                 Time-Varying Fitler Banks",
  author =       "Cormac Herley",
  journal =      IEEETCS2,
  volume =       "42",
  number =       "2",
  year =         "1995",
  pages =        "102--114",
}

@Article{hes-wic:wavelets,
  title =        "Wavelets and time-frequency analysis",
  author =       "Nikolaj Hess-Nielsen and Mladen Victor Wickerhauser",
  journal =      PIEEE,
  volume =       "84",
  number =       "4",
  year =         "1996",
  pages =        "523--540",
  keywords =     "time-frequency analysis, wavelet packet analysis,
                 wavelet analysis, numerical algorithms, continuous
                 models, frequency spreading control, high frequencies,
                 nonstationary filtering, periodic wavelet packets, time
                 localization, linear phase filters, signal
                 decomposition",
  abstract =     "We present a selective overview of time-frequency
                 analysis and some of its key problems. In particular we
                 motivate the introduction of wavelet and wavelet packet
                 analysis. Different types of decompositions of an
                 idealized time-frequency plane provide the basis for
                 understanding the performance of the numerical
                 algorithms and their corresponding interpretations
                 within the continuous models. As examples we show how
                 to control the frequency spreading of wavelet packets
                 at high frequencies using nonstationary filtering and
                 study some properties of periodic wavelet packets.
                 Furthermore we derive a formula to compute the time
                 localization of a wavelet packet from its indexes which
                 is exact for linear phase filters, and show how this
                 estimate deteriorates with deviation from linear
                 phase.",
}

@Article{hic-dat:fractal,
  title =        "Estimation of fractal signals using wavelets and
                 filter banks",
  author =       "G. A. Hirchoren and C. E. DAttellis",
  journal =      IEEETSP,
  volume =       "46",
  number =       "6",
  year =         "1998",
  pages =        "1624--1630",
  keywords =     "filter banks fractal signals 1/f processes wavelets",
  abstract =     "A filter bank design based on orthonormal wavelets and
                 equipped with a multiscale Wiener filter mas recently
                 proposed for signal restoration and for signal
                 smoothing of 1/f family of fractal signals corrupted by
                 external noise. The conclusions obtained in these
                 papers are based on the following simplificative
                 hypotheses: 1) The wavelet transformation is a
                 whitening filter, and 2) the approximation term of the
                 wavelet expansion can be avoided when the number of
                 octaves in the multiresolution analysis is large
                 enough. In this paper, we shelf that the estimation of
                 1/f processes in noise can be improved avoiding these
                 two hypotheses. Explicit expressions of the mean-square
                 error are given, and numerical comparisons with
                 previous results are shown.",
}

@InCollection{hil-etal:mri,
  title =        "Wavelet denoising of functional {MRI} Data",
  author =       "M. Hilton and Ogden T. and D. Hattery and G. Jawerth
                 and B. Eden",
  pages =        "93--114",
  crossref =     "ald-uns:medicine",
}

@Article{hir-dat:estimation,
  title =        "Estimation of Fractal Signals Using Wavelets and
                 Filter Banks",
  author =       "G. A. Hirchoren and C. E. {D'Attellis}",
  journal =      IEEETSP,
  volume =       "46",
  number =       "6",
  year =         "1998",
  pages =        "1624--1630",
}

@InCollection{hol-etal:real-time,
  title =        "A Real-Time Algorithm for Signal Analysis with the
                 Help of the Wavelet Transform",
  author =       "M. Holschneider and R. Kronland-Martinet and J. Morlet
                 and Ph. Tchamitchian",
  pages =        "286--297",
  crossref =     "com-gro-tch:wavelets",
}

@InCollection{hon:bridges,
  title =        "Wavelets, probability and statistics: some bridges",
  author =       "C. Hondr{\'e}",
  crossref =     "ben-fra:wavelets",
}

@Article{how-per:wavelet,
  title =        "Wavelet variance, {A}llan variance, and leakage",
  author =       "David A. Howe and Donald B. Percival",
  journal =      IEEETIM,
  volume =       "44",
  number =       "2",
  year =         "1995",
  pages =        "94--97",
  url =          "http://weber.u.washington.edu/~dbp/PSFILES/wvavleak.ps.Z",
  keywords =     "Analysis of variance; Atomic clocks; Frequency
                 stability; Power-law processes",
  abstract =     "Wavelets have recently been a subject of great
                 interest in geophysics, mathematics and signal
                 processing. The discrete wavelet transform can be used
                 to decompose a time series with respect to a set of
                 basis functions, each one of which is associated with a
                 particular scale. The properties of a time series at
                 different scales can then be summarized by the wavelet
                 variance, which decomposes the variance of a time
                 series on a scale by scale basis. The wavelet variance
                 corresponding to some of the recently discovered
                 wavelets can provide a more accurate conversion between
                 the time and frequency domains than can be accomplished
                 using the Allan variance. This increase in accuracy is
                 due to the fat that these wavelet variances give better
                 protection against leakage than does the Allan
                 variance.",
}

@Article{hoy-sch:sunspot,
  title =        "Group Sunspot Numbers: {A} New Solar Activity
                 Reconstruction",
  author =       "Douglas V. Hoyt and Kenneth H. Schatten",
  journal =      "Solar Physics",
  volume =       "181",
  year =         "1998",
  pages =        "491--512",
}

@Unpublished{hua-cre:deterministic,
  title =        "Deterministic/Stochastic Wavelet Decomposition for
                 Recovery of Signal from Noise Data",
  author =       "Hsin-Cheng Huang and Noel Cressie",
  year =         "1999",
  note =         "Submitted to {\em Technometrics}",
}

@InCollection{hua-cre:empirical,
  title =        "Empirical {B}ayesian spatial prediction using
                 wavelets",
  authors =      "Hsin-Cheng Huang and Noel Cressie",
  crossref =     "mul-vid:biwbm",
  pages =        "203--222",
  url =          "http://wagner.stat.sinica.edu.tw/~hchuang/decomp.ps",
}

@Article{hua:density,
  title =        "Density estimation by wavelet-based reproducing
                 kernels",
  author =       "S. Y. Huang",
  journal =      SSin,
  volume =       "9",
  number =       "1",
  year =         "1999",
  pages =        "137--151",
  keywords =     "asymptotics Bernoulli numbers Bernoulli polynomials
                 density estimation efficiency multiresolution
                 approximation projection kernel reproducing kernel
                 reproducing kernel Hilbert space wavelets",
  abstract =     "Density estimation by wavelet-based reproducing
                 kernels is studied. Asymptotic bias and variance are
                 derived. Estimators using spline- wavelets and
                 Daubechies wavelets are presented as examples. Kernel
                 order and kernel efficiency are also discussed. By an
                 integral property of the bias and an idea from Scott's
                 averaged shifted histograms, a bias reduction technique
                 based on a grid point average is proposed. This bias
                 reduction technique is shown to be variance stable.",
}

@Article{hua:projection,
  title =        "Projection estimation in multiple regression with
                 application to functional {ANOVA} models",
  author =       "J.-H. Z. Huang",
  journal =      AofS,
  volume =       "26",
  number =       "1",
  year =         "1998",
  pages =        "242--272",
  keywords =     "ANOVA curse of dimensionality finite elements
                 interaction least squares polynomials rate of
                 convergence regression splines tensor product
                 trigonometric polynomials wavelets",
  abstract =     "A general theory on rates of convergence of the
                 least-squares projection estimate in multiple
                 regression is developed. The theory is applied to the
                 functional ANOVA model, where the multivariate
                 regression function is modeled as a specified sum of a
                 constant term, main effects (functions of one variable)
                 and selected interaction terms (functions of two or
                 more variables). The least-squares projection is onto
                 an approximating space constructed from arbitrary
                 linear spaces of functions and their tensor products
                 respecting the assumed ANOVA structure of the
                 regression function. The linear spaces that serve as
                 building blocks can be any of the ones commonly used in
                 practice: polynomials, trigonometric polynomials,
                 splines, wavelets and finite elements. The rate of
                 convergence result that is obtained reinforces the
                 intuition that low-order ANOVA modeling can achieve
                 dimension reduction and thus overcome the curse of
                 dimensionality. Moreover, the components of the
                 projection estimate in an appropriately defined ANOVA
                 decomposition provide consistent estimates of the
                 corresponding components of the regression function.
                 When the regression function does not satisfy the
                 assumed ANOVA form, the projection estimate converges
                 to its best approximation of that form.",
}

@Book{hub:world,
  title =        "The World According to Wavelets: The Story of a
                 Mathematical Technique in the Making",
  author =       "Barbara Burke Hubbard",
  year =         "1996",
  publisher =    "A K Peters",
  address =      "Wellesley, Massachusetts",
  ISBN =         "1-56881-047-4",
  abstract =     "This book, lovingly written and highly accessible,
                 embraces the often unheralded notion that mathematics
                 contains ideas that can, and deserve, to be
                 communicated to a wider public &shyp; even if what is
                 communicated is at the level of appreciation rather
                 than practical knowledge. Put simply, it is a book
                 about the wavelet transform, that strange and
                 scientifically intriguing new method of encoding
                 information with an abundance of practical
                 applications. This book is a wonderfully successful
                 attempt to entice the non-mathematical reader into
                 formerly uncharted territory without sacrificing
                 precision. The material is masterfully organized so
                 mathematical details can be assimilated at one's own
                 pace; the main text is devoid of formulas and relates a
                 story of people and ideas, while separate boxes and
                 appendices contain intricate discussions for the more
                 mathematically adventurous. This book is a rarity in
                 mathematics books in that it recognizes that both
                 mathematicians and readers interested in mathematics
                 have a human side.",
}

@Article{hud-fri-may:atmospheric,
  title =        "Wavelet Transforms and Atmospheric Turbulence",
  author =       "Lonnie Hudgins and Carl. A. Friehe and Meinhard E.
                 Mayer",
  journal =      PRL,
  volume =       "71",
  number =       "20",
  year =         "1993",
  pages =        "3279--3282",
  abstract =     "Wavelet cross spectra and cross scalograms are used to
                 analyze the time-scale structure of bivariate
                 turbulence data from the boundary layer over the ocean.
                 The cross scalogram for the streamwise and vertical
                 turbulent velocity components shows a highly
                 intermittent pattern with significant contributions of
                 opposite signs appearing at two specific scales,
                 approximately 60 m and approximately 2 km, believed to
                 be related to small- scale turbulent mixing and
                 large-scale secondary flow in the boundary layer.",
}

@InCollection{hud-fri-may:fourier,
  title =        "Fourier and wavelet analysis of atmospheric
                 turbulence",
  author =       "Lonnie Hudgins and Carl. A. Friehe and Meinhard E.
                 Mayer",
  pages =        "491--498",
  crossref =     "mey-roq:progress",
}

@Article{hud-hua:bivariate,
  title =        "Bivariate wavelet analysis of {A}sia monsoon and
                 {ENSO}",
  author =       "Lonnie Hudgins and Jianping Huang",
  journal =      "Advances in Atmospheric Sciences",
  volume =       "13",
  year =         "1996",
  url =          "http://www.eurandom.tue.nl/whitcher/other_papers/hud0hua96.pdf",
}

@PhdThesis{hud:thesis,
  title =        "Wavelet Analysis of Atmospheric Turbulence",
  author =       "Lonnie H. Hudgins",
  school =       "University of California, Irvine",
  year =         "1992",
  email =        "lonnie@lynx.ps.uci.edu",
}

@Article{hwa:estimation,
  title =        "Estimation of fractional Brownian motion embedded in a
                 noisy environment using nonorthogonal wavelets",
  author =       "W. L. Hwang",
  journal =      IEEETSP,
  volume =       "47",
  number =       "8",
  year =         "1999",
  pages =        "2211--2219",
  abstract =     "We show that nonorthogonal wavelets can characterize
                 the fractional Brownian motion (fBm) that is in white
                 noise. We demonstrate the point that discriminating the
                 parameter of an fBm from that of noise is equivalent to
                 discriminating the composite singularity formed by
                 superimposing a peak singularity on a Dirac
                 singularity. We characterize the composite singularity
                 by formalizing this problem as a nonlinear optimization
                 problem, This yields our parameter estimation
                 algorithm. For fractal signal estimation, Wiener
                 filtering is explicitly formulated as a function of the
                 signal and noise parameters and the wavelets. We show
                 that the estimated signal is a 1/f process, Comparative
                 studies through numerical simulations of our methods
                 with those of Wornell and Oppenheim are presented.",
}

@Article{imh:computing,
  title =        "Computing the distribution of a quadratic form in
                 normal variables",
  author =       "J. P. Imhof",
  journal =      BKA,
  volume =       "48",
  pages =        "419--426",
  year =         "1961",
}

@Article{iss:product-moment,
  title =        "On a Formula for the Product-Moment Coefficient of Any
                 Order of a Normal Frequency Distribution in Any Number
                 of Variables",
  author =       "L. Isserlis",
  journal =      BKA,
  volume =       "12",
  pages =        "134--139",
  year =         "1918",
}

@Article{ist:coefficients,
  title =        "Wavelet Coefficients of a {G}aussian Process and
                 Applications",
  author =       "Jacques Istas",
  journal =      "Annales de l'Institut Henri Poincare, Section B,
                 Calcul des Probabilities et Statistique",
  volume =       "28",
  pages =        "537--556",
  year =         "1992",
  note =         "In French",
  keywords =     "covariance functions, spectral densities, Gaussian
                 stationary process, square error, wavelet transform",
  abstract =     "The author gives the relations between the covariance
                 functions and the spectral densities of the
                 approximation and the details of a Gaussian stationary
                 process at different resolutions. He studies the rate
                 of convergence of the square error between the process
                 and its wavelet transform. Then he shows the
                 convergence in distribution of the projection of the
                 process to the original process. Finally, proposes a
                 choice of the regularity of the wavelet in order to
                 minimize the correlation between the approximation and
                 the details.",
}

@Article{iya-kuw:earthquake,
  title =        "Application of wavelets to analysis and simulation of
                 earthquake motions",
  author =       "H. {Iyama, J. Kuwamura}",
  journal =      "Earthquake Engineering \& Structural Dynamics",
  volume =       "28",
  number =       "3",
  pages =        "255--272",
  year =         "1999",
  keywords =     "wavelet transform simulated earthquake motions energy
                 input Fourier transform time-frequency characteristics
                 energy input rate",
  abstract =     "A method of applying wavelet transform to earthquake
                 motion analysis is developed from the viewpoint of
                 energy input structures, in which relationships between
                 wavelet coefficients and energy input, namely energy
                 principles in wavelet analysis are derived. By using
                 the principles, time-frequency characteristics of the
                 1995 Hyogoken-Nanbu earthquake ground motions are
                 analysed and time histories of energy input for various
                 ranges of frequencies and epicentral distances are
                 identified. Furthermore, a technique to simulate
                 earthquake ground accelerations by wavelet inverse
                 transform is developed on the condition that target
                 time-frequency characteristics are specified.
                 Structural responses to the simulated accelerations are
                 compared with the target time-frequency
                 characteristics, which shows satisfactory correlations
                 between wavelet coefficients and energy responses in
                 both time and frequency domains.",
}

@Article{jaw-swe:overview,
  author =       "B. Jawerth and Wim Sweldens",
  title =        "An overview of wavelet based multiresolution
                 analyses",
  journal =      "SIAM Rev.",
  volume =       "36",
  number =       "3",
  pages =        "377--412",
  year =         "1994",
  url =          "http://cm.bell-labs.com/who/wim/papers/overview.ps",
  abstract =     "Wavelet-based multiresolution analysis helps in data
                 compression, operator analysis and developing a
                 periodic fast wavelet transform algorithm. The analysis
                 requires definition of a multiresolution analysis and
                 investigation of the method in which wavelets fit into
                 the multiresolution analysis. The fitting process
                 requires a consideration of the semiorthogonal,
                 orthogonal and biorthogonal wavelets. The application
                 process requires an understanding of the wavelets on an
                 interval, wavelet packets, multidimensional waves and
                 fast wavelet transforms.",
}

@Unpublished{jen-whi:local,
  title =        "A Semiparametric Wavelet-Based Estimator of a Locally
                 Stationary Long-Memory Model",
  author =       "Mark J. Jensen and Brandon Whitcher",
  year =         "1999",
  note =         "Under preparation",
}

@Unpublished{jen:alternative,
  title =        "An Alternative Maximum Likelihood Estimator of
                 Long-Memeory Processes Using Compactly Supported
                 Wavelets",
  author =       "Mark J. Jensen",
  journal =      JEDC,
  volume =       "24",
  number =       "3",
  year =         "1997",
  pages =        "361--387",
  url =          "http://econwpa.wustl.edu/eprints/em/papers/9709/9709002.abs",
  keywords =     "ARFIMA, Fractional Integration, Long-memory, MLE,
                 Wavelets",
  abstract =     "In this paper we apply compactly supported wavelets to
                 the ARFIMA(p,d,q) long-memory process to develop an
                 alternative maximum likelihood estimator of the
                 differencing parameter, d, that is invariant to unknown
                 means, model specification, and contamination. We show
                 that this class of time series have wavelet transforms
                 whose covariance matrix is sparse when the wavelet is
                 compactly supported. It is shown that the sparse
                 covariance matrix can be approximated to a high level
                 of precision by a matrix equal to the covariance matrix
                 except with the off-diagonal elements set equal to
                 zero. This diagonal matrix is shown to reduce the order
                 of calculating the likelihood function to an order
                 smaller than those associated with the exact MLE
                 method. We test the robustness of the wavelet MLE of
                 the fractional differencing parameter to a variety of
                 compactly supported wavelets, series length, and
                 contamination levels by generating ARFIMA(p,d,q)
                 processes for different values of p, d, and q, and
                 calculating the wavelet MLE using only the main
                 diagonal elements of its covariance matrix. In our
                 simulations we find the wavelet MLE to be superior to
                 the approximate frequency MLE when estimating
                 contaminated ARFIMA(0,d,0), and uncontaminated
                 ARFIMA(1,d,0) and ARFIMA(0,d,1) processes except when
                 the MA parameter is close to one. We also find the
                 wavelet MLE to be robust to model specification and as
                 such is an attractive alternative semiparameter
                 estimator to the Geweke, Porter--Hudak estimator.",
}

@Article{jen:approximate,
  title =        "An approximate wavelet {MLE} of short and long memory
                 parameters",
  author =       "Mark J. Jensen",
  journal =      SNDE,
  volume =       "3",
  number =       "4",
  pages =        "239--253",
  year =         "1999",
  url =          "http://econwpa.wustl.edu/eprints/em/papers/9802/9802003.abs",
  keywords =     "Long Memory, Fractional Integration, ARFIMA,
                 Wavelets",
  abstract =     "By design a wavelet's strength rests in its ability to
                 localize a process simultaneously in time-scale space.
                 The wavelet's ability to localize a time series in
                 time-scale space directly leads to the computational
                 efficiency of the wavelet representation of a N x N
                 matrix operator by allowing the N largest elements of
                 the wavelet represented operator to represent the
                 matrix operator [Devore, et al. (1992a) and (1992b)].
                 This property allows many dense matrices to have sparse
                 representation when transformed by wavelets.In this
                 paper we generalize the long-memory parameter estimator
                 of McCoy and Walden (1996) to estimate simultaneously
                 the short and long-memory parameters. Using the sparse
                 wavelet representation of a matrix operator, we are
                 able to approximate an ARFIMA model's likelihood
                 function with the series' wavelet coefficients and
                 their variances. Maximization of this approximate
                 likelihood function over the short and long-memory
                 parameter space results in the approximate wavelet
                 maximum likelihood estimates of the ARFIMA model. By
                 simultaneously maximizing the likelihood function over
                 both the short and long-memory parameters and using
                 only the wavelet coefficient's variances, the
                 approximate wavelet MLE provides a fast alternative to
                 the frequency-domain MLE. Furthermore, the simulation
                 studies found herein reveal the approximate wavelet MLE
                 to be robust over the invertible parameter region of
                 the ARFIMA model's moving average parameter, whereas
                 the frequency-domain MLE dramatically deteriorates as
                 the moving average parameter approaches the boundaries
                 of invertibility.",
}

@Article{jen:ols,
  title =        "Using wavelets to obtain a consistent ordinary least
                 squares estimator of the long-memory parameter",
  author =       "Mark J. Jensen",
  journal =      JF,
  volume =       "18",
  number =       "1",
  year =         "1999",
  pages =        "17--32",
  email =        "jensen@haar.econ.siu.edu",
  url =          "http://econwpa.wustl.edu/eprints/em/papers/9710/9710002.abs",
  keywords =     "fractionally integrated processes long-memory
                 wavelets",
  abstract =     "We develop an ordinary least squares estimator of the
                 long-memory parameter from a fractionally integrated
                 process that is an alternative to the Geweke and
                 Porter-Hudak (1983) estimator. Using the wavelet
                 transform from a fractionally integrated process, we
                 establish a log-linear relationship between the wavelet
                 coefficients' variance and the scaling parameter equal
                 to the log-memory parameter. This log-linear
                 relationship yields a consistent ordinary least squares
                 estimator of the long-memory parameter when the wavelet
                 coefficients' population variance is replaced by their
                 sample variance. We derive the small sample bias and
                 variance of the ordinary least squares estimator and
                 test it against the GPH estimator and the McCoy-Walden
                 maximum likelihood wavelet estimator by conducting a
                 number of Monte Carlo experiments. Based upon the
                 criterion of choosing the estimator which minimizes the
                 mean squared error, the wavelet OLS approach was
                 superior to the GPH estimator, but inferior to the
                 McCoy-Walden wavelet estimator for the processes
                 simulated. However, given the simplicity of programming
                 and running the wavelet OLS estimator and its
                 statistical inference of the long-memory parameter we
                 feel the general practitioner will be attracted to the
                 wavelet OLS estimator.",
}

@Unpublished{jen:wafip,
  title =        "Wavelet Analysis of Fractionally Integrated
                 Processes",
  author =       "Mark J. Jensen",
  year =         "1994",
  note =         "Department of Economics, Washington University",
  email =        "jensen@wuecona.wustl.edu",
  url =          "http://econwpa.wustl.edu/eprints/em/papers/9405/9405001.abs",
  keywords =     "Long-Memory, Wavelets, Spectral Analysis, 1/f
                 Processes",
  abstract =     "In this paper we apply wavelet analysis to the class
                 of fractionally integrated processes to show that this
                 class is a member of the $1/f$ family of processes as
                 defined by Wornell (1993) and to produce an alternative
                 method of estimating the fractional differencing
                 parameter. Currently the method by Geweke and
                 Porter-Hudak (1983) is used most often to estimate and
                 test the fractional differencing parameter. The GPH
                 approach, however, has been shown to have poor
                 statistical properties and suffers from subjective
                 decisions that the users must make. The wavelet
                 analysis estimate of the fractional differencing
                 parameter is shown to be more straightforward and to
                 provide results that are more robust than the GPH
                 method.",
}

@Book{joh-kot:book70,
  title =        "Continuous Univariate Distributions",
  booktitle =    "Continuous Univariate Distributions",
  author =       "Norman L. Johnson and Samuel Kotz",
  publisher =    "Houghton Mifflin",
  address =      NY,
  year =         "1970",
}

@Book{joh-kot:book72,
  title =        "Continuous Multivariate Distributions",
  booktitle =    "Continuous Multivariate Distributions",
  author =       "Norman L. Johnson and Samuel Kotz",
  publisher =    "John Wiley \& Sons, Inc.",
  address =      NY,
  year =         "1972",
}

@Article{joh-sil:correlated,
  journal =      JRSSB,
  volume =       "59",
  number =       "2",
  year =         "1997",
  pages =        "319--351",
  title =        "{W}avelet threshold estimators for data with
                 correlated noise",
  author =       "I. M. Johnstone and B. W. Silverman",
  url =          "http://playfair.Stanford.EDU/reports/johnstone/correl.ps.gz",
  abstract =     "Wavelet threshold estimators for data with stationary
                 correlated noise are constructed by applying a
                 level-dependent soft threshold to the coefficients in
                 the wavelet transform. A variety of threshold choices
                 is proposed, including one based on an unbiased
                 estimate of mean-squared error. The practical
                 performance of the method is demonstrated on examples,
                 including data from a neurophysiological context. The
                 theoretical properties of the estimators are
                 investigated by comparing them with an ideal but
                 unattainable 'bench-mark', that can be considered in
                 the wavelet context as the risk obtained by ideal
                 spatial adaptivity, and more generally is obtained by
                 the use of an 'oracle' that provides information that
                 is not actually available in the data. It is shown that
                 the level-dependent threshold estimator performs well
                 relative to the bench-mark risk, and that its minimax
                 behaviour cannot be improved on in order of magnitude
                 by any other estimator. The wavelet domain structure of
                 both short-and long-range dependent noise is
                 considered, and in both cases it is shown that the
                 estimators have near optimal behaviour simultaneously
                 in a wide range of function classes, adapting
                 automatically to the regularity properties of the
                 underlying model. The proofs of the main results are
                 obtained by considering a more general multivariate
                 normal decision theoretic problem.",
  keywords =     "decomposition. regression. shrinkage.",
}

@Book{joh-wic:multivariate,
  title =        "Applied Multivariate Statistical Analysis",
  booktitle =    "Applied Multivariate Statistical Analysis",
  author =       "Richard A. Johnson and Dean W. Wichern",
  edition =      "4",
  publisher =    "Prentice-Hall, Inc.",
  address =      "Englewood Cliffs, NJ",
  year =         "1998",
  pages =        "799",
}

@Article{joh:adaptivity,
  title =        "Wavelet shrinkage for correlated data and inverse
                 problems: {A}daptivity results",
  author =       "I. M. Johnstone",
  journal =      SSin,
  volume =       "9",
  number =       "1",
  year =         "1999",
  pages =        "51--83",
  keywords =     "adaptation correlated data fractional Brownian motion
                 linear inverse problems long range dependence mixing
                 conditions oracle inequalities rates of convergence
                 unbiased risk estimate wavelet Vaguelette decomposition
                 wavelet shrinkage wavelet thresholding",
  abstract =     "Johnstone and Silverman (1997) described a
                 level-dependent thresholding method for extracting
                 signals from correlated noise. The thresholds were
                 chosen to minimize a data based unbiased risk
                 criterion. Here we show that in certain asymptotic
                 models encompassing short and long range dependence,
                 these methods are simultaneously asymptotically minimax
                 up to constants over a broad range of Besov classes. We
                 indicate the extension of the methods and results to a
                 class of linear inverse problems possessing a wavelet
                 vaguelette decomposition.",
}

@Article{jon-lon-mai:hurst,
  title =        "Wavelet packet computation of the {H}urst exponent",
  author =       "C. L. Jones and G. T. Lonergan and D. E. Mainwaring",
  journal =      JPA,
  volume =       "29",
  number =       "10",
  year =         "1996",
  pages =        "2509--2527",
  keywords =     "signals representations diffusion fractals",
  abstract =     "Wavelet packet analysis was used to measure the global
                 scaling behaviour of homogeneous fractal signals from
                 the slope of decay for discrete wavelet coefficients
                 belonging to the adapted wavelet best basis. A new
                 scaling function for the size distribution correlation
                 between wavelet coefficient energy magnitude and
                 position in a sorted vector listing is described in
                 terms of a power law to estimate the Hurst exponent.
                 Profile irregularity and long-range correlations in
                 self-affine systems can be identified and indexed with
                 the Hurst exponent, and synthetic one-dimensional
                 fractional Brownian motion (fBm) type profiles are used
                 to illustrate and test the proposed wavelet packet
                 expansion. We also demonstrate an initial application
                 to a biological problem concerning the spatial
                 distribution of local enzyme concentration in fungal
                 colonies which can be modelled as a self-affine trace
                 or an `enzyme walk'. The robustness of the wavelet
                 approach applied to this stochastic system is
                 presented, and comparison is made between the wavelet
                 packet method and the root-mean-square roughness and
                 second-moment approaches for both examples. The wavelet
                 packet method to estimate the global Hurst exponent
                 appears to have similar accuracy compared with other
                 methods, but its main advantage is the extensive choice
                 of available analysing wavelet filter functions for
                 characterizing periodic and oscillatory signals.",
}

@InProceedings{kad:choice,
  title =        "On the Choice of a Wavelet, and the Energy and the
                 Phase Distributions of the Wavelet Transform",
  author =       "Shubha Kadambe",
  booktitle =    "Time-Frequency and Time-Scale Analysis",
  organization = IEEESPS,
  year =         "1992",
  pages =        "379--382",
  address =      "Victoria, B.C., Canada",
}

@InProceedings{kai:filtering,
  title =        "Wavelet filtering in the scale domain",
  author =       "Gerald Kaiser",
  pages =        "51--54",
  crossref =     "szu:wavelet3",
  abstract =     "It is shown that any convolution operator in the time
                 domain can be represented exactly as a multiplication
                 operator in the time-scale (wavelet) domain. The Mellin
                 transform establishes a one-to-one correspondence
                 between frequency filters (system or transfer
                 functions) and scale filters, which are defined as
                 multiplication operators in the scale domain, subject
                 to the convergence of the defining integrals.
                 Applications to the denoising of random signals are
                 proposed. We argue that the present method is more
                 suitable for removing the effects of atmospheric
                 turbulence than the conventional procedures based on
                 Fourier analysis because it is ideally suited for
                 resolving spectral power laws.",
}

@Book{kai:friendly,
  title =        "A Friendly Guide to Wavelets",
  author =       "Gerald Kaiser",
  publisher =    "Springer-Verlag",
  address =      NY,
  year =         "1994",
  pages =        "300",
  ISBN =         "0-8176-3711-7",
  keywords =     "Suggestions to the Reader. List of Symbols,
                 Conventions and Transforms. Preliminaries: Background
                 and Notation. Windowed Fourier Transforms. Continuous
                 Wavelet Transforms. Generalized Frames: Key to Analysis
                 and Synthesis. Discrete Time-Frequency Analysis and
                 Sampling. Discrete Time-Scale Analysis. Multiresolution
                 Analysis. Daubechies' Orthonormal Wavelet Bases.
                 Introduction to Wavelet Electromagnetics. Applications
                 to Radar and Scattering. Wavelet Acoustics",
  abstract =     "This volume consists of two parts. The first part,
                 forming chapters 1-8, is designed as a textbook for an
                 introductory one-semester course on wavelet analysis
                 and time-frequency analysis aimed at graduate students
                 or advanced undergraduates in science and engineering.
                 Each of the first eight chapters ends with a set of
                 straightforward exercises designed to drive home the
                 concepts just covered, and the graphics should further
                 facilitate absorption. The second part, form-ing
                 chapters 9-11, represents original research and is
                 written in a more advanced style. This section can be
                 used as a textbook for a second-semester course or,
                 when combined with chapters 1 \& 3, as a reference for
                 an advanced research-level seminar.",
}

@Article{kai:mellin,
  title =        "Wavelet filtering with the {M}ellin transform",
  author =       "Gerald Kaiser",
  journal =      AML,
  volume =       "9",
  number =       "5",
  year =         "1996",
  pages =        "69--74",
  abstract =     "It is shown that any convolution operator in the time
                 domain can be represented exactly as a multiplication
                 operator in the time-scale (wavelet) domain. The Mellin
                 transform gives a one-to-one correspondence between
                 frequency filters (system functions) and scale filters
                 (multiplication operators in the scale domain), subject
                 to the convergence of the defining integrals.
                 Applications to the denoising of random signals are
                 proposed. It is argued that the present method is more
                 suitable for removing the effects of atmospheric
                 turbulence than the conventional procedures because it
                 is ideally suited for resolving spectral power laws.",
}

@Article{kai:physical,
  title =        "Physical wavelets and radar: {A} variational approach
                 to remote sensing",
  author =       "Gerald Kaiser",
  journal =      IEEEAPM,
  volume =       "38",
  number =       "1",
  year =         "1996",
  pages =        "15--24",
  abstract =     "Physical wavelets are acoustic or electromagnetic
                 waves, resulting from the emission of a time signal by
                 a localized acoustic or electromagnetic source moving
                 along an arbitrary trajectory in space. Thus, they are
                 localized solutions of the wave equation or Maxwell`s
                 equations. Under suitable conditions, such wavelets can
                 be used as ``basis'' functions, to construct general
                 acoustic or electromagnetic waves. This gives a local
                 alternative to the construction of such waves in terms
                 of (nonlocal) plane waves, via Fourier transforms. We
                 give a brief, self-contained introduction to physical
                 wavelets, and apply them to remote sensing. We define
                 the ambiguity functional, generalization of the radar
                 and sonar ambiguity functions, which applies not only
                 to wideband signals, but also to targets and radar
                 platforms executing arbitrary nonlinear motions.",
}

@Article{kap-kuo:fractal,
  title =        "Fractal Estimation from Noisy Data via Discrete
                 Fractional Gaussian Noise ({DFGN}) and the Haar Basis",
  author =       "Lance M. Kaplan and C.-C. Jay Kuo",
  journal =      IEEETSP,
  volume =       "41",
  number =       "12",
  year =         "1993",
  pages =        "3554--3562",
  abstract =     "The authors show that the application of the discrete
                 wavelet transform (DWT) using the Haar basis to the
                 increments of fractional Brownian motion (fBm), also
                 known as discrete fractional Gaussian noise (DFGN),
                 yields coefficients which are weakly correlated and
                 have a variance that is exponentially related to scale.
                 Similar results were derived by Flandrin (1989),
                 Tewfik, and Kim for a continuous-time fBm going through
                 a continuous wavelet transform (CWT). The new
                 theoretical results justify an improvement to a fractal
                 estimation algorithm recently proposed by Wornell and
                 Oppenheim. The performance of the new algorithm is
                 compared with that of Wornell and Oppenheim's (see IEEE
                 Trans. Signal Processing, vol. 40, p. 611-623, Mar.
                 1992) algorithm in numerical simulation.",
}

@Article{kar-jon-kni:bias,
  title =        "Testing for Bias in the Climate Record",
  author =       "Thomas R. Karl and Philip D. Jones and Richard W.
                 Knight",
  journal =      "Science",
  volume =       "271",
  number =       "5257",
  year =         "1996",
  pages =        "1879--1883",
  abstract =     "The method climatologists use to calculate trends on
                 monthly and annual time series do not introduce
                 significant bias as has been suggested. Perihelion
                 calender shifts were used to test for bias because they
                 have no impact on annual mean temperature trends.
                 Monthly differences were insignificant.",
}

@TechReport{kat-vid-alb:global-local,
  author =       "Gabriel Katul and Brani Vidakovic and John Albertson",
  title =        "Estimating Global and Local Scaling Exponents in
                 Turbulent Flows using Wavelet Transformations",
  institution =  "Institute for Statistics and Decision Sciences, Duke
                 University",
  year =         "1999",
  number =       "99-24",
}

@Article{kat-mas:fBm,
  title =        "On the spectral density of the wavelet transform of
                 fractional {B}rownian motion",
  author =       "Takeshi Kato and Elias Masry",
  journal =      JTSA,
  volume =       "20",
  number =       "5",
  year =         "1999",
  pages =        "559--563",
}

@Article{kaw-ari:matching,
  title =        "Signal matching using wavelet correlation",
  author =       "Kouzou Kawata and Suguru Arimoto",
  journal =      ECJ3,
  volume =       "79",
  number =       "9",
  year =         "1996",
  pages =        "23--34",
  note =         "Translated from Denshi Joho Tsushin Gakkai Ronbunshi,
                 Vol. 78-A, No. 12, December 1995, pp. 1655--1664",
  keywords =     "wavelet correlation, local correlation, bandpass cross
                 correlation, corresponding problem, complex filter",
  abstract =     "The problem of detecting corresponding points is
                 studied in the case in which local deformations exist
                 and a new method named ``wavelet correlation'' is
                 proposed. There is a difficulty in that a reasonable
                 window width cannot be designed in local correlation,
                 which is one of the methods for a corresponding
                 problem. The wavelet correlation is derived by
                 extending the notion of local correlation and is
                 considered to overcome difficulty. The fundamental
                 concept is derived by the belief that a signal can be
                 decomposed to several (sinusoidal) components and the
                 window width can be varied according to each component.
                 It is claimed that any algorithm using local
                 correlation can be replaced by the one using wavelet
                 correlation. In this paper, the wavelet correlation
                 derived from local correlation is compared with the
                 Laplacian distance and the local correlation itself by
                 experiments. Further, a matching method that uses a
                 narrow-band property of a wavelet correlation function
                 is proposed and the matching error is evaluated through
                 experiments using one-dimensional signals. Finally, an
                 absolute measure of matching by using normalized
                 wavelet correlation is introduced and applied for
                 detecting discontinuities of local deformations.",
}

@Article{ken-woo:fractal,
  title =        "Estimating the fractal dimension of a locally
                 self-similar {G}aussian process by using increments",
  author =       "J. T. Kent and A. T. A. Wood",
  journal =      JRSSB,
  volume =       "59",
  number =       "3",
  year =         "1997",
  pages =        "679--700",
}

@Article{ker-pic-tri:lp,
  title =        "Lp adaptive density estimation",
  author =       "G{\'e}rard Kerkyacharian and Dominique Picard and
                 Karine Tribouley",
  journal =      Ber,
  volume =       "2",
  number =       "3",
  year =         "1996",
  pages =        "229--247",
  abstract =     "We provide global adaptive wavelet-type density
                 estimates. Our procedures illustrate the refinement
                 which can be obtained by replacing the Fourier basis by
                 the wavelet basis in estimation methods. The main
                 argument consists in observing that the estimated total
                 energy of the details of a specified level j will be
                 smaller or greater than some known threshold if
                 precisely j is above or below the theoretical optimal
                 level calculated with the a priori knowledge of the
                 regularity of the density. This balancing effect leads
                 directly to an adaptation procedure, and some natural
                 extensions. We investigate the minimax properties of
                 these procedures and explain their evolution for
                 different global error measures.",
  keywords =     "adaptive estimation Besov spaces density estimation
                 minimax estimation U-estimate wavelet orthonormal
                 bases",
}

@Article{kes-mou:matching,
  title =        "Matching wavelet packets to Gaussian random
                 processes",
  author =       "N. Keshava and J. M. F. Moura",
  journal =      IEEETSP,
  volume =       "47",
  number =       "6",
  year =         "1999",
  pages =        "1604--1614",
  keywords =     "basis functions best basis search Bhattacharyya
                 coefficient binary detection classification nonadditive
                 cost function random processes wavelet packet",
  abstract =     "In this paper, we consider the problem of
                 approximating a set of arbitrary, discrete-time,
                 Gaussian random processes by a single, representative
                 wavelet-based, Gaussian process. We measure the
                 similarity between the original processes and the
                 wavelet-based process with the Bhattacharyya
                 coefficient, By manipulating the Bhattacharyya
                 coefficient, we reduce the task of defining the
                 representative process to finding an optimal unitary
                 matrix of wavelet-based eigenvectors, an associated
                 diagonal matrix of eigenvalues, and a mean vector. The
                 matching algorithm we derive maximizes the nonadditive
                 Bhattacharyya coefficient in three steps: a migration
                 algorithm that determines the best basis by searching
                 through a wavelet packet tree for the optimal unitary
                 matrix of wavelet-based eigenvectors; and two separate
                 fixed-point algorithms that derive an appropriate set
                 of eigenvalues and a mean vector. We illustrate the
                 method with two different classes of processes:
                 first-order Markov and bandlimited, The technique is
                 also applied to the problem of robust terrain
                 classification in polarimetric SAR images.",
}

@Article{kha-duc:detection,
  title =        "Detection and classification of multiple events in
                 piecewise stationary signals: {C}omparison between
                 autoregressive and multiscale approaches",
  author =       "M. Khalil and J. Duch{\^e}ne",
  journal =      SP,
  volume =       "75",
  number =       "3",
  year =         "1999",
  pages =        "239--251",
  email =        "mohamad.khalil@univ-troyes.fr",
  url =          "http://www.elsevier.nl/cas/tree/store/sigpro/sub/1999/75/3/1382.pdf",
  keywords =     "detection classification rejection wavelet AR
                 modelling multiscale decomposition",
  abstract =     "In this paper, we present methods of detection and
                 classification of events in nonstationary signals which
                 are well adapted to uterine EMG processing. Two
                 sequential methods of detection are presented: the
                 first one is monodimensional and based on AR modelling,
                 the second is multidimensional and achieved by
                 decomposing the signal onto scales using wavelet
                 transform. Hypothesis rejection is achieved using
                 either AR coefficients or a variance covariance matrix
                 computed from the scales. Both methods are adaptive and
                 allow event detection without necessarily returning to
                 the null hypothesis H-o. They have been applied to
                 simulated data and uterine EMG. Their performances have
                 been compared together.",
}

@InCollection{kol:application,
  title =        "An application of wavelet shrinkage to tomography",
  author =       "Eric D. Kolaczyk",
  pages =        "77--92",
  crossref =     "ald-uns:medicine",
}

@Article{kol:burst,
  title =        "Non-Parametric Estimation of Gamma-Ray Burst
                 Intensities Using Haar Wavelets",
  author =       "Eric D. Kolaczyk",
  journal =      ApJ,
  volume =       "483",
  number =       "1",
  year =         "1997",
  pages =        "340--349",
  url =          "ftp://galton.uchicago.edu/pub/kolaczyk/TIPSH_Appl.ps.Z",
  abstract =     "In this article, I present a method for the
                 non-parametric (model-free) estimation of intensity
                 profiles underlying gamma-ray bursts. The method,
                 TIPSH, is based on applying specially calibrated
                 thresholds to the Haar wavelet coefficients of binned
                 counts gathered from such bursts. As functions
                 well-localized with respect to both time and scale,
                 wavelets are an ideal tool for working with the often
                 sharp, abrupt nature of gamma-ray burst signals. When
                 applied to an idealized signal in a small simulation
                 study and a selection of actual gamma-ray bursts, the
                 TIPSH algorithm is found to be well capable of
                 simultaneously estimating the smooth, uniform
                 background and the pulse-like structure of gamma-ray
                 burst signals.",
}

@Article{kol:method,
  title =        "Wavelet shrinkage estimation of certain Poisson
                 intensity signals using corrected thresholds",
  author =       "Eric D. Kolaczyk",
  journal =      SSin,
  volume =       "9",
  number =       "1",
  year =         "1999",
  pages =        "119--135",
  url =          "ftp://galton.uchicago.edu/pub/kolaczyk/PoisTholds.ps.Z",
  keywords =     "gamma-ray bursts. large deviations. Poisson processes.
                 wavelets",
  abstract =     "Wavelet shrinkage estimation has been found to be a
                 powerful tool for the non-parametric estimation of
                 spatially variable phenomena. Most work in this area to
                 date has concentrated primarily on the use of wavelet
                 shrinkage techniques in contexts where the data are
                 modeled as observations of a signal plus additive,
                 Gaussian noise. In this paper, I introduce an approach
                 to estimating intensity functions for a certain class
                 of ``burst-like'' Poisson processes using wavelet
                 shrinkage. The proposed method is based on the
                 shrinkage of wavelet coefficients of the original count
                 data, as opposed to the current approach of
                 pre-processing the data using Anscombe's square root
                 transform and working with the resulting data in a
                 Gaussian framework. ``Corrected'' versions of the usual
                 Gaussian-based shrinkage thresholds are used. The
                 corrections explicitly account for effects of the first
                 few cumulants of the Poisson distribution on the tails
                 of the coefficient distributions. A large deviations
                 argument is used to justify these corrections. The
                 performance of the new method is examined, and compared
                 to that of the pre-processing approach, in the context
                 of an application to an astronomical gamma-ray burst
                 signal.",
}

@Unpublished{kol:poisson,
  title =        "Estimation of Intensities of Burst-Like Poisson
                 Processes Using Haar Wavelets",
  author =       "Eric D. Kolaczyk",
  note =         "Submitted to the {\em Journal of the Royal Statistical
                 Society, Series B}",
  year =         "1997",
  url =          "ftp://galton.uchicago.edu/pub/kolaczyk/TIPSH_Mod.ps.Z",
  abstract =     "I present a method for producing estimates of the
                 intensity function of certain `burst-like'
                 inhomogeneous Poisson processes, based on the shrinkage
                 of Haar wavelet coefficients of the observed counts.
                 The Haar basis is a natural wavelet basis in which to
                 work in this context, and I derive thresholds for
                 shrinkage estimation based on the distribution of the
                 coefficients. The translation-invariant de-noising
                 approach of Donoho and Coifman (1995) is used in
                 conjunction with these level-dependent thresholds to
                 yield smooth estimates, without the usual `staircase'
                 structure associated with Haar wavelets. This work is
                 motivated by recent efforts in astronomy to model the
                 intensity functions underlying gamma-ray bursts. It is
                 demonstrated that the method proposed herein (TIPSH)
                 yields sharper estimates of the detail structure in
                 these signals than those obtained through an analogous
                 version of the standard adaptation of wavelet shrinkage
                 for Poisson counts, based on the square-root
                 transformation.",
}

@Article{kol:shrinkage,
  journal =      JASA,
  volume =       "91",
  number =       "435",
  year =         "1996",
  pages =        "1079--1090",
  title =        "{A} wavelet shrinkage approach to tomographic image
                 reconstruction",
  author =       "E. D. Kolaczyk",
  abstract =     "A method is proposed for reconstructing images from
                 tomographic data with respect to a two-dimensional
                 wavelet basis. The Wavelet-vaguelette decomposition
                 (WVD) is used as a framework within which expressions
                 for the necessary wavelet coefficients may be derived.
                 These coefficients are calculated using a version of
                 the filtered back-projection algorithm as a
                 computational tool, in a multiresolution fashion. The
                 necessary filters are defined in terms of the
                 underlying wavelets. Denoising is accomplished through
                 an adaptation of the wavelet shrinkage (WS) approach of
                 Donoho et al. and amounts to a form of regularization.
                 Combining these two steps yields the proposed WVD/WS
                 reconstruction algorithm, which is compared to the
                 traditional filtered backprojection method in a small
                 study.",
  keywords =     "decomposition, backprojection. tomography.
                 wavelet-vaguelette",
}

@Article{kom-etal:helioseismic,
  title =        "Multitaper spectral analysis and wavelet denoising
                 applied to helioseismic data",
  author =       "R. W. Komm and Y. Gu and F. Hill and P. B. Stark and
                 I. K. Fodor",
  journal =      ApJ,
  volume =       "519",
  number =       "1",
  year =         "1999",
  pages =        "407--421",
  abstract =     "Estimates of solar normal mode frequencies from
                 helioseismic observations can be improved by using
                 multitaper spectral analysis (MTSA) to estimate spectra
                 from the time series, then using wavelet denoising of
                 the log spectra. MTSA leads to a power spectrum
                 estimate with reduced variance and better leakage
                 properties than the conventional periodogram. Under the
                 assumption of stationarity and mild regularity
                 conditions, the log multitaper spectrum has a
                 statistical distribution that is approximately
                 Gaussian, so wavelet denoising is asymptotically an
                 optimal method to reduce the noise in the estimated
                 spectra. We find that a single m-v spectrum benefits
                 greatly from MTSA followed by wavelet denoising and
                 that wavelet denoising by itself can be used to improve
                 m-averaged spectra. We compare estimates using two
                 different five-taper estimates (Slepian and sine
                 tapers) and the periodogram estimate for Global
                 Oscillation Network Group (GONG) time series at
                 selected angular degrees l. We compare those three
                 spectra with and without wavelet denoising, both
                 visually and in terms of the mode parameters estimated
                 from the preprocessed spectra using the GONG
                 peak-fitting algorithm. The two multitaper estimates
                 give equivalent results. The number of modes fitted
                 well by the GONG algorithm is 20%-60% larger (depending
                 on l and the temporal frequency) when applied to the
                 multitaper estimates than when applied to the
                 periodogram. The estimated mode parameters (frequency,
                 amplitude, and width) are comparable for the three
                 power spectrum estimates, except for modes with very
                 small mode widths (a few frequency bins), where the
                 multitaper spectra broaden the modes compared with the
                 periodogram. At frequencies below 3 mHz, wavelet
                 denoising of the log multitaper power spectra tends to
                 increase the number of modes for which the GONG
                 peak-fitting algorithm converges well. Close to 3 mHz,
                 where all modes are resolved, wavelet denoising makes
                 little difference. At higher frequencies close to the
                 acoustic cutoff frequency, where modes are blended into
                 ridges, wavelet denoising the multitaper spectra
                 reduces the number of good fits. We tested the
                 influence of the number of tapers used and found that
                 narrow modes at low n-values are broadened to the
                 extent that they can no longer be fitted if the number
                 of tapers is too large. For helioseismic time series of
                 this length and temporal resolution, the optimal number
                 of tapers is less than 10.",
}

@Book{koo:wavelets,
  title =        "Wavelets: {A}n Elementary Treatment of Theory and
                 Applications",
  editor =       "Tom H. Koornwinder",
  series =       "Approximations and Decompositions",
  volume =       "1",
  publisher =    "World Scientific",
  address =      "Singapore",
  pages =        "225",
  year =         "1993",
}

@Book{kot-joh-rea:encyclopedia,
  title =        "Encyclopedia of Statistical Sciences",
  booktitle =    "Encyclopedia of Statistical Sciences",
  editor =       "Samuel Kotz and Norman L. Johnson and Campbell B.
                 Read",
  publisher =    "Wiley",
  address =      NY,
  year =         "1982",
}

@Article{kov-sil:extending,
  title =        "Extending the scope of wavelet regression methods by
                 coefficient-dependent thresholding",
  author =       "Arne Kovac and Bernard W. Silverman",
  journal =      JASA,
  volume =       "95",
  number =       "449",
  year =         "2000",
  pages =        "172--183",
}

@InProceedings{kri-dro-pes:multiscale,
  title =        "{M}ultiscale detection of nonstationary signals",
  booktitle =    "Time-Frequency and Time-Scale Analysis",
  organization = IEEESPS,
  year =         "1992",
  pages =        "105--108",
  address =      "Victoria, B.C., Canada",
  author =       "H. Krim and K. Drouiche and J. C. Pesquet",
  abstract =     "A statistical method for detecting and/or localizing
                 nonstationarities in a process observed over a time
                 interval T is presented. Stationarity is induced by
                 taking a wavelet transform of the process. A parametric
                 model is fitted to the result. The error incurred in
                 fitting the model is shown to preserve the singularity
                 manifested in the transform. The error is then used to
                 establish a statistical detection test that is free of
                 any prior knowledge about the class of signals being
                 analyzed, and of any user input.",
  keywords =     "multiscale detection. nonstationary signals.
                 statistical method. time interval. wavelet transform.
                 parametric model. singularity. statistical detection
                 test.",
}

@InProceedings{kri-pes-wil:robust,
  title =        "{R}obust multiscale representation of processes and
                 optimal signal reconstruction",
  booktitle =    "Proceedings of the IEEE-SP International Symposium on
                 Time-Frequency and Time-Scale Analysis",
  pages =        "1--4",
  year =         "1994",
  author =       "H. Krim and J. C. Pesquet and A. S. Willsky",
  note =         "25-28 Oct. 1994, Philadelphia, PA, USA",
  abstract =     "We propose a statistical approach to obtain a ``best
                 basis'' representation of an observed random process.
                 We derive statistical properties of a criterion first
                 proposed to determine the best wavelet packet basis,
                 and, proceed to use it in constructing a statistically
                 sound algorithm. For signal enhancement, this best
                 basis algorithm is followed by a nonlinear filter based
                 on the minimum description length (MDL) criterion. We
                 show that it is equivalent to a min-max based algorithm
                 proposed by Donoho and Johnstone (1992).",
  keywords =     "optimal signal reconstruction. statistical approach.
                 robust multiscale representation. random process.
                 wavelet packet basis. statistically sound algorithm.
                 signal enhancement. best basis algorithm. nonlinear
                 filter. minimum description length criterion. min-max
                 based algorithm. white noise. Gaussian noise.",
}

@Article{kri-pes:nonstationary,
  title =        "Multiresolution analysis of a class of nonstationary
                 processes",
  author =       "H. Krim and J. C. Pesquet",
  journal =      IEEETIT,
  volume =       "41",
  number =       "4",
  year =         "1995",
  pages =        "1010--1020",
  keywords =     "multiresolution analysis, nonstationary processes,
                 signal processing, nonstationary signals, multiscale
                 framework, discrete-time analysis, parametric model,
                 wide-sense stationarity, analysis wavelet, wavelet
                 packet analysis, nonstationarities",
  abstract =     "Processing nonstationary signals is an important and
                 challenging problem. We focus on the class of
                 nonstationary processes with stationary increments of
                 an arbitrary order, and place them in a multiscale
                 framework. Unlike other related studies, we concentrate
                 on the discrete-time analysis and derive a number of
                 new results in addition to placing the related existing
                 ones in the same framework. We extend the study to
                 various parametric models for which we derive the
                 resulting multiresolution description. We show that
                 wide-sense stationarity may be achieved by adequately
                 selecting the analysis wavelet. After generalizing the
                 study to wavelet packet analysis, we show that the
                 latter possesses additional properties which are useful
                 in the presence of other types of nonstationarities.",
}

@Article{kri-etal:denoising,
  title =        "On denoising and best signal representation",
  author =       "H. Krim and D. Tucker and S. Mallat and D. Donoho",
  journal =      IEEETIT,
  volume =       "45",
  number =       "7",
  year =         "1999",
  pages =        "2225--2238",
  abstract =     "We propose a best basis algorithm for signal
                 enhancement in white Gaussian noise. The best basis
                 search is performed in families of orthonormal bases
                 constructed with wavelet packets or local cosine bases.
                 We base our search for the ``best'' basis on a
                 criterion of minimal reconstruction error of the
                 underlying signal. This approach is intuitively
                 appealing because the enhanced or estimated signal has
                 an associated measure of performance, namely, the
                 resulting mean-square error. Previous approaches in
                 this framework have focused on obtaining the most
                 ``compact'' signal representations, which consequently
                 contribute to effective denoising, These approaches,
                 however, do not possess the inherent measure of
                 performance which our algorithm provides. We first
                 propose an estimator of the mean-square error, based on
                 a heuristic argument and subsequently compare the
                 reconstruction performance based upon it to that based
                 on the Stein unbiased risk estimator. We compare the
                 two proposed estimators by providing both qualitative
                 and quantitative analyses of the bias term. Having two
                 estimators of the mean-square error, we incorporate
                 these cost functions into the search for the ``best''
                 basis, and subsequently provide a substantiating
                 example to demonstrate their performance.",
}

@Article{kro-ram-jon:frequency-shift-invariant,
  title =        "Frequency-shift-invariant orthonormal wavelet packet
                 representations",
  author =       "B. S. Krongold and K. Ramchandran and D. L. Jones",
  journal =      IEEETSP,
  volume =       "47",
  number =       "9",
  pages =        "2579--2582",
  abstract =     "It is commonly known that the dyadic structure of
                 wavelet expansions results in both time- and
                 frequency-translation sensitivity of an input signal.
                 We develop the first efficient method to reduce
                 frequency-alignment sensitivity by introducing a
                 wavelet packet decomposition that is invariant to
                 frequency shifts of a signal. A frequency-shifted
                 wavelet packet library is presented, and an efficient
                 best-basis algorithm is developed to determine the best
                 signal representation among all frequency shifts of a
                 signal. The algorithm computes all frequency-shifted
                 coefficients in O(N-2) operations, followed by an
                 efficient depth-first tree search of the same
                 complexity.",
}

@Article{kul-sad-mur:trough,
  title =        "Wavelet analysis of intermittent turbulent transport
                 in the atmospheric surface layer over a monsoon trough
                 region",
  author =       "J. R. Kulkarni and L. K. Sadani and B. S. Murthy",
  journal =      BLM,
  volume =       "90",
  number =       "2",
  year =         "1999",
  pages =        "217--239",
  keywords =     "atmospheric surface layer quadrant analysis turbulence
                 intermittency turbulent fluxes wavelet analysis",
  abstract =     "The structure of the turbulence in the atmospheric
                 surface layer over a monsoon trough region has been
                 studied using structural analysis based on wavelet
                 transform. The observational site is located at the
                 eastern (wet) end of the monsoon trough region,
                 characterized by high moisture in the atmospheric
                 surface layer. On the average relative humidity varied
                 from 70% to 100% during the experiment. The wind and
                 temperature data, collected at Kharagpur (22 degrees
                 25' N, 87 degrees 18' E) at six observational hours of
                 a day in June 1990 during the Monsoon Trough Boundary
                 Layer Experiment (MONTBLEX), have been utilized in the
                 study. The wind and instantaneous momentum flux time
                 series were decomposed into 12 scales using the Haar
                 wavelet transform. The eddies exhibited a large
                 temporal variability generating intermittency in the
                 energy and Bur distributions. A criterion based on the
                 isotropy has been suggested for separating the large
                 eddies from the small eddies. At the separation scale
                 the isotropy coefficient drops sharply. It is shown
                 that the intermittency in the small eddies resulted
                 from the spatial variation of energy, and deviation of
                 velocity statistics from the Gaussian distribution
                 known as flatness. The deviation from the -5/3 power
                 law has been attributed to the increased mean values
                 of, (i) the coefficient of variation of energy, and
                 (ii) the flatness factor, in the inertial subrange. The
                 decomposition of the instantaneous momentum Bur time
                 series reveals that the major contribution to the total
                 flux arises from the large eddies. The quadrant
                 analysis of the momentum flux shows that ejections and
                 sweeps account for a substantial part of the total
                 flux. and quantifies the relative importance of the
                 various spatial scales that contribute to the transport
                 of momentum.",
}

@Article{kul:monsoon,
  title =        "Wavelet analysis of the association between the
                 {S}outhern {O}scillation and the {I}ndian {S}ummer
                 {M}onsoon",
  author =       "J. R. Kulkarni",
  journal =      IJC,
  volume =       "20",
  number =       "1",
  year =         "2000",
  pages =        "89--104",
  abstract =     "A new aspect of the monsoon-Southern Oscillation (SO)
                 link has been investigated. All India Summer Monsoon
                 Rainfall (AISMR) and Southern Oscillation Index (SOI)
                 data (for August-September-October months) for the
                 period 1871-1998 have been processed for wavelet
                 analysis. Using the Haar wavelet function, the data are
                 decomposed into seven dyadic scales corresponding to
                 periods of 2, 4, 8, 16, 32, 64 and 128 years. The time
                 frequency localization in the wavelet analysis was used
                 to study the temporal variability of modes in AISMR and
                 SOI. The 2 and 8 year modes in both are found to
                 exhibit low frequency modulation. The 4 year mode in
                 both showed large intermittency. The periods of
                 high/low activities of 2, 4 and 8 year modes were
                 associated with a large/low number of deficient AISMR
                 years. The SOI derived from 2, 4 and 8 year modes in
                 the ENSO years, is found to be related to AISMR
                 variability, at 1% level of significance. The 2, 4 and
                 8 year modes in AISMR and SOI are found to be
                 correlated at a 5% level of significance. There is a
                 large temporal variability in the correlations of these
                 modes. The occurrences of maxima and minima in these
                 correlations followed a sequence, first in the 8 year
                 mode, then in the 4 year mode and in the end, in the 2
                 year mode. The reasons for de-association between AISMR
                 activity and SOI in the last 8 years of the present
                 decade have been attributed to (i) the negative
                 contributions by 128, 64, 32 and 16 year modes, (ii)
                 the low activity of 4 and 8 year modes and (iii) the
                 weak correlation between AISMR and SOI in 4 and 8 year
                 modes during this period.",
}

@InCollection{kum-fou:introduction,
  title =        "Wavelet analysis in geophysics: {A}n introduction",
  author =       "Praveen Kumar and Efi Foufoula-Georgiou",
  pages =        "1--43",
  crossref =     "fou-kum:geophysics",
}

@Article{kum-fou:rainfall,
  title =        "A New Look at Rainfall Fluctuations and Scaling
                 Properties of Spatail Rainfall Using Orthogonal
                 Wavelets",
  author =       "Praveen Kumar and Efi Foufoula-Georgiou",
  journal =      JAM,
  volume =       "32",
  year =         "1993",
  pages =        "209--222",
  abstract =     "Orthogonal wavelet transforms of the rainfall fields
                 are analyzed. Results show that wavelet multiresolution
                 analysis provides methods for the study of
                 nonhomogeneous anisotropic processes and for defining
                 fluctuations in two dimensions. Moreover, orthogonal
                 wavelet transforms segregate large-scale features from
                 small-scale features by providing convenient orthogonal
                 decompositions with directionality. Lastly, orthogonal
                 wavelet analysis is applied to a squall-line storm.",
}

@Article{kum-fou:review,
  title =        "Wavelet analysis for geophysical applications",
  author =       "Praveen Kumar and Efi Foufoula-Georgiou",
  journal =      "Review of Geophysics",
  volume =       "35",
  number =       "4",
  year =         "1997",
  pages =        "385--412",
  keywords =     "fractional brownian motion 2-scale difference
                 equations turbulent coherent motions spatial rainfall
                 fields signal analysis forest canopy multicomponent
                 decomposition sampling theory transforms
                 representation",
  abstract =     "Wavelet transforms originated in geophysics in the
                 early 1980s for the analysis of seismic signals. Since
                 then, significant mathematical advances in wavelet
                 theory have enabled a suite of applications in diverse
                 fields. In geophysics the power of wavelets for
                 analysis of nonstationary processes that contain
                 multiscale features, detection of singularities,
                 analysis of transient phenomena, fractal and
                 multifractal processes, and signal compression is now
                 being exploited for the study of several processes
                 including space-time precipitation, remotely sensed
                 hydrologic fluxes, atmospheric turbulence, canopy
                 cover, land surface topography, seafloor bathymetry,
                 and ocean wind waves. It is anticipated that in the
                 near future, significant further advances in
                 understanding and modeling geophysical processes will
                 result from the use of wavelet analysis. In this paper
                 we review the basic properties of wavelets that make
                 them such an attractive and powerful tool for
                 geophysical applications, We discuss continuous,
                 discrete, orthogonal wavelets and wavelet packets and
                 present applications to geophysical processes.",
}

@Article{kum:role,
  title =        "Role of Coherent Structures in the Stochastic-Dynamic
                 Variability of Precipitation",
  author =       "Praveen Kumar",
  journal =      JGRA,
  volume =       "101",
  number =       "D21",
  year =         "1996",
  pages =        "26,393--26,404",
  keywords =     "spatial rainfall fields, multicomponent decomposition,
                 wave-propagation, sampling theory, signal",
  abstract =     "Using time-frequency-scale elements obtained from
                 wavelet packets as a basis, we describe a broad
                 framework of analysis which can be used to reveal the
                 essential dynamics, identified as coherent structures,
                 of precipitation. We show that the matching pursuits
                 algorithm with nearly symmetric orthogonal wavelets
                 provides an optimal representation of the inner
                 structure of rainfall time series and can describe
                 features that range from scales of isolated singularity
                 to synoptically forced large-scale features. We
                 describe the analysis of time series of several storms
                 and show that there exist distinct scales of variation
                 identifiable with rain cell and synoptic-scale
                 activity, which is in contradistinction to the scale
                 invariance hypothesis.",
}

@Article{kum:scale-space,
  title =        "A Wavelet Based Methodology for Scale-Space
                 Anisotropic Analysis",
  author =       "Praveen Kumar",
  journal =      "Geophysical Research Letters",
  volume =       "22",
  number =       "20",
  year =         "1995",
  pages =        "2777--2780",
  abstract =     "It is well known that several geophysical fields
                 exhibit characteristic features at different scales.
                 For some such fields scale-space anisotropy is also
                 present, that is, features contributing a significant
                 fraction of energy are oriented in different directions
                 at different scales. Examples of such fields include
                 clouds, rainfall, hurricanes etc. A technique based on
                 wavelet transforms (with two-dimensional directionally
                 oriented Morlet wavelet) is developed to analyze such
                 random fields. This methodology has significant
                 advantage over Fourier transform based techniques and
                 is demonstrated using the analysis of a spatial
                 rainfall field.",
}

@Article{lan-etal:noise,
  title =        "Noise reduction using an undecimated discrete wavelet
                 transform",
  author =       "M. Lang and H. Guo and J. E. Odegard and C. S. Burrus
                 and R. O. Wells",
  journal =      IEEESPL,
  volume =       "3",
  number =       "1",
  year =         "1996",
  pages =        "10--12",
  abstract =     "A new nonlinear noise reduction method is presented
                 that uses the discrete wavelet transform. Similar to
                 Donoho (1995) and Donoho and Johnstone (1994, 1995),
                 the authors employ thresholding in the wavelet
                 transform domain but, following a suggestion by
                 Coifman, they use an undecimated, shift-invariant,
                 nonorthogonal wavelet transform instead of the usual
                 orthogonal one. This new approach can be interpreted as
                 a repeated application of the original Donoho and
                 Johnstone method for different shifts. The main feature
                 of the new algorithm is a significantly improved noise
                 reduction compared to the original wavelet based
                 approach. This holds for a large class of signals, both
                 visually and in the l/sub 2/ sense, and is shown
                 theoretically as well as by experimental results.",
}

@InProceedings{lan-etal:nonlinear,
  title =        "Nonlinear processing of a shift invariant {DWT} for
                 noise reduction",
  author =       "M. Lang and H. Guo and J. E. Odegard and C. S. Burrus
                 and R. O. Wells",
  pages =        "640--651",
  crossref =     "szu:wavelet2",
  keywords =     "nonlinear processing, shift invariant DWT, noise
                 reduction, thresholding, redundant wavelet transform,
                 nondecimated redundant wavelet transform, synthetic
                 aperture radar, SAR images",
  abstract =     "A novel approach for noise reduction is presented.
                 Similar to Donoho, we employ thresholding in some
                 wavelet transform domain but use a nondecimated and
                 consequently redundant wavelet transform instead of the
                 usual orthogonal one. Another difference is the shift
                 invariance as opposed to the traditional orthogonal
                 wavelet transform. We show that this new approach can
                 be interpreted as a repeated application of Donoho`s
                 original method. The main feature is, however, a
                 dramatically improved noise reduction compared to
                 Donoho`s approach, both in terms of the l/sub 2/ error
                 and visually, for a large class of signals. This is
                 shown by theoretical and experimental results,
                 including synthetic aperture radar (SAR) images.",
}

@InProceedings{lar-zak:automatic,
  title =        "Automatic Classification of Active Sonar Data Using
                 Time-Frequency Transforms",
  author =       "Francesco Lari and Avideh Zakhor",
  booktitle =    "Time-Frequency and Time-Scale Analysis",
  organization = IEEESPS,
  year =         "1992",
  pages =        "21--24",
  address =      "Victoria, B.C., Canada",
  abstract =     "Automatic classification of active sonar signals using
                 the Wigner-Ville transform (WVT), the wavelet transform
                 (WT) and the scalogram is addressed. Features are
                 extracted by integrating over regions in the
                 time-frequency (TF) distribution, and are classified by
                 a decision tree. Experimental results show
                 classification and detection rates of up to 92% at -4
                 dB of SNR. The WT outperforms the WVT and the
                 scalogram, particularly at high noise levels. This can
                 be partially attributed to the absence of cross terms
                 in the WT.",
}

@Article{lau-wen:climate,
  title =        "Climate signal detection using wavelet transform:
                 {H}ow to make a time series sing",
  author =       "K. M. Lau and Hengyi Weng",
  journal =      BAMetS,
  volume =       "76",
  number =       "12",
  pages =        "23--41",
  year =         "1995",
  abstract =     "In this paper, the application of the wavelet
                 transform (WT) to climate time series analyses is
                 introduced. A tutorial description of the basic concept
                 of WT, compared with similar concepts used in music, is
                 also provided. Using an analogy between WT
                 representation of a time series and a music score, the
                 authors illustrate the importance of local versus
                 global information in the time-frequency localization
                 of climate signals. Examples of WT applied to climate
                 data analysis are demonstrated using analytic signals
                 as well as real climate time series. Results of WT
                 applied to two climate time series - that is, a proxy
                 paleoclimate time series with a 2.5-Myr deep-sea
                 sediment record of [[Delta].sup.18]O and a 140-yr
                 monthly record of Northern Hemisphere surface
                 temperature - are presented. The former shows the
                 presence of a 40-kyr and a 100-kyr oscillation and an
                 abrupt transition in the oscillation regime at 0.7 Myr
                 before the present, consistent with previous studies.
                 The latter possesses a myriad of oscillatory modes from
                 interannual (2-5 yr), interdecadal (10-12 yr, 20-25 yr,
                 and 40-60 yr), and century ([approximately]180 yr)
                 scales at different periods of the data record. In
                 spite of the large difference in timescales, common
                 features in time-frequency characteristics of these two
                 time series have been identified. These features
                 suggest that the variations of the earth's climate are
                 consistent with those exhibited by a nonlinear
                 dynamical system under external forcings.",
}

@Article{leb-vet:balanced,
  title =        "Balanced multiwavelets theory and design",
  author =       "J{\'e}r{\^o}me Lebrun and Martin Vetterli",
  journal =      IEEETSP,
  volume =       "46",
  number =       "4",
  pages =        "1119--1125",
  year =         "1998",
  keywords =     "balanced multiwavelets time-varying filter banks
                 signal compression multichannel signal processing
                 multifilter banks multiwavelets filter bank design
                 multiresolution analysis",
  abstract =     "This article deals with multiwavelets, which are a
                 generalization of wavelets in the context of
                 time-varying filter banks and with their applications
                 to signal processing and especially compression. By
                 their inherent structure, multiwavelets are fit for
                 processing multichannel signals. This is the main issue
                 in which we are interested. First, we review material
                 on multiwavelets and their links with multifilter banks
                 and, especially, time-varying filter banks. Then, we
                 have a close look at the problems encountered when
                 using multiwavelets in applications, and we propose new
                 solutions for the design of multiwavelets filter banks
                 by introducing the so-called balanced multiwavelets",
}

@Unpublished{led-muj-mur-smi:motion,
  title =        "Spatio-Temporal Wavelet Transforms for Motion
                 Tracking",
  author =       "Jean-Pierre Leduc and Fernando Mujica and Romain
                 Murenzi and Mark Smith",
  year =         "1997",
  email =        "leduc@ee.gatech.edu",
  note =         "Georgia Institute of Technology",
}

@Article{led:spatio-temporal,
  title =        "Spatio-Temporal Wavelet Transforms for Digital Signal
                 Analysis",
  author =       "Jean-Pierre Leduc",
  journal =      SP,
  volume =       "60",
  number =       "1",
  pages =        "23--41",
  year =         "1997",
  email =        "leduc@ee.gatech.edu, leduc@irisa.fr",
  keywords =     "Wavelet transforms; Spatio-temporal signals; Image
                 seqeunces; Motion analysis; Group of transfromations;
                 Regions of interest; Selective feature extraction",
  abstract =     "The goal of this paper is to investigate
                 spatio-temporal continuous wavelet transforms. A new
                 wavelet family called the Galilean wavelet has been
                 designed to tune to four main parameters namely the
                 scale, the spatio-temporal position, the spatial
                 orientation, and the velocity. The paper starts with
                 the theory of motion-compensated wavelet filtering in
                 the discrete realm of image processing. As a major
                 difference to multi-dimensional homogeneous spaces, the
                 spatio-temporal signals involve motions that warp the
                 signal along the temporal dimension. Modeling motion
                 with 2-D affine transformations leads to
                 spatio-temporal generalizations. Decomposition in to
                 elementary operators lead to developing transformation
                 groups and exploiting the related representation
                 theory. The construction of continuous spatio-temporal
                 wavelets in $R^n \times R$ spaces is then handled with
                 classical techniques of calculation. Close connections
                 may then be established among all the spatio-temp oral
                 wavelet transforms through different sets of
                 transformations. This approachgenerates a general
                 framework for the study of future tools. Frames of
                 wavelets are thereafter investigated to revisit
                 discrete wavelet transforms in a more general way.
                 Eventually illustrations demonstrate the ability of the
                 Galilean wavelet transforms to analyze spatio-temporal
                 contents.",
}

@TechReport{lee-har-spe:tides,
  title =        "Automated Smoothing of Tides Data Using Wavelets",
  author =       "GeungHee Lee and Jeffrey D. Hart and F. Michael
                 Speed",
  institution =  "Department of Statistics, Texas A\&M University",
  number =       "268",
  year =         "1996",
  keywords =     "automatic trend, jump, outlier, shrinkage estimator,
                 wavelet packet",
}

@Article{lee:wavelets,
  title =        "Wavelets and wavelet estimation: {A} review",
  author =       "G. H. Lee",
  journal =      JETE,
  volume =       "4",
  number =       "1",
  year =         "1998",
  pages =        "123--157",
  abstract =     "Wavelets have received a lot of attention in
                 statistics since Donoho and Johnstone (1994) introduced
                 wavelet shrinkage estimators, which include some
                 important ideas--wavelets as a new local basis,
                 multiresolution analysis and thresholding. From these
                 ideas, we can reilluminate the methods and data
                 analyses based on Fourier series and truncated
                 estimators. In this paper, we review wavelets, wavelet
                 series estimators, their model selection methods and
                 their applications in econometrics and economics.",
}

@Book{leh:tpe,
  title =        "Theory of Point Estimation",
  author =       "E. L. Lehmann",
  publisher =    "Wiley",
  address =      NY,
  pages =        "506",
  year =         "1983",
}

@Book{leh:tsh,
  title =        "Testing Statistical Hypotheses",
  author =       "E. L. Lehmann",
  publisher =    "Wiley",
  address =      NY,
  edition =      "2",
  pages =        "600",
  year =         "1986",
}

@TechReport{len:denoising,
  title =        "Denoising not equispaced data with wavelets",
  author =       "L. Lenarduzzi",
  year =         "1997",
  number =       "IAMI 97.1",
  institution =  "Instituto per le Applicazioni della Matematica e
                 dell'Informatica",
}

@InProceedings{lew-bur:approximate,
  title =        "Approximate continuous wavelet transform with an
                 application to noise reduction",
  author =       "James M. Lewis and C. Sidney Burrus",
  booktitle =    "Proceedings of the International Conference on
                 Acoustics, Speech, and Signal Processing",
  pages =        "???--???",
  year =         "1998",
  url =          "http://www-dsp.rice.edu/publications/pub/lewi-icassp98.ps.Z",
  abstract =     "We describe a generalized scale-redundant wavelet
                 transform which approximates a dense sampling of the
                 continuous wavelet transform (CWT) in both time and
                 scale. The dyadic scaling requirement of the usual
                 wavelet transform is relaxed in favor of an approximate
                 scaling relationship which in the case of a Gaussian
                 scaling function is known to be asymptotically exact
                 and irrational. This scheme yields an arbitrarily dense
                 sampling of the scale axis in the limit. Similar
                 behavior is observed for other scaling functions with
                 no explicit analytic form. We investigate
                 characteristics of the family of Lagrange interpolating
                 filters (related to the Daubechies family of
                 compactly-supported orthonormal wavelets), and finally
                 present applications of the transform to denoising and
                 edge detection.",
}

@Article{li-noz:cross-correlation,
  journal =      "Japanese Society of Mechanical Engineers International
                 Journal, Series B",
  volume =       "40",
  number =       "1",
  year =         "1997",
  pages =        "58--66",
  title =        "{A}pplication of wavelet cross-correlation analysis to
                 a plane turbulent jet",
  author =       "Hui Li and Tsutomu Nozaki",
  abstract =     "A new cross-correlation method, which is called
                 wavelet cross-correlation analysis and is used to
                 express the statistical cross-correlation of two
                 arbitrary signals in terms of scale and time delay, is
                 proposed and its main properties are presented,
                 analyzing two test signals, it is shown that wavelet
                 cross-correlation does not have the limitations of
                 classical cross-correlation. As a practical application
                 to fluid mechanics, wavelet cross-correlation is
                 employed to determine the cross-correlation
                 relationships between the x-components of the
                 fluctuation velocities at two points on opposite sides
                 of the centerline and along the centerline of a plane
                 turbulent jet in terms of period and time delay. In the
                 distributions of the wavelet cross-correlation
                 coefficients, similar structures with various scales
                 are observed instantaneously, and the period of eddy
                 and apparent flapping motions can be determined easily
                 in terms of period and time delay. It is found that the
                 apparent flapping behavior appears first in region with
                 an intermediate period. It is also revealed that a
                 similar structure with a high period consists of
                 similar structures with a low period, i.e., a large
                 eddy contains small eddies.",
  keywords =     "turbulent flow, jet, eddy, coherent structure,
                 branching structure, mixing layer, wavelet analysis,
                 wavelet cross-correlation function, wavelet
                 cross-correlation coefficient, local wavelet
                 cross-spectrum",
}

@Article{li-ulr:well-log,
  title =        "Well-log analysis using localized transforms",
  author =       "X. G. Li and T. J. Ulrych",
  journal =      "Journal of Seismic Exploration",
  volume =       "8",
  number =       "3",
  year =         "1999",
  pages =        "243--260",
  abstract =     "The wavelet transform (WT) is used to analyze and
                 characterize well-logs in location and scale. In the WT
                 domain, a well-log can be decomposed into deterministic
                 and statistical components. The deterministic component
                 consists of smooth WT coefficients at the largest scale
                 and large WT coefficients at the rest of the scales.
                 The remaining coefficients represent the statistical
                 component which can be modeled as a fractional Brownian
                 motion (FBM). A well-log is used to illustrate this
                 decomposition. To test the fractal model, we have used
                 both 1-D and 2-D wavelet transforms to simulate FBM
                 processes. These simulated FBM series look like
                 well-logs, which verifies the proposed approach. Both
                 orthogonal and continuous WT's are used for analyzing
                 fractal parameters of FBM processes. The orthogonal WT
                 is used to compute a fractal parameter for a particular
                 time series,and the continuous WT is used to estimate
                 the time variant fractal parameter.",
}

@Article{li:identification,
  title =        "The wavelet identification of thresholds and time
                 delay of threshold autoregressive models",
  author =       "Y. Li",
  journal =      SSin,
  volume =       "9",
  number =       "1",
  year =         "1999",
  pages =        "153--166",
  keywords =     "thresholds time delay wavelets",
  abstract =     "In this paper, we consider identification of the
                 thresholds and time delay of threshold autoregressive
                 models with p- dependence and an unknown number of
                 thresholds. By checking p different empirical wavelets
                 of the data to see which have significantly large
                 absolute values, the time delay is identified first. By
                 further checking the empirical wavelets corresponding
                 to the time delay across the fine scale levels, the
                 thresholds and their number are identified. All
                 estimators are shown to be strongly consistent.",
}

@InProceedings{lia-li-kuo:image,
  title =        "Image compression with embedded multiwavelet coding",
  author =       "Kai-Chieh Liang and Jin Li and C.-C. Jay Kuo",
  crossref =     "szu:wavelet3",
  url =          "http://sipi.usc.edu/~lijin/paper/aero96_mwt.ps",
}

@InProceedings{lia-par:2d,
  title =        "A two-dimensional translation invariant wavelet
                 representation and its applications",
  author =       "Jie Liang and Thomas W. Parks",
  booktitle =    "Proceedings ICIP-94",
  volume =       "1",
  pages =        "66--70",
  year =         "1994",
  keywords =     "two-dimensional translation invariant wavelet
                 representation. sensitivity. two-dimensional signals.
                 fast algorithm. circular translates. input image.
                 optimal translate. decomposition. quadtree search
                 algorithm. complexity. translation invariant wavelet
                 transform. data compression.",
  abstract =     "Addresses the problem of the sensitivity of wavelet
                 representations to translations for two-dimensional
                 signals. The authors describe a fast algorithm to
                 calculate the two-dimensional wavelet transforms for
                 all the circular translates of an input image. They
                 select the optimal translate for the decomposition
                 using a quadtree search algorithm. The resulted wavelet
                 representation is invariant under translations measured
                 by an additive cost criterion. The complexity of the
                 whole algorithm is O(N/sup 2/ log N) for a N*N input
                 block. They apply this translation invariant wavelet
                 transform to data compression. The results show that by
                 taking into account the effect of translations,
                 additional compression can be achieved beyond that
                 achieved by a standard wavelet transform.",
}

@Article{lia-par:image,
  title =        "Image coding using translation invariant wavelet
                 transforms with symmetric extensions",
  author =       "Jie Liang and Thomas W. Parks",
  journal =      IEEETIP,
  volume =       "7",
  number =       "5",
  year =         "1998",
  pages =        "762--769",
  keywords =     "representation",
  abstract =     "In this correspondence, we address the problem of
                 translation sensitivity of conventional wavelet
                 transforms for two-dimensional (2-D) signals. We
                 propose wavelet transform algorithms that achieve the
                 following desirable properties simultaneously: i)
                 translation invariance, ii) reduced edge effects, and
                 iii) sice-limitedness. We apply this translation
                 invariant biorthogonal wavelet transform with symmetric
                 extensions to image coding applications with good
                 results.",
}

@Article{lia-par:translation,
  title =        "A translation-invariant wavelet representation
                 algorithm with applications",
  author =       "Jie Liang and Thomas W. Parks",
  journal =      IEEETSP,
  volume =       "44",
  number =       "2",
  year =         "1996",
  pages =        "225--232",
  abstract =     "We address the time-varying problem of wavelet
                 transforms, and a new translation-invariant wavelet
                 representation algorithm is proposed. Using the
                 algorithm introduced by Beylkin (see SIAM J. Numer.
                 Anal., vol. 29, p.1716-1740, 1992), we compute the
                 wavelet transform for all the circular time shifts of a
                 length- N signal in O(N log N) operations. The wavelet
                 coefficients of the time shift with minimal cost are
                 selected as the best representation of the signal using
                 a binary tree search algorithm with an appropriate cost
                 function. We apply the translation-invariant
                 representation algorithm to a geoacoustic data
                 compression application. The results show that the new
                 algorithm can reduce the distortion (the squared error
                 in our case) substantially, if the input signals are
                 transients that are sensitive to time shifts.",
}

@Article{lil-par:multiwavelet,
  title =        "Multiwavelet spectral and polarization analyses of
                 seismic records",
  author =       "J. M. Lilly and J. Park",
  journal =      GJI,
  volume =       "122",
  number =       "3",
  year =         "1995",
  pages =        "1001--1021",
  keywords =     "multiwavelet spectral analysis polarization analysis
                 seismic records wavelet transform multiple taper
                 spectral analysis low-variance spectrum estimate
                 nonstationary data process multiwavelet algorithm
                 mutually orthogonal Slepian wavelets time-varying
                 spectral density matrix three-component seismic data
                 three-component motion singular value decomposition
                 seismic body waves elliptical polarization polarization
                 estimators earthquakes",
  abstract =     "Presents an algorithm, based on the wavelet transform
                 and multiple taper spectral analysis, for providing a
                 low-variance spectrum estimate of a non-stationary data
                 process. The `multiwavelet' algorithm uses, within each
                 frequency band, a number of mutually orthogonal Slepian
                 wavelets, optimally concentrated in frequency. The sum
                 of squared wavelet transforms with the Slepian wavelets
                 results in a spectrum estimate that is both
                 low-variance and resistant to broad-band bias. The
                 multiwavelet algorithm is used to estimate the
                 time-varying spectral density matrix S(f,t) for two or
                 more time series, in particular for three-component
                 seismic data. Coherent three-component motion is
                 described by motion along a single trajectory, with
                 appropriate projections onto the three component axes.
                 This trajectory is found by applying a singular value
                 decomposition (SVD) to a matrix M(f,t) of wavelet
                 transform values. The normalized first singular value
                 of the SVD determines whether a correlation among the
                 three components of the seismogram is statistically
                 significant. Where significant, coherent particle
                 motion is reconstructed by a linear combination of the
                 wavelets with coefficients specified by the first
                 left-singular vector. The polarization of this motion
                 with respect to the coordinate axes is given by the
                 first right-singular vector. Where the wavelets are
                 real-valued, the usefulness of this method is limited
                 to cases in which the three components of the seismic
                 record oscillate in phase with each other, as is often
                 the case for seismic body waves. Elliptical
                 polarization is handled by pairing even and odd Slepian
                 wavelets into complex-valued wavelets, capable of
                 detecting phase shifts between components. The authors
                 demonstrate the multiwavelet spectrum and polarization
                 estimators on seismic data from a large shallow
                 earthquake in the Solomon Islands, and from the deep
                 earthquakes beneath Fiji (1994 March 9) and Bolivia
                 (1994 June 9).",
}

@Article{lin-per-rot:ice,
  title =        "The Discrete Wavelet Transform and the Scale Analysis
                 of the Surface Properties of Sea Ice",
  author =       "Ronald W. Lindsay and Donald B. Percival and D. Andrew
                 Rothrock",
  journal =      IEEETGRS,
  volume =       "34",
  number =       "3",
  year =         "1996",
  pages =        "771--787",
  keywords =     "Sea ice; Radar remote sensing; Discrete wavelet
                 transform; Scale analysis; Daubechies wavelet filter;
                 scale-dependent wavelet variance; Wavelet covariance;
                 Mallat orthogonal-pyramid algorithm; Spring pack ice;
                 Beaufort Sea",
  abstract =     "The formalism of the one-dimensional discrete wavelet
                 transform (DWT) based on Daubechies wavelet filters is
                 outlined in terms of finite vectors and matrices. Both
                 the scale-dependent wavelet variance and wavelet
                 covariance are considered and confidence intervals for
                 each are determined. The variance estimates are more
                 accurately determined with a maximal-overlap version of
                 the wavelet transform. The properties of several
                 Daubechies wavelet filters and the associated basis
                 vectors are discussed. Both the Mallat
                 orthogonal-pyramid algorithm for determining the DWT
                 and a pyramid algorithm for determining the
                 maximal-overlap version of the transform are presented
                 in terms of finite vectors. As an example, the authors
                 investigate the scales of variability of the surface
                 temperature and albedo of spring pack ice in the
                 Beaufort Sea. The data analyzed are from individual
                 lines of a Landsat TM image (25-m sample interval) and
                 include both reflective (channel 3, 30-m resolution)
                 and thermal (channel 6, 120-m resolution) data. The
                 wavelet variance and covariance estimates are presented
                 and more than half of the variance is accounted for by
                 scales of less than 800 m. A wavelet-based technique
                 for enhancing the lower-resolution thermal data using
                 the reflected data is introduced. The simulated effects
                 of poor instrument resolution on the estimated lead
                 number density and the mean lead width are investigated
                 using a wavelet-based smooth of the observations.",
}

@InCollection{liu:new-perspective,
  title =        "Wavelet Transform and New Perspective on Coastal and
                 Ocean Engineering Data Analysis",
  booktitle =    "Advances in Coastal and Ocean Engineering",
  author =       "P. C. Liu",
  editor =       "P. L-F Liu",
  volume =       "6",
  pages =        "???--???",
  year =         "2000",
  email =        "liu@glerl.noaa.gov",
}

@InCollection{liu:wavelet-spectrum,
  title =        "Wavelet Spectrum Analysis and Ocean Wind Waves",
  author =       "Paul C. Liu",
  pages =        "151--166",
  email =        "liu@glerl.noaa.gov",
  crossref =     "fou-kum:geophysics",
}

@InCollection{lum-etal:optimization,
  title =        "Optimization of Bias-Variance Trade-Off in Non
                 Parametric Spectral Analysis by Decomposition into
                 Wavelet Packets",
  author =       "B. Lumeau and J. C. Pesquet and J. F. Bercher and L.
                 Louveau",
  pages =        "285--290",
  crossref =     "mey-roq:progress",
}

@TechReport{ma-str-vid:first-moment,
  title =        "The First Moment of Wavelet Random Variables",
  author =       "Yanyuan Ma and Gilbert Strang and Brani Vidakovic",
  number =       "97-10",
  institution =  "Institute of Statistics and Decision Sciences, Duke
                 University",
  year =         "1997",
  url =          "ftp://ftp.isds.duke.edu/pub/WorkingPapers/97-10.ps",
}

@Article{mah:eddy,
  title =        "Eddy asymmetry in the sheared heated boundary layer",
  author =       "L. Mahrt",
  journal =      JAS,
  volume =       "48",
  number =       "3",
  year =         "1991",
  pages =        "472--482",
  abstract =     "Statistical measures are developed to study the
                 influence of mean shear on the asymmetry of eddy
                 updrafts as observed from low-level aircraft flights in
                 HAPEX, FIFE, and SESAME. This asymmetry involves
                 formation of microfronts between updrafts with slow
                 horizontal motion and downdrafts with faster horizontal
                 motion. The variance of the Haar-wavelet transform
                 (step-function basis) is found to be a superior
                 indicator of the dominant scales of such eddies
                 compared to the structure function. For those analyses
                 where scale dependence is not of interest, the simpler
                 structure function is applied. The coherent structures
                 at the dominant scale are examined by computing
                 eigenvectors of the lagged correlation matrix based on
                 conditionally sampled events.",
}

@Article{mak:sst,
  title =        "Orthogonal wavelet analysis: {I}nterannual variability
                 in the sea surface temperature",
  author =       "Mankin Mak",
  journal =      BAMetS,
  volume =       "76",
  year =         "1995",
  pages =        "2179--2186",
  keywords =     "ocean, environmental aspects, signal processing
                 technique, ocean temperature analysis",
  abstract =     "The unique capability of orthogonal wavelets, which
                 have attractive time-frequency localization properties
                 as exemplified by the Meyer wavelet, is demonstrated in
                 a diagnosis of the interannual variability using a
                 44-year dataset of the sea surface temperature (SST).
                 This wavelet analysis is performed in conjunction with
                 an empirical orthogonal function analysis and a Fourier
                 analysis to illustrate their complementary capability.
                 The focus of this article is on the equatorial Pacific
                 SST, which is known to have far-reaching impacts on
                 short-term climate variability. The Meyer spectrum
                 brings to light intriguing episodic characteristics of
                 three separate sequences of El Ni{\~n}o (abnormally
                 warm) and La Ni{\~n}a (abnormally cold) events during
                 the past 42 years. It quantifies the relative
                 contributions to the variability associated with
                 different frequency ranges at different times. Through
                 a wavelet cross-spectral analysis with the SST at an
                 equatorial location and at a midlatitude location in
                 the Pacific Ocean, the planetary character of the SST
                 field associated with such events is also
                 illustrated.",
}

@Article{mal-hwa:singularity,
  title =        "Singularity detection and processing with wavelets",
  author =       "S. G. Mallat and W. L. Hwang",
  journal =      IEEETIT,
  volume =       "38",
  number =       "2",
  year =         "1992",
  pages =        "617--643",
  url =          "ftp://cs.nyu.edu/pub/tech-reports/tr549-R245.ps.Z",
  keywords =     "one dimensional signals, signal analysis, signal
                 processing, image edge location, white noise removal,
                 image processing, singularities, Lipschitz exponents,
                 wavelet transform, irregular structures, fast
                 oscillations, modulus maxima, two-dimensional signals",
  abstract =     "The mathematical characterization of singularities
                 with Lipschitz exponents is reviewed. Theorems that
                 estimate local Lipschitz exponents of functions from
                 the evolution across scales of their wavelet transform
                 are reviewed. It is then proven that the local maxima
                 of the wavelet transform modulus detect the locations
                 of irregular structures and provide numerical
                 procedures to compute their Lipschitz exponents. The
                 wavelet transform of singularities with fast
                 oscillations has a particular behavior that is studied
                 separately. The local frequency of such oscillations is
                 measured from the wavelet transform modulus maxima. It
                 has been shown numerically that one- and
                 two-dimensional signals can be reconstructed, with a
                 good approximation, from the local maxima of their
                 wavelet transform modulus. As an application, an
                 algorithm is developed that removes white noises from
                 signals by analyzing the evolution of the wavelet
                 transform maxima across scales. In two dimensions, the
                 wavelet transform maxima indicate the location of edges
                 in images.",
}

@Article{mal-pap-zha:covariance,
  title =        "Adaptive covariance estimation of locally stationary
                 processes",
  author =       "S. Mallat and G. Papicolaou and Z. Zhang",
  journal =      AofS,
  volume =       "26",
  number =       "1",
  year =         "1998",
  pages =        "1--47",
  url =          "ftp://math.Stanford.EDU/pub/papers/papanicolaou/lsb.ps.gz",
}

@Article{mal-zha:matching,
  title =        "Matching pursuits with time-frequency dictionaries",
  author =       "S. Mallat and Z. Zhang",
  journal =      IEEETSP,
  volume =       "41",
  number =       "12",
  year =         "1993",
  pages =        "3397--3415",
}

@Article{mal-zho:characterization,
  title =        "Characterization of signals from multiscale edges",
  author =       "S. Mallat and S. Zhong",
  journal =      IEEETPAMI,
  volume =       "14",
  number =       "7",
  year =         "1992",
  pages =        "710--732",
  keywords =     "1D signals, 2D signals, picture processing, multiscale
                 Canny edge detection, local maxima, wavelet theory,
                 pattern recognition, multiscale edge representation,
                 image coding",
  abstract =     "A multiscale Canny edge detection is equivalent to
                 finding the local maxima of a wavelet transform. The
                 authors study the properties of multiscale edges
                 through the wavelet theory. For pattern recognition,
                 one often needs to discriminate different types of
                 edges. They show that the evolution of wavelet local
                 maxima across scales characterize the local shape of
                 irregular structures. Numerical descriptors of edge
                 types are derived. The completeness of a multiscale
                 edge representation is also studied. The authors
                 describe an algorithm that reconstructs a close
                 approximation of 1-D and 2-D signals from their
                 multiscale edges. For images, the reconstruction errors
                 are below visual sensitivity. As an application, a
                 compact image coding algorithm that selects important
                 edges and compresses the image data by factors over 30
                 has been implemented.",
}

@Article{mal:multiresolution,
  title =        "A theory for multiresolution signal decomposition:
                 {T}he wavelet representation",
  author =       "S. Mallat",
  journal =      IEEETPAMI,
  volume =       "11",
  number =       "7",
  year =         "1989",
  pages =        "674--693",
  keywords =     "picture processing, encoding, pattern recognition,
                 multiresolution signal decomposition, wavelet
                 representation, pyramidal algorithm, convolutions,
                 quadrature mirror filters, data compression, image
                 coding, texture discrimination, fractal analysis",
  abstract =     "Multiresolution representations are effective for
                 analyzing the information content of images. The
                 properties of the operator which approximates a signal
                 at a given resolution were studied. It is shown that
                 the difference of information between the approximation
                 of a signal at the resolutions 2/sup j+1/ and 2/sup j/
                 (where j is an integer) can be extracted by decomposing
                 this signal on a wavelet orthonormal basis of L/sup
                 2/(R/sup n/), the vector space of measurable,
                 square-integrable n-dimensional functions. In L/sup
                 2/(R), a wavelet orthonormal basis is a family of
                 functions which is built by dilating and translating a
                 unique function psi (x). This decomposition defines an
                 orthogonal multiresolution representation called a
                 wavelet representation. It is computed with a pyramidal
                 algorithm based on convolutions with quadrature mirror
                 filters. Wavelet representation lies between the
                 spatial and Fourier domains. For images, the wavelet
                 representation differentiates several spatial
                 orientations. The application of this representation to
                 data compression in image coding, texture
                 discrimination and fractal analysis is discussed.",
}

@Book{mal:tour,
  title =        "A Wavelet Tour of Signal Processing",
  author =       "St\'{e}phane Mallat",
  publisher =    "Academic Press",
  address =      "San Diego",
  year =         "1998",
  abstract =     "A Wavelet Tour of Signal Processing begins with a
                 presentation of the wonders of the Fourier transform,
                 and then describes its failures for transient signal
                 processing. It presents local time-frequency methods
                 and the related mathematical tools. The book uses an
                 intuitive approach to important mathematical results,
                 and emphasizes practical applications rather than
                 proofs. It describes numerical discrete algorithms as
                 well as some applications to information processing,
                 fractal analysis, noise removal, and compact signal
                 coding. A Wavelet Tour of Signal Processing is intended
                 for signal processing engineers who want to discover
                 the potential applications of recent mathematical
                 advances in time-frequency signal representations. Of
                 interest to researchers in applied mathematics, the
                 book highlights the applications of these new
                 techniques and also provides an overview of signal
                 processing problems",
}

@Article{mal:vision,
  title =        "{W}avelets for a vision",
  author =       "S. Mallat",
  journal =      PIEEE,
  volume =       "84",
  number =       "4",
  year =         "1996",
  pages =        "604--614",
  abstract =     "Early on, computer vision researchers have realized
                 that multiscale transforms are important to analyze the
                 information content of images. The wavelet theory gives
                 a stable mathematical foundation to understand the
                 properties of such multiscale algorithms. This tutorial
                 describes major applications to multiresolution search,
                 multiscale edge detection, and texture
                 discrimination.",
}

@Article{mal:zero,
  title =        "Zero-crossings of a wavelet transform",
  author =       "S. G. Mallat",
  journal =      IEEETIT,
  volume =       "37",
  number =       "4",
  year =         "1991",
  pages =        "1019--1033",
  keywords =     "signal reconstruction, wavelet transform,
                 completeness, stability, pattern recognition,
                 multiscale representation, zero-crossings, projection
                 algorithm, fast convergence, iteration, coarse-to-fine
                 stereo-matching algorithm",
  abstract =     "The completeness, stability, and application to
                 pattern recognition of a multiscale representation
                 based on zero-crossings is discussed. An alternative
                 projection algorithm is described that reconstructs a
                 signal from a zero-crossing representation, which is
                 stabilized by keeping the value of the wavelet
                 transform integral between each pair of consecutive
                 zero-crossings. The reconstruction algorithm has a fast
                 convergence and each iteration requires O(N log/sup 2/
                 (N)) computation for a signal of N samples. The
                 zero-crossings of a wavelet transform define a
                 representation which is particularly well adapted for
                 solving pattern recognition problems. As an example,
                 the implementation and results of a coarse-to-fine
                 stereo-matching algorithm are described.",
}

@Proceedings{man-hus:asymptotic,
  title =        "Asymptotic Statistics: Proceedings of the fifth Prague
                 Symposium",
  booktitle =    "Asymptotic Statistics: Proceedings of the fifth Prague
                 Symposium",
  editor =       "Petr Mandl and Marie Huskova",
  publisher =    "Physica-Verlag",
  address =      "Heidelberg",
  series =       "Contributions to Statistics",
  year =         "1994",
}

@Article{man-lee:robust,
  title =        "Robust Estimation of Background Noise and Signal
                 Detection in Climatic Time Series",
  author =       "Michael E. Mann and Jonathan M. Lees",
  journal =      "Climate Change",
  volume =       "33",
  year =         "1996",
  pages =        "409--445",
  url =          "http://love.geology.yale.edu/mtm/",
  abstract =     "We present a new technique for isolating climate
                 signals in time series with a characteristic 'red'
                 noise background which arises from temporal
                 persistence. This background is estimated by a 'robust'
                 procedure that, unlike conventional techniques, is
                 largely unbiased by the presence of signals immersed in
                 the noise. Making use of multiple-taper spectral
                 analysis methods, the technique further provides for a
                 distinction between purely harmonic (periodic) signals,
                 and broader-band ('quasiperiodic') signals. The
                 effectiveness of our signal detection procedure is
                 demonstrated with synthetic examples that simulate a
                 variety of possible periodic and quasiperiodic signals
                 immersed in red noise. We apply our methodology to
                 historical climate and paleoclimate time series
                 examples. Analysis of a approximate to 3 million year
                 sediment core reveals significant periodic components
                 at known astronomical forcing periodicities and a
                 significant quasiperiodic 100 year peak. Analysis of a
                 roughly 1500 year tree-ring reconstruction of
                 Scandinavian summer temperatures suggests significant
                 quasiperiodic signals on a near-century timescale, an
                 interdecadal 16-18 year timescale, within the
                 interannual El Ninio/Southem Oscillation (ENSO) band,
                 and on a quasibiennial timescale. Analysis of the 144
                 year record of Great Salt Lake monthly volume change
                 reveals a significant broad band of significant
                 interdecadal variability, ENSO-timescale peaks, an
                 annual cycle and its harmonics. Focusing in detail on
                 the historical estimated global-average surface
                 temperature record, we find a highly significant
                 secular trend relative to the estimated red noise
                 background, and weakly significant quasiperiodic
                 signals within the ENSO band. Decadal and quasibiennial
                 signals are marginally significant in this series.",
}

@Article{man-wal:stochastic,
  title =        "On stochastic limit and order relationships",
  author =       "H. B. Mann and A. Wald",
  journal =      AofMS,
  volume =       "14",
  year =         "1943",
  pages =        "217--226",
}

@Article{man:multifractal,
  title =        "A Multifractal Walk Down Wall Street",
  author =       "Benoit B. Mandelbrot",
  journal =      "Scientific American",
  month =        feb,
  year =         "1999",
  pages =        "50--53",
}

@Unpublished{mar-ada-joh-neu-pat:exact,
  title =        "Exact Risk Analysis of Wavelet Regression",
  author =       "S. J. Marron and S. Adak and Iain Johnstone and
                 Michael H. Neumann and P. Patil",
  year =         "1996",
  note =         "To appear in {\em Journal of Computational and
                 Graphical Statistics}",
}

@Article{mar-wil:indirect,
  title =        "Indirect estimation of {ARFIMA} and {VARFIMA} models",
  author =       "V. L. Martin and N. P. Wilkins",
  journal =      JEcon,
  volume =       "93",
  number =       "1",
  year =         "1999",
  pages =        "149--175",
  abstract =     "Indirect estimation methods are proposed for
                 estimating ARFIMA, as well as more complex VARFIMA
                 models. A general framework for conducting indirect
                 estimation of fractional models is developed that
                 covers simulation methods, choice of auxiliary model
                 and estimation algorithm. Special attention is given to
                 comparing the finite sampling properties of the
                 indirect estimator with Sowell's (1992a) exact time
                 domain maximum-likelihood estimator, the spectral
                 maximum-likelihood estimator of Fox and Taqqu (1986)
                 and the Geweke and Porter-Hudak (1983) spectral
                 regression estimator. The indirect estimator can be
                 computationally faster than the exact time domain
                 maximum-likelihood estimator while generating similar
                 small sample properties. The computational gains of the
                 indirect estimator over maximum likelihood increase as
                 the complexity of the data generating process
                 increases.",
}

@Article{mar:effective,
  title =        "Effective writing in mathematical statistics",
  author =       "J. S. Marron",
  journal =      SN,
  volume =       "53",
  number =       "1",
  year =         "1999",
  pages =        "68--75",
}

@Article{mas:application,
  title =        "The wavelet transform of stochastic processes with
                 stationary increments and its application to fractional
                 {B}rownian motion",
  author =       "Elias Masry",
  journal =      IEEETIT,
  volume =       "39",
  number =       "1",
  year =         "1993",
  pages =        "260--264",
  keywords =     "wavelet transform, stochastic processes, fractional
                 Brownian motion, random processes, wide-sense
                 stationary increments, correlation function, spectral
                 distribution, orthonormal series expansion, spectral
                 analysis",
  abstract =     "The wavelet transform of random processes with
                 wide-sense stationary increments is shown to be a
                 wide-sense stationary process whose correlation
                 function and spectral distribution are determined. The
                 second-order properties of the coefficients in the
                 wavelet orthonormal series expansion of such processes
                 is obtained. Applications to the spectral analysis and
                 to the synthesis of fractional Brownian motion are
                 given.",
}

@Article{mas:convergence,
  title =        "Convergence properties of wavelet series expansions of
                 fractional {B}rownian motion",
  author =       "Elias Masry",
  journal =      ACHA,
  volume =       "3",
  number =       "3",
  year =         "1996",
  pages =        "239--253",
  keywords =     "convergence properties, wavelet series expansions,
                 Brownian motion, approximation error, finite intervals,
                 convergence rates, signal processing",
  abstract =     "We consider the approximation of a fractional Brownian
                 motion by a wavelet series expansion at resolution
                 $2^{-l}$. The approximation error is measured in the
                 integrated mean squared sense over finite intervals and
                 we obtain its expansion as a sum of terms with
                 increasing rates of convergence. The dependence of the
                 coefficients in the expansion of the error on the scale
                 function is explicitly determined.",
}

@TechReport{mcc-per-wal:phase,
  title =        "On the Phase of Least-Asymmetric Scaling and Wavelet
                 Filters",
  author =       "Emma J. McCoy and Donald B. Percival and Andrew T.
                 Walden",
  institution =  "Dept. of Mathematics, Imperial College of Science,
                 Technology and Medicine",
  number =       "TR-95-15",
  year =         "1995",
  note =         "Submitted to {\em IEEE Transactions on Signal
                 Processing}",
  url =          "ftp://ftp.statsci.com/pub/WAVELETS/papers/wavephase.ps.gz",
  abstract =     "The advance applied to Daubechies' least-asymmetric
                 wavelet filters at each scale, in order to obtain near
                 zero phase, is derived. The appropriate advance depends
                 on whether half the length of each of the original
                 quadrature mirror filters is even or odd. The
                 departures from zero phase are illustrated.",
}

@Article{mcc-wal:long-memory,
  title =        "Wavelet Analysis and Synthesis of Stationary
                 Long-Memory Processes",
  author =       "Emma J. McCoy and Andrew T. Walden",
  journal =      JCGS,
  volume =       "5",
  number =       "1",
  year =         "1996",
  pages =        "26--56",
  abstract =     "The discrete wavelet transform (DWT) can be
                 interpreted as a filtering of a time series by a set of
                 octave band filters such that the width of each band as
                 a proportion of its center frequency is constant. A
                 long-memory process having a power spectrum that plots
                 as a straight line on log-frequency/log-power scales
                 over many octaves of frequency is intrinsically related
                 to such a structure. As an example of such processes,
                 we focus on one class of discrete-time, stationary,
                 long-memory processes, the fractionally differenced
                 Gaussian white noise processes (fdGn). We show how the
                 DWT breaks down a fdGn, and show the exact correlation
                 structure of the resulting coefficients for different
                 wavelets (Daubechies' minimum-phase and
                 least-asymmetric and Haar). The DWT is an impressive
                 ``whitening filter.'' A discrete wavelet-based scheme
                 for simulating fdGn's is discussed and is shown to be
                 equivalent to a spectral decomposition of the
                 covariance matrix of the process; however, it can be
                 carried out using only information on the nature of the
                 spectrum of the process --- that is, time-domain
                 information is not required. It produces results
                 comparable with theexact Hosking method. We then show
                 that, using wavelet methods, the spectral slope
                 parameter $d$ can be estimated as well, or better, than
                 when using the best Fourier-based method known to us,
                 namely regression on multitaper spectral ordinates.
                 Since wavelet analysis and synthesis methods can be
                 applied to a much wider variety of empirical or
                 theoretical long-memory processes, wavelet methods
                 could prove a valuable tool in the future in the
                 analysis and synthesis of stochastic processes.",
}

@PhdThesis{mcc:thesis,
  title =        "Some New Statistical Approaches to the Analysis of
                 Long Memory Processes",
  author =       "Emma J. McCoy",
  school =       "Imperial College, UK, Deptartment of Mathematics",
  year =         "1994",
  postscript =   "http://www.ma.ic.ac.uk/statistics/links/stafflinks/ejm.link/papers/report.ps.gz",
}

@TechReport{mcn-mau:applications,
  title =        "Applications of wavelet analysis for determining
                 glucose concentration of aqueous solutions using {NIR}
                 spectroscopy",
  author =       "Christopher S. McNulty and Ganapati Mauze",
  number =       "HPL-98-53",
  institution =  "Hewlett-Packard Laboratories",
  year =         "1998",
  url =          "http://www.hpl.hp.com/techreports/98/HPL-98-53.ps",
}

@Article{mee-esc:algorithm,
  title =        "An algorithm to compute the {CDF} of the product of
                 two normal random variables",
  author =       "William Q. Meeker and Luis A. Escobar",
  journal =      CSA,
  volume =       "23",
  number =       "1",
  year =         "1994",
  pages =        "271--280",
}

@Article{men:analysis,
  title =        "Analysis of turbulence in the orthonormal wavelet
                 representation",
  author =       "C. Meneveau",
  journal =      JFM,
  volume =       "232",
  year =         "1991",
  pages =        "469--520",
  keywords =     "turbulence, orthonormal wavelet, turbulent velocity
                 fields, wavelet-transformed Navier-Stokes equations,
                 kinetic energy, one-dimensional velocity signals,
                 boundary layer, turbulent wake, circular cylinder,
                 three-dimensional velocity fields, multifractal
                 scaling",
  abstract =     "A decomposition of turbulent velocity fields into
                 modes that exhibit both localization in wavenumber and
                 physical space is performed. The author reviews some
                 basic properties of such a decomposition, the wavelet
                 transform. The wavelet-transformed Navier-Stokes
                 equations are derived, and he defines new quantities
                 such as e(r,x), t(r,x) and pi (r,x) which are the
                 kinetic energy, the transfer of kinetic energy and the
                 flux of kinetic energy through scale r at position x.
                 The discrete version of e(r,x) is computed from
                 laboratory one-dimensional velocity signals in a
                 boundary layer and in a turbulent wake behind a
                 circular cylinder. The author also computes (r,x),
                 t(r,x) and pi (r,x) from three-dimensional velocity
                 fields obtained from direct numerical simulations. His
                 findings are that the localized kinetic energies become
                 very intermittent in x at small scales and exhibit
                 multifractal scaling. The transfer and flux of kinetic
                 energy are found to fluctuate greatly in physical space
                 for scales between the energy containing scale and the
                 dissipative scale.",
}

@InProceedings{men:mixed,
  title =        "Wavelet analysis of turbulence: {T}he mixed energy
                 cascade",
  author =       "C. Meneveau",
  pages =        "251--264",
  crossref =     "far-hun-vas:wavelets",
  keywords =     "wavelets, turbulence",
  abstract =     "The wavelet-transformed Navier-Stokes equations are
                 used to define quantities such as the transfer of
                 kinetic energy and the flux of kinetic energy by scale
                 and position. Direct numerical simulations are
                 performed which show large spatial variability at every
                 scale and non-Gaussian statistics. The local energy
                 flux exhibits large spatial intermittency and is often
                 negative, indicating local inverse cascades.",
}

@Article{mey-sel-taq:wavelets,
  title =        "Wavelets, generalized white noise and fractional
                 integration: {T}he synthesis of fractional {B}rownian
                 motion",
  author =       "Y. Meyer and F. Sellan and M. S. Taqqu",
  journal =      JFAA,
  volume =       "5",
  number =       "5",
  year =         "1999",
  pages =        "465--494",
  abstract =     "We provide an almost sure convergent expansion of
                 fractional Brownian motion in wavelets which
                 decorrelates the high frequencies. Our approach
                 generalizes Levy's midpoint displacement technique
                 which is used to generate Brownian motion. The
                 low-frequency terms in the expansion involve all
                 independent fractional Brownian motion evaluated at
                 discrete times or, alternatively, partial sums of a
                 stationary fractional ARIMA time series. The wavelets
                 fill in the gaps and provide the necessary high
                 frequency corrections We also obtain a way of
                 constructing an arbitrary number of non-Gaussian
                 continuous time processes whose second order properties
                 are the same as those of fractional Brownian motion.",
}

@Book{mey-roq:progress,
  title =        "Progress in Wavelet Analysis and Applications",
  booktitle =    "Progress in Wavelet Analysis and Applications",
  editor =       "Yves Meyer and Sylvie Roques",
  publisher =    "Editions Fronti{\`e}res",
  address =      "Paris",
  year =         "1993",
  pages =        "785",
}

@Book{mey:algorithms,
  title =        "Wavelets: Algorithms \& Applications",
  author =       "Yves Meyer",
  publisher =    SIAM,
  address =      "Philadelphia",
  year =         "1993",
  keywords =     "Wavelets, Mathematics",
  note =         "Translated and revised by Robert D. Ryan",
  loc =          "QA403.3 .M4913 1993",
}

@Book{mey:wavelets,
  title =        "Wavelets and Operators",
  author =       "Yves Meyer",
  publisher =    "Cambridge University Press",
  series =       "Cambridge Studies in Advanced Mathematics 37",
  year =         "1992",
  note =         "Translated to English by D. H. Salinger",
  ISBN =         "0-521-42000-8",
  keywords =     "Fourier Series and Integrals, Filtering and Sampling /
                 Multiresolution Approximation of L2(Rn) / Orthonormal
                 Wavelet Bases / Non-orthogonal Wavelets / Wavelets the
                 Hardy Space H1 and Its Dual BMO / Wavelets and Spaces
                 of Functions and Distributions",
  url =          "http://www.cup.org/Titles/42/0521420008.html",
  abstract =     "The first book in English to provide a comprehensive
                 account of the mathematical theory of wavelets which
                 has proved to be a powerful tool for harmonic analysts,
                 and an alternative to the standard theory of Fourier
                 analysis",
}

@Article{mih-etal:low-complexity,
  title =        "Low-complexity image denoising based on statistical
                 modeling of wavelet coefficients",
  author =       "M. K. Mihcak and I. Kozintsev and K. Ramchandran and
                 P. Moulin",
  journal =      IEEESPL,
  volume =       "6",
  number =       "12",
  year =         "1999",
  pages =        "300--303",
  abstract =     "We introduce a simple spatially adaptive statistical
                 model for wavelet image coefficients and apply it to
                 image denoising, Our model is inspired by a recent
                 wavelet image compression algorithm, the
                 estimation-quantization (EQ) coder. We model wavelet
                 image coefficients as zero-mean Gaussian random
                 variables with high local correlation. We assume a
                 marginal prior distribution on wavelet coefficients
                 variances and estimate them using an approximate
                 maximum a posteriori probability rule. Then we apply an
                 approximate minimum mean squared error estimation
                 procedure to restore the noisy wavelet image
                 coefficients. Despite the simplicity of our method,
                 both in its concept and implementation, our denoising
                 results are among the best reported in the
                 literature.",
}

@Article{mor-per:mbdtw,
  title =        "Minimum-bandwidth discrete-time wavelets",
  author =       "J. M. Morris and R. Peravali",
  journal =      SP,
  volume =       "76",
  number =       "2",
  year =         "1999",
  pages =        "181--193",
  keywords =     "minimum bandwidth wavelet transform discrete-time
                 wavelets adaptive simulated annealing",
  abstract =     "In this paper we present a class of minimum-bandwidth,
                 discrete-time orthonormal wavelets (MBDTWs), The
                 wavelets were generated via the filter bank framework
                 and were optimized using the global optimization
                 technique, adaptive simulated annealing (ASA). The
                 objective function is the average normalized bandwidth
                 of the wavelets over all scales as obtained from the
                 filter bank structure. We tabulate the wavelet-defining
                 low-pass filter coefficients {g(n)} for filter lengths
                 of N = 4, 8, 10, 12, 14, 16, 18, 24 and 32 and for L =
                 2, 3 and 4. We provide comparisons with Daubeohies'
                 discrete wavelets and other classes of optimum
                 wavelets. Finally, we present examples that demonstrate
                 the advantage of our MBDTWs for certain narrowband
                 applications: de-noising of an ECG signal, and
                 compression of an ECG signal and a bird call signal. We
                 compare the performance of our wavelets in these
                 examples with that of Daubechies' least-asymmetric
                 wavelets which are closest to the MBDTWs with respect
                 to our bandwidth measure.",
}

@InProceedings{mor:from,
  title =        "From Fourier to Wavelet Analysis of Time Series",
  author =       "Pedro A. Morettin",
  booktitle =    "Proceedings in Computational Statistics",
  editor =       "A. Prat",
  year =         "1996",
  pages =        "111--122",
}

@Article{mou:power,
  title =        "Wavelet Thresholding Techniques for Power Spectrum
                 Estimation",
  author =       "Pierre Moulin",
  journal =      IEEETSP,
  volume =       "42",
  number =       "11",
  year =         "1994",
  pages =        "3126--3136",
  url =          "ftp://flash.bellcore.com/pub/moulin/wavSE.tar.Z",
  abstract =     "Estimation of the power spectrum S(f) of a stationary
                 random process can be viewed as a nonparametric
                 statistical estimation problem. We introduce a
                 nonparametric approach based on a wavelet
                 representation for the logarithm of the unknown S(f).
                 This approach offers the ability to capture
                 statistically significant components of ln S(f) at
                 different resolution levels and guarantees
                 nonnegativity of the spectrum estimator. The spectrum
                 estimation problem is set up as a problem of inference
                 on the wavelet coefficients of a signal corrupted by
                 additive non-Gaussian noise. We propose a wavelet
                 thresholding technique to solve this problem under
                 specified noise/resolution tradeoffs and show that the
                 wavelet coefficients of the additive noise may be
                 treated as independent random variables. The thresholds
                 are computed using a saddle-point approximation to the
                 distribution of the noise coefficients.",
}

@TechReport{mul-vid:density-estimation,
  title =        "Bayesian Inference with Wavelets: {D}ensity
                 Estimation",
  author =       "Peter M{\"u}ller and Brani Vidakovic",
  year =         "1995",
  number =       "95-34",
  institution =  "Institute of Statisics and Decision Sciences, Duke
                 University",
  url =          "http://www.isds.duke.edu/~brani/papers/ModMixWav.ps",
}

@TechReport{mul-vid:MCMC,
  title =        "{MCMC} Methods in Wavelet Shrinkage: {N}on-Equally
                 Spaced Regression, Density and Spectral Density
                 Estimation",
  author =       "Peter M{\"u}ller and Brani Vidakovic",
  year =         "1999",
  number =       "99-01",
  institution =  "Institute of Statisics and Decision Sciences, Duke
                 University",
  url =          "ftp://ftp.isds.duke.edu/pub/WorkingPapers/99-01.ps",
}

@Unpublished{mur-aus:using,
  title =        "Using the Wavelet Transform for Multivariate Data
                 Analysis and Time Series Forecasting",
  author =       "Fionn Murtagh and Alex Aussem",
  year =         "1996",
  note =         "Proc. IFCS'96, Kobe, Springer-Verlag, accepted
                 (subject to minor revision)",
  url =          "ftp://ftp.infm.ulst.ac.uk/pub/Papers/neural-nets/kobe.ps",
}

@Unpublished{mur:wedding,
  title =        "Wedding the Wavelet Transform and Multivariate Data
                 Analysis",
  author =       "Fionn Murtagh",
  year =         "1996",
  note =         "To appear {\em Journal of Classification}",
  url =          "ftp://ftp.infm.ulst.ac.uk/pub/Papers/neural-nets/wt-mda-new.ps",
}

@Book{mye:book,
  title =        "Classical and Modern Regression with Applications",
  author =       "Raymond H. Myers",
  edition =      "2",
  publisher =    "PWS--KENT",
  address =      "Boston",
  series =       "The Duxbury Advanced Series in Statistics and Decision
                 Sciences",
  year =         "1990",
}

@TechReport{nas-sap-saw:modelling,
  title =        "Statistical modelling of time series using
                 non-decimated wavelet representations",
  author =       "G. P. Nason and T. Sapatinas and A. Sawczenko",
  institution =  "Department of Mathematics, University of Bristol,
                 Bristol",
  year =         "1997",
  url =          "http://www.stats.bris.ac.uk/pub/reports/Wavelets/smotsunwr.ps.gz",
}

@InProceedings{nas-sil:stationary,
  title =        "The Stationary Wavelet Transform and some Statistical
                 Applications",
  author =       "Guy P. Nason and Bernard W. Silverman",
  pages =        "281--300",
  url =          "http://www.stats.bris.ac.uk:81/pub/reports/Silverman/swtsa.ps.gz",
  crossref =     "ant-opp:wavelets",
}

@Article{nas-sil:transform,
  title =        "The Discrete Wavelet Transform in {S}",
  author =       "Guy P. Nason and Bernard W. Silverman",
  journal =      JCGS,
  volume =       "3",
  number =       "2",
  pages =        "163--191",
  year =         "1994",
  url =          "http://www.stats.bris.ac.uk:81/pub/reports/Wavelets/tdwtis.ps.gz",
  keywords =     "Curve estimation; Image compression; Nonparametric
                 regression; Smoothing; Software; Statistical
                 algorithms; Thresholding",
  abstract =     "The theory of wavelets has recently undergone a period
                 of rapid development. We introduce a software package
                 called {\tt wavethresh} that works within the
                 statistical language S to perform one- and
                 two-dimensional discrete wavelet transforms. The
                 transforms and their inverses can be computed using any
                 particular wavelet selected from a range of different
                 families of wavelets. Pictures can be drawn of any of
                 the one- or two-dimensional wavelets available in the
                 package. The wavelet coefficients can be presented in a
                 variety of ways to aid in the interpretation of data.
                 The package's wavelet transform ``engine'' is written
                 in C for speed and the object-oriented functionality of
                 S makes {\tt wavethresh} easy to use. We provide a
                 tutorial introduction to wavelets and the {\tt
                 wavethresh} software. We also discuss how the software
                 may be used to carry out nonlinear regression and image
                 compression. In particular, thresholding of wavelet
                 coefficients is a method for attempting to extract
                 signal from noise and {\tt wavethresh} includes
                 functions to perform thresholding according to methods
                 in the literature.",
}

@InCollection{nas-sil:wavelets,
  title =        "Wavelets for regression and other statistical
                 problems",
  author =       "Guy P. Nason and Bernard W. Silverman",
  booktitle =    "Smoothing and Regression: Approaches, Computation and
                 Application",
  editor =       "M. G. Schimek",
  publisher =    "Wiley",
  year =         "1997",
}

@Article{nas-von:witsa,
  title =        "Wavelets in time series analysis",
  author =       "Guy P. Nason and Rainer {von Sachs}",
  journal =      PTRSLA,
  volume =       "357",
  number =       "1760",
  year =         "1999",
  pages =        "2511--2526",
}

@Unpublished{nas-von-kro:evolutionary,
  title =        "Wavelet processes and adaptive estimation of the
                 evolutionary wavelet spectrum",
  author =       "Guy P. Nason and Rainer {von Sachs} and Gerald
                 Kroisandt",
  year =         "2000",
  url =          "http://playfair.Stanford.EDU/reports/rvs/NvSK.ps.Z",
  note =         "{\em Journal of the Royal Statistical Society Series
                 B}, to appear",
}

@InProceedings{nas:choice,
  title =        "Choice of the threshold parameter in wavelet function
                 estimation",
  author =       "Guy P. Nason",
  pages =        "261--280",
  crossref =     "ant-opp:wavelets",
}

@TechReport{nas:regression,
  title =        "Wavelet regression by cross-validation",
  author =       "Guy P. Nason",
  year =         "1994",
  institution =  "Deptartment of Mathematics, University of Bristol",
  url =          "http://www.stats.bris.ac.uk:81/pub/reports/Wavelets/wvcx.ps.gz",
  pages =        "45",
  keywords =     "wavelets",
  abstract =     "This paper is about using wavelets for regression. The
                 main aim is to introduce and develop a cross-validation
                 method for selecting a wavelet regression threshold
                 that produces good estimates with respect to $L_2$
                 error. The selected threshold determines which
                 coefficients to keep in an orthogonal wavelet expansion
                 of noisy data and acts in a similar way to a smoothing
                 parameter in non-parametric regression.",
}

@Article{nas:shrinkage,
  title =        "Wavelet shrinkage by cross-validation",
  author =       "Guy P. Nason",
  journal =      JRSSB,
  volume =       "58",
  year =         "1996",
  pages =        "463--479",
  url =          "http://www.stats.bris.ac.uk:81/pub/reports/Wavelets/wvcxPAPER.ps.gz",
  abstract =     "Wavelets are orthonormal basis functions with special
                 properties that show potential in many areas of
                 mathematics and statistics. This paper concentrates on
                 the estimation of functions and images from noisy data
                 by using wavelet shrinkage. A modified form of twofold
                 cross-validation is introduced to choose a threshold
                 for wavelet shrinkage estimators operating on data sets
                 of length a power of 2. The cross-validation algorithm
                 is then extended to data sets of any length and to
                 multidimensional data sets.The algorithms are compared
                 with established threshold choosers by using
                 simulation. An application to a real data set arising
                 from anaesthesia is presented.",
  keywords =     "ADAPTIVE ESTIMATION ANAESTHETICS NONPARAMETRIC
                 REGRESSION SMOOTHING PARAMETER SPATIAL ADAPTATION
                 THRESHOLD",
}

@Article{nas:wavelets,
  title =        "Wavelets",
  author =       "Guy P. Nason",
  journal =      "New Electronics",
  month =        apr,
  year =         "1997",
  url =          "http://www.stats.bris.ac.uk:81/pub/reports/Wavelets/ne.ps.gz",
}

@Unpublished{nav-bro:dependence,
  title =        "Dependence Structure of Random Wavelets Coefficients
                 in function of higher Cumulants for Non-Gaussian and
                 Non-Linear processes",
  author =       "Philippe Naveau and Peter Brockwell",
  year =         "1999",
  note =         "Geophysical Statistics Project, National Center for
                 Atmospheric Research",
}

@Unpublished{nav-etal:exploratory,
  title =        "Exploratory statistical analysis of tropical oceanic
                 convection using discrete wavelet transforms",
  author =       "Philippe Naveau and Mitchell Moncrieff and Jun-Ichi
                 Yano and Xiaoqing Wu",
  year =         "1999",
  note =         "Submitted in the book ``Case Studies in Statistics and
                 the Atmospheric Sciences''",
}

@Article{nen-rid-zei:infrared,
  title =        "Wavelet analysis of low altitude infrared transmission
                 in the coastal environment",
  author =       "B. D. Nener and T. A. Ridsdill-Smith and C. Zeisse",
  journal =      "Infrared Physics and Technology",
  volume =       "40",
  number =       "5",
  year =         "1999",
  pages =        "399--409",
  abstract =     "Analysis of medium and long wavelength infrared light
                 transmission measurements collected during an intensive
                 experimental investigation over San Diego Bay, CA, USA,
                 has been performed using Morlet wavelets. Wavelet
                 analysis shows locally periodic trends in signals and
                 shows how these trends evolve in time. The analysis has
                 shown the effect of the relative humidity and the
                 windspeed on the transmission in both mid- and
                 long-wave bands of the LR. The effect of air mass
                 parameter does not appear to be strongly correlated.
                 The wavelet representations of the data given in the
                 figures provide a useful overview of the effects of the
                 atmosphere on infrared transmission.",
}

@Article{neu-von:anisotropic,
  title =        "Wavelet thresholding in anisotropic function classes
                 and application to adaptive estimation of evolutionary
                 spectra",
  author =       "Michael H. Neumann and Ranier von Sachs",
  journal =      AofS,
  volume =       "25",
  number =       "1",
  year =         "1997",
  pages =        "38--76",
}

@InCollection{neu-von:beyond,
  title =        "Wavelet thresholding: {B}eyond the {G}aussian {I.I.D}
                 situation",
  author =       "Michael H. Neumann and Ranier von Sachs",
  pages =        "301--329",
  crossref =     "ant-opp:wavelets",
}

@TechReport{neu:spectral94,
  title =        "Spectral Density Estimation via Nonlinear Wavelet
                 Methods for Stationary Non-Gaussian Time Series",
  author =       "Michael H. Neumann",
  year =         "1994",
  institution =  "Statistics Research Report SRR 028-94, CMA, Australian
                 National University, Canberra",
  url =          "http://wilton.anu.edu.au/research.reports/94srr.html",
}

@Article{neu:spectral96,
  title =        "Spectral Density Estimation via Nonlinear Wavelet
                 Methods for Stationary Non-Gaussian Time Series",
  author =       "Michael H. Neumann",
  journal =      JTSA,
  volume =       "17",
  number =       "6",
  year =         "1996",
  pages =        "601--633",
  abstract =     "In the present paper we consider nonlinear wavelet
                 estimators of the spectral density f of a zero mean,
                 not necessarily Gaussian, stochastic process, which is
                 stationary in the wide sense. It is known in the case
                 of Gaussian regression that these estimators outperform
                 traditional linear methods if the degree of smoothness
                 of the regression function varies considerably over the
                 interval of interest. Such methods are based on a
                 nonlinear treatment of empirical coefficients that
                 arise from an orthonormal series expansion according to
                 a wavelet basis. The main goal of this paper is to
                 transfer these methods to spectral density estimation.
                 This is done by showing the asymptotic normality of
                 certain empirical coefficients based on the tapered
                 periodogram.Using these results we can show the risk
                 equivalence to the Gaussian case for monotone
                 estimators based on such empirical coefficients. The
                 resulting estimator of f keeps all interesting
                 properties such as high spatial adaptivity that are
                 already known for wavelet estimators in the case of
                 Gaussian regression. It turns out that appropriately
                 tuned versions of this estimator attain the optimal
                 uniform rate of convergence of their L 2 risk in a wide
                 variety of Besov smoothness classes, including classes
                 where linear estimators (kernel, spline) are not able
                 to attain this rate. Some simulations indicate the
                 usefulness of the new method in cases of high spatial
                 inhomogeneity.",
  keywords =     "Spectral density estimation wavelet estimators
                 nonlinear wavelet shrinkage asymptotic normality large
                 deviations",
}

@Article{new:analysis1,
  title =        "{W}avelet analysis of vibration, {P}art {I}: theory",
  journal =      "Transactions of the ASME. Journal of Vibration and
                 Acoustics",
  volume =       "116",
  number =       "4",
  year =         "1994",
  pages =        "409--416",
  author =       "D. E. Newland",
  abstract =     "Wavelets provide a new tool for the analysis of
                 vibration records. They allow the changing spectral
                 composition of a nonstationary signal to be measured
                 and presented in the form of a time-frequency map. The
                 purpose of this paper, which is Part I of a pair, is to
                 introduce and review the theory of orthogonal wavelets
                 and their application to signal analysis. It includes
                 the theory of dilation wavelets, which have been
                 developed over a period of about ten years, and of
                 harmonic wavelets which have been proposed recently by
                 the author. Part II is about presenting the results on
                 wavelet maps and gives a selection of examples. The
                 papers will interest those who work in the field of
                 vibration measurement and analysis and who are in
                 positions where it is necessary to understand and
                 interpret vibration data.",
  keywords =     "wavelet analysis. vibration. changing spectral
                 composition. nonstationary signal. time-frequency map.
                 orthogonal wavelets. signal analysis. dilation
                 wavelets. harmonic wavelets. wavelet maps. vibration
                 measurement.",
}

@Article{new:analysis2,
  title =        "{W}avelet analysis of vibration, {P}art 2: wavelet
                 maps",
  journal =      "Transactions of the ASME. Journal of Vibration and
                 Acoustics",
  volume =       "116",
  number =       "4",
  year =         "1994",
  pages =        "417--25",
  author =       "D. E. Newland",
  abstract =     "For pt. 1, see ibid., vol. 116, p. 409-16, (1994).
                 Wavelet maps provide a graphical picture of the
                 frequency composition of a vibration signal. This
                 paper, which is Part 2 of a pair, describes their
                 construction and properties. In the case of harmonic
                 wavelets, there are close similarities between wavelet
                 maps and sonograms. A range of practical examples
                 illustrate how the wavelet method may be applied to
                 vibration analysis and some of its advantages.",
  keywords =     "wavelet maps. graphical picture. frequency
                 composition. vibration signal. harmonic wavelets.
                 sonograms. vibration analysis.",
}

@Book{new:book3,
  title =        "An Introduction to Random Vibrations, Spectral \&
                 Wavelet Analysis",
  author =       "David Edward Newland",
  edition =      "3",
  publisher =    "Longman Scientific \& Technical",
  address =      NY,
  year =         "1993",
  pages =        "477",
  ISBN =         "0-470-22153-4",
  keywords =     "Random vibration, Spectral theory, Mathematics, Data
                 processing, Wavelets",
}

@Article{new:harmonic,
  title =        "{H}armonic wavelet analysis",
  journal =      PRSLA,
  volume =       "443",
  number =       "1917",
  year =         "1993",
  pages =        "203--225",
  author =       "D. E. Newland",
  keywords =     "harmonic wavelet. frequency spectrum. octave band.
                 fast Fourier transform. Fourier coefficients. FFT.
                 inverse transform.",
  abstract =     "A new harmonic wavelet is suggested. Unlike wavelets
                 generated by discrete dilation equations, whose shape
                 cannot be expressed in functional form, harmonic
                 wavelets have the simple structure w(x)=(exp(i4 pi
                 x)-exp(i2 pi x))/i2 pi x. This function w(x) is
                 concentrated locally around x=0, and is orthogonal to
                 its own unit translations and octave dilations. Its
                 frequency spectrum is confined exactly to an octave
                 band so that it is compact in the frequency domain
                 (rather than in the x domain). An efficient
                 implementation of a discrete transform using this
                 wavelet is based on the fast Fourier transform (FFT).
                 Fourier coefficients are processed in octave bands to
                 generate wavelet coefficients by an orthogonal
                 transformation which is implemented by the FFT. The
                 same process works backwards for the inverse
                 transform.",
}

@Article{new:properties,
  title =        "Some properties of discrete wavelet maps",
  author =       "D. E. Newland",
  journal =      PEM,
  volume =       "9",
  number =       "1",
  year =         "1994",
  pages =        "59--69",
}

@Article{nin:estimation,
  title =        "Estimation of 1/f noise",
  author =       "B. Ninness",
  journal =      IEEETIT,
  volume =       "44",
  number =       "1",
  pages =        "32--46",
  year =         "1998",
  keywords =     "flicker noise fractional Brownian motion Hurst
                 exponent maximum-likelihood estimation 1/f noise
                 wavelet analysis",
  abstract =     "Several models have emerged for describing 1/f(gamma)
                 noise processes. Based on these, various techniques for
                 estimating the properties of such processes have been
                 developed. This paper provides theoretical analysis of
                 a new wavelet-based approach which has the advantages
                 of having low computational complexity and being able
                 to handle the case where the 1/f(gamma) noise might be
                 embedded in a further white-noise process. However, the
                 analysis conducted here shows that these advantages are
                 balanced by the fact that the wavelet-based scheme is
                 only consistent for spectral exponents gamma in the
                 range gamma is an element of (0, 1). This is in
                 contradiction to the results suggested in previous
                 empirical studies. When gamma is an element of (0, 1)
                 this paper also establishes that wavelet-based
                 maximum-likelihood methods are asymptotically Gaussian
                 and efficient. Finally, the asymptotic rate of
                 mean-square convergence of the parameter estimates Is
                 established and is shown to slow as gamma approaches
                 one. Combined with a survey of non-wavelet-based
                 methods, these new results give a perspective on the
                 various tradeoffs to be considered when modeling and
                 estimating 1/f(gamma) noise processes",
}

@Unpublished{now:shift-invariant,
  title =        "Shift invariant wavelet-based statistical models and
                 $1/f$ processes",
  author =       "R. D. Nowak",
  note =         "IEEE DSP Workshop, Bryce Canyon, UT",
  year =         "1998",
}

@Unpublished{ode-bur:class,
  title =        "New Class of Wavelets for Signal Approximation",
  author =       "Jan E. Odegard and C. Signey Burrus",
  note =         "Department of Electrical and Computer Engineering,
                 Rice University",
  year =         "1996",
  email =        "odegard@rice.edu, csb@rice.edu",
}

@InProceedings{ogd-che:abrupt,
  title =        "Testing for Abrupt Jumps with Wavelets",
  author =       "R. Todd Ogden and Cheng Cheng",
  booktitle =    "Proceedings of the 1997 Conference on the Interface of
                 Statistics and Computer Science",
  year =         "1997",
}

@Article{ogd-hil:2D,
  title =        "Data Analytic Wavelet Threshold Selection in 2-{D}
                 Signal Denoising",
  author =       "R. Todd Ogden and M. Hilton",
  journal =      IEEETSP,
  volume =       "45",
  number =       "2",
  year =         "1997",
  pages =        "496--500",
  url =          "http://www.stat.sc.edu/~ogden/papers/technote.ps",
  abstract =     "A data adaptive scheme for wavelet shrinkage-based
                 noise removal is developed. The method involves a
                 statistical test of hypothesis that takes into account
                 the wavelet coefficients' magnitudes and relative
                 positions. The amount of smoothing performed during
                 noise removal is controlled by the user-supplied
                 confidence level of the tests.",
}

@InBook{ogd-lyn:bayesian,
  title =        "Bayesian analysis of change-point models",
  authors =      "R. Todd Ogden and James D. Lynch",
  crossref =     "mul-vid:biwbm",
  pages =        "???--???",
  url =          "http://www.stat.sc.edu/~ogden/papers/springer4.ps",
}

@Article{ogd-par:change-point,
  title =        "Change-point Approach to Data Analytic Wavelet
                 Thresholding",
  author =       "R. Todd Ogden and Emanuel Parzen",
  journal =      SC,
  volume =       "6",
  number =       "2",
  year =         "1996",
  pages =        "93--99",
  url =          "http://www.stat.sc.edu/~ogden/papers/datana.ps",
}

@Article{ogd-par:data-dependent,
  title =        "Data Dependent Wavelet Thresholding in Nonparametric
                 Regression with Change-point Applications",
  author =       "R. Todd Ogden and Emanuel Parzen",
  journal =      CSDA,
  volume =       "22",
  year =         "1996",
  pages =        "53--70",
  url =          "http://www.stat.sc.edu/~ogden/papers/datdep.ps",
}

@Unpublished{ogd:bayesian,
  title =        "Wavelets in {B}ayesian Change-Point Analysis",
  author =       "R. Todd Ogden",
  note =         "Department of Statistics, University of South
                 Carolina",
  year =         "1996",
  url =          "http://www.stat.sc.edu/~ogden/papers/bayes.ps",
}

@Book{ogd:book,
  title =        "Essential Wavelets for Statistical Applications and
                 Data Analysis",
  author =       "R. Todd Ogden",
  year =         "1996",
  publisher =    "Birkhauser",
  address =      "Boston",
  url =          "http://www.birkhauser.com/cgi-win/ISBN/0-8176-3864-4",
  abstract =     "Exciting new developments in wavelet theory have
                 attracted much attention and sparked new research in
                 many fields of applied mathematics. New tools are
                 available for efficient data compression, image
                 analysis, and signal processing, and there is a great
                 deal of activity in developing new wavelet methods. The
                 same features that make wavelets useful in these fields
                 also make wavelets a natural and attractive choice in
                 many areas of statistical data analysis. {\em Essential
                 Wavelets for Statistical Applications and Data
                 Analysis} presents an accesible, introductory survey
                 for new wavelet analysis tools and how they can be
                 applied to fundamental data analysis problems. A
                 variety of problems in statistics are discussed in a
                 non-theoretical style, with an emphasis on
                 understanding of wavelet methods. The only technical
                 prerequisite is basic knowledge of undergraduate
                 calculus, linear algebra, and basic statistical
                 theory.",
}

@Article{ogd:preconditioning,
  title =        "On Preconditioning the Data for the Wavelet Transform
                 When the Sample Size is Not a Power of Two",
  author =       "R. Todd Ogden",
  journal =      CSB,
  volume =       "26",
  year =         "1997",
  pages =        "267--285",
  url =          "http://www.stat.sc.edu/~ogden/papers/notpow2.ps",
}

@PhdThesis{ogd:thesis,
  title =        "Wavelet Thresholding in Nonparametric Regression with
                 Change-Point Applications",
  author =       "R. Todd Ogden",
  school =       "Texas A\&M University",
  year =         "1994",
  postscript =   "http://www.stat.sc.edu/~ogden/diss.ps",
}

@Article{ohs-iji-kur:online,
  title =        "Online detection of pulse sequence in random noise
                 using a wavelet",
  author =       "A Ohsumi and H. Ijima and T Kuroishi",
  journal =      IEEETSP,
  volume =       "47",
  number =       "9",
  pages =        "2526--2531",
  year =         "1999",
  abstract =     "Two types of wavelet-based algorithms are proposed for
                 an online detection of a train of unknown pulse signals
                 corrupted by random noise. The mechanism of detecting
                 singularities hidden in the noisy observation data is
                 analyzed, and the performance of the proposed signal
                 detectors is evaluated. Simulation studies are provided
                 to confirm the effectiveness of the algorithms.",
}

@Unpublished{omb-etal:automatic,
  title =        "Automatic Statistical Analysis of Bivariate
                 Non-Stationary Time Series",
  author =       "Hernando C. Ombao and Jonathan A. Raz and Rainer {von
                 Sachs} and Beth A. Malow",
  year =         "1999",
  note =         "Submitted to {\em JASA}",
}

@Article{oon:detecting,
  title =        "A Wavelet Method for Detecting {S}-Waves in Seismic
                 Data",
  author =       "P. J. Oonicnx",
  journal =      "Computational Geosciences",
  volume =       "3",
  pages =        "111--134",
  year =         "1999",
}

@Article{pan-fan:wavelet-spectrum,
  title =        "Discrete wavelet transform power spectrum estimator",
  author =       "Jes{\'u}s Pando and Li-Zhi Fang",
  journal =      PRE,
  volume =       "57",
  number =       "3",
  year =         "1998",
  pages =        "3593--3601",
  url =          "http://ojps.aip.org/PLEEE8-bt/html/57_3.html",
  keywords =     "nucleus-nucleus collisions high-energies distributions
                 fluctuations turbulence",
  abstract =     "A method for measuring the spectrum of a density field
                 by the discrete wavelet transform (DWT) is studied. We
                 show how the Fourier power spectrum can be detected by
                 using the wavelet function coefficients (WFC) of the
                 DWT. This method can successfully measure the power
                 spectrum in samples for which traditional methods often
                 fail because the samples are finite sized, have a
                 complex geometry, or are varyingly sampled. We
                 demonstrate that the spectrum features, such as the
                 power law index, the magnitude, and the typical scales
                 can be determined by the DWT reconstructed spectrum. We
                 apply this method to analyze the power spectrum of the
                 spatial distribution of the Ly-alpha clouds. The two
                 popular data sets used for the spectrum detection have
                 quite different geometries and samplings, yet the
                 one-dimensional (1D) power spectra and their 3D
                 reconstruction given by the DWT estimator show the same
                 features. The analysis makes clear that the DWT
                 estimator is a sensitive tool in revealing common and
                 physical properties from diverse data sets.",
}

@Article{pan-wan:stochastic,
  title =        "A Stochastic Nonlinear Regression Estimator Using
                 Wavelets",
  author =       "Zuohong Pan and Xiaodi Wang",
  journal =      CE,
  volume =       "11",
  number =       "1-2",
  year =         "1998",
  pages =        "89--102",
  keywords =     "capital markets empirical studies including
                 regulation",
  abstract =     "A new wavelet-based estimator is introduced which
                 combines the state-space model with the wavelet
                 transform in an effort to explore the stock market
                 inefficiency. The new estimator possesses some superior
                 qualities that are illustrated through its actual
                 performance in forecasting the S&P 500.",
}

@Article{pap-sik-wei:characterization,
  title =        "The characterization of low pass filters and some
                 basic properties of wavelets, scaling functions and
                 related concepts",
  author =       "M. Papadakis and H. \v{S}iki\'{c} and G. Weiss",
  journal =      JFAA,
  volume =       "5",
  number =       "5",
  year =         "1999",
  pages =        "495--521",
  abstract =     "The ``classical'' wavelets, those psi is an element of
                 L-2(R) such that {2(j/2)psi(2(j)x - k)}, j, k is an
                 element of Z, is an orthonormal basis for L-2(R), are
                 known to be characterized by two simple equations
                 satisfied by <(psi)over cap>. The ``multiresolution
                 analysis'' wavelets (briefly, the MRA wavelets) have a
                 simple characterization and so do the scaling functions
                 that produce these wavelets. Only certain smooth
                 classes of the low pass filters that are determined by
                 these scaling functions, however, appear to be
                 characterized in the literature (see Chapter 7 of [3]
                 for an account of these matters). In this paper we
                 present a complete characterization of all these
                 filters. This somewhat technical result does provide a
                 method for simple constructions of low pass filters
                 whose only smoothness assumption is a Holder condition
                 at the origin. We also obtain a characterization of all
                 scaling sets and, in particular a description of all
                 bounded scaling sets as well as a detailed description
                 of the class of scaling functions.",
}

@InProceedings{pap-sol-was:segmentation,
  title =        "Segmentation-independent estimates of turbulence
                 parameters",
  author =       "G. C. Papanicolaou and Knut S{\o}lna and Donald C.
                 Washburn",
  booktitle =    "Airborne Laser Advanced Technology",
  editor =       "T. D. Steiner and P. H. Merritt",
  series =       "Proceedings of the SPIE",
  volume =       "3381",
  pages =        "256--267",
  year =         "1998",
  url =          "ftp://math.Stanford.EDU/pub/papers/papanicolaou/maint.ps.gz",
  abstract =     "We present a new approach for analyzing local power
                 law processes and apply it to temperature measurements
                 from the upper atmosphere. We segment the data and use
                 the wavelet scale spectrum to estimate the parameters
                 of the power law, the scale factor and the exponent.
                 These parameters vary from segment to segment. Part of
                 this variation is due to the non-stationary of the
                 data. Another part is due to estimation errors that
                 depend on the segmentation. In this paper show how to
                 remove effectively these segmentation dependent
                 variations.",
}

@Unpublished{pap-sol:local,
  title =        "Wavelet based estimation of local {K}olmogorov
                 turbulence",
  author =       "G. Papanicolaou and K. S{\o}lna",
  year =         "1999",
  url =          "ftp://math.Stanford.EDU/pub/papers/papanicolaou/main.ps.gz",
  note =         "Submitted to the {\em Journal of the American
                 Statistical Association}",
}

@Article{par-man:interannual,
  title =        "Interannual Temperature Events and Shifts in Global
                 Temperature: {A} ``Multiwavelet'' Correlation
                 Approach",
  author =       "Jeffrey Park and Michael E. Mann",
  journal =      EI,
  volume =       "4",
  year =         "2000",
  pages =        "???--???",
}

@InProceedings{pat-sim:texture,
  title =        "Texture modelling and synthesis using joint statistics
                 of complex wavelet coefficients",
  author =       "J. Portilla and E. P. Simoncelli",
  booktitle =    "IEEE Workshop on Statistical and Computational
                 Theories of Vision",
  year =         "1999",
  url =          "ftp://ftp.cns.nyu.edu/pub/eero/portilla99a.ps.gz",
  abstract =     "We present a statistical characterization of texture
                 images in the context of an overcomplete complex
                 wavelet transform. The characterization is based on
                 empirical observations of statistical regularities in
                 such images, and parameterized by (1) the local
                 auto-correlation of the coefficients in each subband;
                 (2) both the local auto-correlation and
                 cross-correlation of coefficient magnitudes at other
                 orientations and spatial scales; and (3) the first few
                 moments of the image pixel histogram. We develop an
                 efficient algorithm for synthesizing random images
                 subject to these constraints using alternated
                 projections, and demonstrate its effectiveness on a
                 wide range of synthetic and natural textures. In
                 particular, we show that many important structural
                 elements in textures (e.g., edges, repeated patterns or
                 alternated patches of simpler texture), can be captured
                 through joint second order statistics of the
                 coefficient magnitudes. We also show the flexibility of
                 the representation, by applying to a variety of tasks
                 which can be viewed as constrained image synthesis
                 problems, such as spatial and spectral extrapolation.",
}

@TechReport{pen-vid:non-equally,
  title =        "On non-equally spaced wavelet regression",
  author =       "Marianna Pensky and Brani Vidakovic",
  number =       "98-06",
  institution =  "Institute of Statistics and Decision Sciences, Duke
                 University",
  year =         "1998",
  url =          "ftp://ftp.isds.duke.edu/pub/WorkingPapers/98-06.ps",
  abstract =     "Wavelet-based regression analysis is widely used
                 mostly for equally-spaced designs. For such designs
                 wavelets are superior to other traditional orthonormal
                 bases because of their versatility and ability to
                 parsimoniously describe irregular functions. If the
                 regression design is random, an automatic solution is
                 not available. Given the observations (X_i, Y_i), i =
                 1,..., n, we estimate the regression function
                 m(x)=E(Y|X=x) as a series \sum_k \hat c_{jk}
                 \phi_{jk}(x) where \{ \phi_{jk}(x), ~k \in Z \} are
                 scaling functions spanning the multiresolution subspace
                 V_j. We propose a method that utilizes a probabilistic
                 model on X_i's in defining the empirical coefficients
                 \hat c_{jk}. The paper deals with both theoretical and
                 practical aspects of the proposed estimator. We explore
                 MSE convergence rates of the estimator. The performance
                 of the estimator is compared to that of some
                 traditional regression methods.",
}

@TechReport{per-bru:approximate,
  title =        "Wavelet-Based Approximate Maximum Likelihood
                 Estimation for Trend-Contaminated Fractional Difference
                 Processes",
  author =       "Donald B. Percival and Andrew G. Bruce",
  number =       "67",
  institution =  "MathSoft, Inc., 1700 Westlake Avenue N., Seattle, WA
                 98109-9891",
  year =         "1998",
  url =          "ftp://ftp.statsci.com/pub/longmem/wavelet-mle.ps",
}

@TechReport{per-bru:estimation,
  title =        "Estimation of Long Memory Processes with Missing
                 Data",
  author =       "Donald B. Percival and Andrew G. Bruce",
  number =       "64",
  institution =  "MathSoft, Inc., 1700 Westlake Avenue N., Seattle, WA
                 98109-9891",
  year =         "1997",
  url =          "ftp://ftp.statsci.com/pub/longmem/missing.ps",
}

@Unpublished{per-sar-dav:wavestrapping,
  title =        "Wavestrapping Time Series: {A}daptive Wavelet-Based
                 Bootstrapping",
  author =       "Donald B. Percival and Sylvain Sardy and Anthony
                 Davision",
  year =         "1999",
  note =         "Isaac Newton Institute for Mathematical Sciences",
}

@InCollection{per-gut:introduction,
  title =        "An Introduction to Spectral Analysis and Wavelets",
  author =       "Donald B. Percival and Peter Guttorp",
  pages =        "175--186",
  crossref =     "cia-cox-mon-pav:advanced",
}

@InCollection{per-gut:long-memory,
  title =        "Long-Memory Processes, the {A}llan Variance and
                 Wavelets",
  author =       "Donald B. Percival and Peter Guttorp",
  pages =        "325--344",
  crossref =     "fou-kum:geophysics",
}

@Article{per-mof:subtidal,
  title =        "Analysis of Subtidal Coastal Sea Level Fluctuations
                 Using Wavelets",
  author =       "Donald B. Percival and Harold O. Mofjeld",
  journal =      JASA,
  volume =       "92",
  number =       "439",
  year =         "1997",
  pages =        "868--880",
  keywords =     "coastal sea level variability, discrete wavelet
                 transform, natural hazards, time series analysis,
                 tsunamis",
  abstract =     "Subtidal coastal sea level fluctuations affect coastal
                 ecosystems and the consequences of destructive events
                 such as tsunamis. We analyze a time series of subtidal
                 fluctuations at Crescent City, California, during
                 1980-1991 using the maximal overlap discrete wavelet
                 transform (MODWT). Our analysis shows that the
                 variability in these fluctuations depends on the season
                 for scales of 32 days and less. We show how the MODWT
                 characterizes nonstationary behavior succinctly and how
                 this characterization can be used to improve forecasts
                 of inundation during tsunamis and storm surges. Pie
                 provide pseudocode and enough details so that data
                 analysts in other disciplines can readily apply MODWT
                 analysis to other nonstationary time series.",
}

@Article{per-phi-bas:compared,
  title =        "Wavelet spectra compared to {F}ourier spectra",
  author =       "Val\'{e}rie Perrier and Thierry Philipovitch and
                 Claude Basdevant",
  journal =      "Journal of Mathematical Physics",
  volume =       "36",
  number =       "3",
  year =         "1995",
  pages =        "1506--1519",
  abstract =     "The relation between Fourier spectra and spectra
                 obtained from wavelet analysis is established. Small
                 scale asymptotic analysis shows that the wavelet
                 spectrum is meaningful only when the analyzing wavelet
                 has enough vanishing moments. These results are related
                 to regularity theorems in Besov spaces. For the
                 analysis of infinitely regular signals, a new wavelet,
                 with an infinite number of cancellations is proposed.",
}

@Book{per-wal:wmtsa,
  title =        "Wavelet Methods for Time Series Analysis",
  author =       "Donald B. Percival and Andrew T. Walden",
  year =         "2000",
  publisher =    "Cambridge University Press",
  address =      "Cambridge",
  url =          "http://weber.u.washington.edu/~dbp/",
  note =         "Forthcoming",
}

@Article{per:characterization,
  title =        "{C}haracterization of frequency stability:
                 frequency-domain estimation of stability measures",
  journal =      PIEEE,
  volume =       "79",
  number =       "7",
  year =         "1991",
  pages =        "961--972",
  author =       "Donald B. Percival",
  abstract =     "The author focuses on the frequency domain approach,
                 which provides a complete characterization of
                 frequency. The standard characterization of frequency
                 stability in the frequency domain is the spectral
                 density function (SDF). The author describes SDFs that
                 model sampled frequency stability data and that are
                 related to the SDFs of the standard characterization.
                 On the basis of standard techniques in spectral
                 analysis, he outlines a systematic way of estimating
                 SDFs typical of frequency stability data. The
                 recommended procedure is to check for broadband bias in
                 the periodogram using a sequence of data tapers and, if
                 bias is in evidence, to design an autoregressive
                 prewhitening filter to prewhiten the data. The author
                 considers the relationship between the Allan variance
                 and the SDF and outlines two nonparametric ways of
                 translating stability measures between the two
                 domains-one based upon pilot analysis and the other
                 upon J. Rutman's bandpass variance (1978).",
  keywords =     "frequency stability. frequency domain. spectral
                 density function. spectral analysis. broadband bias.
                 periodogram. sequence of data tapers. autoregressive
                 prewhitening filter. Allan variance. pilot analysis.
                 bandpass variance.",
}

@Article{per:variance,
  title =        "On estimation of the wavelet variance",
  author =       "Donald B. Percival",
  journal =      BKA,
  volume =       "82",
  number =       "3",
  year =         "1995",
  pages =        "619--631",
  url =          "ftp://ftp.statsci.com/pub/WAVELETS/papers/wavevar.ps.gz",
  abstract =     "Thw wavelet variance decomposes the variance of a time
                 series into components associated with differen scales.
                 We consider two estimators of the wavelet variance: the
                 first based upon the discrete wavelet transform, and
                 the second, called the maximal-overlap estimator, based
                 upon a filtering interpretation of wavelets. We
                 determine the large sample distribution for both
                 estimatorsand show that the maximal-overlap estimator
                 ismore efficient for a class of processes of interest
                 in the physical sciences. We discuss methods for
                 determining an approximate confidence interval for the
                 wavelet variance. We demonstrate through Monte Carlo
                 experiments that the large sample distribution for the
                 maximal-overlap estimator is a reasonable approximation
                 even for the moderate sample size of 128 observations.
                 We apply our proposed methodology to a series of
                 observations related to vertical shear in the ocean.",
}

@Article{pes-kri-car:time-invariant,
  title =        "Time-invariant orthonormal wavelet representations",
  author =       "Jean-Christophe Pesquet and Hamid Krim and Herv{\'e}
                 Carfantan",
  journal =      IEEETSP,
  volume =       "44",
  number =       "8",
  year =         "1996",
  pages =        "1964--1970",
  abstract =     "A simple construction of an orthonormal basis starting
                 with a so-called mother wavelet, together with an
                 efficient implementation gained the wavelet
                 decomposition easy acceptanceand generated a great
                 research interest in its applications. An orthonormal
                 basis may not, however, always be a suitable
                 representation of a signal, particularly when time (or
                 space) invariance is a required property. The
                 conventional way around this problem is to use a
                 redundant decomposition. We address the time-invariance
                 problem for orthonormal wavelet transforms and propose
                 an extension to wavelet packet decompositions. We show
                 that it,is possible to achieve time invariance and
                 preserve the orthonormality. We subsequently propose an
                 efficient approach to obtain such a decomposition. We
                 demonstrate the importance of our method by considering
                 some application examples in signal reconstruction and
                 time delay estimation.",
}

@InProceedings{pes-kri-lep-ham:bayesian,
  title =        "{B}ayesian approach to best basis selection",
  booktitle =    "IEEE International Conference on Acoustics, Speech,
                 and Signal Processing",
  volume =       "5",
  year =         "1996",
  pages =        "2634--2637",
  author =       "J. C. Pesquet and H. Krim and D. Leporini and E.
                 Hamman",
  note =         "7-10 May 1996, Atlanta, GA, USA",
  abstract =     "Wavelet packets and local trigonometric bases provide
                 an efficient framework and fast algorithms to obtain a
                 `best basis' or `best representation' of deterministic
                 signals. Applying these deterministic techniques to
                 stochastic processes may, however, lead to variable
                 results. We revisit this problem and introduce a prior
                 model on the underlying signal in noise and account for
                 the contaminating noise model as well. We thus develop
                 a Bayesian-based approach to the best basis problem,
                 while preserving the classical tree search
                 efficiency.",
  keywords =     "deterministic signals, Bayesian approach, wavelet
                 packets, local trigonometric bases, fast algorithms,
                 best basis selection, best signal representation,
                 deterministic techniques, stochastic processes,
                 stochastic signals, contaminating noise model,
                 classical tree search efficiency, Bernoulli-Gaussian
                 mixtures, Bernoulli-Gaussian priors",
}

@Article{pes:statistical,
  title =        "Statistical properties of the wavelet decomposition of
                 certain non-{G}aussian self-similar processes",
  author =       "Pesquet-Popescu B.",
  journal =      SP,
  volume =       "75",
  number =       "3",
  pages =        "303--322",
  year =         "1999",
  email =        "bpopescu@csi.com",
  url =          "http://www.elsevier.nl/cas/tree/store/sigpro/sub/1999/75/3/1386.pdf",
  keywords =     "non-stationary signals self-similarity wavelet
                 analysis higher-order statistics alpha-stable processes
                 lower-order statistics long-range dependence",
  abstract =     "Self-similar processes have recently received
                 increasing attention in the signal processing
                 community, due to their wide applicability in modeling
                 natural phenomena which exhibit ``1/f'' spectra and/or
                 long-range dependence. At the same time, wavelet
                 decomposition has become a very useful tool in
                 describing nonstationary self-similar processes. In
                 this paper, we consider extensions of existing results
                 to non-Gaussian self-similar processes. We first
                 investigate the existence and properties of
                 higher-order statistics of wavelet decomposition for
                 self-similar processes with finite variance. We then
                 consider certain self-similar processes with infinite
                 variance, and study the statistical properties of their
                 wavelet coefficients.",
}

@InProceedings{pet-ben:uranus,
  title =        "A New Insight in {U}ranus Rings: {A} Wavelet Analysis
                 of the {V}oyager 2 Data",
  author =       "J. M. Petit and Ph. Bendjoya",
  booktitle =    "Completing the Inventory of the Solar System",
  editor =       "Terrence W. Rettig and Joseph M. Hahn",
  volume =       "107",
  series =       "Astronomical Society of the Pacific Conference
                 Proceedings",
  pages =        "137--146",
  year =         "1996",
  keywords =     "wavelet analysis, uranus rings",
  abstract =     "A new signal processing analysis, based on the wavelet
                 transform has been developed. It allows the detection
                 and the reconstruction of fine structures in a very
                 noisy signal. It removes the noise and gives a
                 quantified level of detection of the structures against
                 chance fluctuations. This powerful method has been
                 applied on the PPS Voyager 2 data on the Uranus rings.
                 A preliminary catalog of structures found in the
                 $\sigma$ Sagitarii occultation experiment, is proposed
                 here.",
}

@TechReport{pet-ste:gamma,
  title =        "{EDF} statistics for testing for the {G}amma
                 distribution",
  author =       "N. A. Pettitt and M. A. Stephens",
  institution =  "Department of Statistics, Stanford University",
  number =       "323",
  year =         "1982",
}

@TechReport{pet:bayesian,
  title =        "Bayesian Spectral Analysis of Long Memory Time
                 Series",
  author =       "Giovanni Petris",
  number =       "97-08",
  institution =  "Institute of Statistics and Decision Sciences, Duke
                 University",
  year =         "1997",
  url =          "ftp://ftp.isds.duke.edu/pub/WorkingPapers/97-08.ps",
}

@Article{pet:non-parametric,
  title =        "A non-parametric approach to the change point
                 problem",
  author =       "N. A. Pettitt",
  journal =      AS,
  volume =       "28",
  year =         "1979",
  pages =        "126--135",
}

@Article{pet:some,
  title =        "Some results on estimating a change-point using
                 non-parametric type statistics",
  author =       "N. A. Pettitt",
  journal =      JSCS,
  volume =       "11",
  year =         "1980",
  pages =        "261--272",
}

@PhdThesis{pet:thesis,
  title =        "Bayesian Analysis of Long Memory Time Series",
  author =       "Giovanni Petris",
  year =         "1997",
  school =       "Institute of Statistics and Decision Sciences, Duke
                 University",
  postscript =   "ftp://ftp.isds.duke.edu/pub/Theses/giovanni.ps.gz",
}

@Book{pie-etal:quadpack,
  title =        "\nobreak{QUADPACK}: {A} Subroutine Package for
                 Automatic Integration",
  booktitle =    "\nobreak{QUADPACK}: A Subroutine Package for Automatic
                 Integration",
  author =       "R. Piessons and E. {de Doncker-Kapenga} and C. W.
                 {\"U}berhuber and D. K. Kahaner",
  series =       "Springer Series in Computational Mathematics",
  volume =       "1",
  publisher =    "Springer-Verlag",
  address =      "Heidelberg",
  year =         "1983",
}

@Article{pin-vid:estimating,
  title =        "Estimating the square root of a density via compactly
                 supported wavelets",
  author =       "A. Pinheiro and B. Vidakovic",
  journal =      CSDA,
  volume =       "25",
  number =       "4",
  year =         "1997",
  pages =        "399--415",
}

@InCollection{plo-str:from,
  title =        "From Wavelets to Multiwavelets",
  author =       "Gerlind Plonka and Vasily Strela",
  booktitle =    "Mathamatical Methods for Curves and Surfaces II",
  editor =       "M. Dahlem and T. Lyche and L. Shumaker",
  publisher =    "Vanderbilt University Press",
  year =         "1998",
}

@Book{pre-teu-vet-fla:numerical,
  title =        "Numerical Recipes in {C}: The Art of Scientific
                 Computing",
  author =       "William H. Press and Saul A. Teukolsky and William T.
                 Vetterling and Brian P. Flannery",
  edition =      "2",
  year =         "1992",
  publisher =    "Cambridge University Press",
  address =      "Cambridge",
  url =          "http://cfata2.harvard.edu/nr/",
}

@Article{pri:wavelets,
  title =        "Wavelets and Time-Dependent Spectral Analysis",
  author =       "M. B. Priestley",
  journal =      JTSA,
  volume =       "17",
  number =       "1",
  year =         "1996",
  pages =        "85--104",
  abstract =     "One of the key features of wavelet analysis is its
                 potential use for effecting time-frequency
                 decompositions of non-stationary signals. The
                 relationship between wavelet analysis and timedependent
                 spectral analysis has so far rested mainly on heuristic
                 reasoning: in this paper we examine the relationship in
                 a more precise mathematical form. A crucial feature of
                 this analysis is the need to define carefully the
                 notion of `frequency' when applied to non-stationary
                 signals.",
  keywords =     "Wavelets wavelet transforms discrete wavelet
                 transforms multiresolution analysis Fourier transforms
                 windowed Fourier transforms spectral analysis
                 uncertainty principle evolutionary spectra",
}

@InProceedings{pro-smi:multichannel,
  title =        "Multichannel time-series modelling and prediction by
                 wavelet networks",
  author =       "Ale\v{s} Proch{\'a}zka and Jonathan Smith",
  booktitle =    "VIII European Signal Processing Conference
                 EUSIPCO-96",
  year =         "1996",
  pages =        "???--???",
  url =          "http://rex.vscht.cz/prochaz/ps/eusip96.ps",
}

@Article{pro-vei:trends,
  title =        "Trends, cycles and nonstationarities in isotope
                 signals of {P}hanerozoic seawater",
  author =       "A. Prokoph and J. Veizer",
  journal =      CG,
  volume =       "161",
  number =       "1-3",
  year =         "1999",
  pages =        "225--240",
  abstract =     "The new set of Sr-87/Sr-86, delta(18)O and delta(13)C
                 experimental data for Phanerozoic seawater, the
                 ``Bochum/Ottawa Isotope Dataset'', has been tested by
                 wavelet, discontinuity and sliding window correlation
                 dimension analyses for cyclicities and
                 nonstationarities in the isotope signal. The tests
                 indicate discontinuities in the strontium isotope
                 signal at similar to 500, 340, 288, 210, 65 and 28 Ma,
                 while for the oxygen and carbon isotopes they are at
                 similar to 500, 385, 290, 210 and 65 Ma. These
                 discontinuities, often coincident with major stage
                 boundaries, reflect mostly single (likely tectonic)
                 events that do not affect the structure of the
                 underlying system. The two most pronounced
                 nonstationarities in all isotope systematics are at
                 similar to 65 and 210 Ma, respectively, that is at the
                 K/T and Norian/Rhaetian transitions. Wavelet analysis
                 for all three isotope systems yields a long-term
                 quasi-periodicity at similar to 94-125 Ma, best
                 developed during the Paleozoic, with superimposed
                 intermittent 48-57 and 29-35 Ma oscillations, all
                 likely a reflection of plate reorganizations within the
                 Caledonian, Hercynian and Alpine tectonic cycles.",
}

@Article{qiu-er:wavspect,
  title =        "Wavelet spectrogram of noisy signals",
  author =       "Lunji Qiu and Meng Hwa Er",
  journal =      IJE,
  volume =       "79",
  number =       "5",
  year =         "1995",
  pages =        "665--677",
  email =        "elqiu@ntuvax.ntu.ac.sg",
  abstract =     "The wavelet transform is of interest for analysing
                 non- stationary signals. The squared modulus of the
                 wavelet transform leads to the wavelet spectrogram or
                 scalogram. When signals are embedded in additive noise,
                 it is important to study the estimation accuracy in
                 terms of bias and variance. The mean and variance
                 statistical properties of the wavelet spectrogram of a
                 signal embedded in additive gaussian white noise are
                 derived in this paper. Examples and simulation results
                 are also presented.",
}

@Article{qiu-u-sha:leakeage,
  title =        "The leakage problem of orthonormal wavelet transforms
                 when applied to atmospheric turbulence",
  author =       "Jie Qiu and Kyaw Tha Paw U and Roger H. Shaw",
  journal =      JGRA,
  volume =       "100",
  number =       "D12",
  year =         "1995",
  pages =        "25,769--25,779",
  abstract =     "Orthonormal wavelet transforms are becoming common in
                 the study of turbulence phenomena. Although they are
                 powerful tools in representing a signal, their use as
                 tools to study the characteristics of turbulent
                 structures can create appreciable errors in
                 interpretation. It is shown here that although the
                 orthonormal wavelet transform is computationally
                 economical by taking advantage of multiresolution
                 analysis, it has insufficient resolution in both scale
                 and location to resolve detailed information of
                 turbulence structures. Lacking in resolution, the
                 energy at a particular frequency (or wavelength) may
                 leak into neighboring frequencies and may pass down to
                 smaller scales to produce an artificial ``cascade'' of
                 energy (with a slope close to -2/3). The choice of
                 wavelet basis function is important to the wavelet
                 spectrum, especially in the study of turbulence flows
                 dominated by coherent structures, since the method most
                 accurately senses energy contained in pulses that have
                 a similar pattern to the wavelet function. To use the
                 method as a filter can be problematic owing to the low
                 resolution of the orthonormal wavelet transform;
                 nonorthonormal wavelet analysis should be employed when
                 high resolution is important. When orthonormal wavelet
                 transforms have to be used for signal analysis,
                 segmented averaging should be employed.",
}

@Book{rai:book,
  title =        "Special Functions",
  author =       "Earl D. Rainville",
  year =         "1960",
  publisher =    "The Macmillan Company",
  address =      NY,
}

@Article{rai:minimax,
  title =        "Minimax estimation of sharp change points",
  author =       "M. Raimondo",
  journal =      AofS,
  volume =       "26",
  number =       "4",
  year =         "1998",
  pages =        "1379--1397",
  keywords =     "change point cusp jump minimax estimation
                 nonparametric regression wavelets",
  abstract =     "We define the sharp change point problem as an
                 extension of earlier problems in change point analysis
                 related to nonparametric regression. As particular
                 cases, these include estimation of jump points in
                 smooth curves. More generally, we give a systematic
                 treatment of the correct rate of convergence for
                 estimating the position of a `cusp' of an arbitrary
                 order. We propose a test function for the local
                 regularity of a signal sample implementation of our
                 method, from observations of the signal at discrete
                 time positions i/n, i = 1,..., n, we use a wavelet
                 transformation to approximate the position of the
                 change point in the no-noise case. We study the noise
                 effect, in the worst case scenario over a wide class of
                 functions having a unique irregularity of `order alpha'
                 and propose a sequence of estimators which converge at
                 the rate n(-1/(1+2 alpha)), as n tends to infinity.
                 Finally we analyze the likelihood ratio of the problem
                 and show that this is actually the minimax rate of
                 convergence. Examples of thresholding empirical wavelet
                 coefficients to estimate the position of sharp change
                 points are also presented.",
}

@Article{ram-lam:decomposition,
  title =        "Decomposition of economic relationships by timescale
                 using wavelets - {M}oney and income",
  author =       "J. B. Ramsey and C. Lampart",
  journal =      "Macroeconomic Dynamics",
  volume =       "2",
  number =       "1",
  year =         "1998",
  pages =        "49--71",
  keywords =     "wavelets timescale velocity money income permanent
                 income hypothesis money-income causality",
  abstract =     "Economists have long known that timescale matters in
                 that the structure of decisions as to the relevant time
                 horizon, degree of time aggregation, strength of
                 relationship, and even the relevant variables differ by
                 timescale. Unfortunately, until recently it was
                 difficult to decompose economic time series into
                 orthogonal timescale components except for the shea or
                 long run in which the former is dominated by noise.
                 Wavelets are used to produce an orthogonal
                 decomposition of some economic variables by timescale
                 over six different timescales. The relationship of
                 interest is that between money and income, i.e.,
                 velocity. We confirm that timescale decomposition is
                 very important for analyzing economic relationships.
                 The analysis indicates the importance of recognizing
                 variations in phase between variables when
                 investigating the relationships between them and throws
                 considerable light on the conflicting results that have
                 been obtained in the literature using Granger causality
                 tests.",
}

@Article{ram-lam:decomposition2,
  title =        "The Decomposition of economic relationships by time
                 scale using wavelets: {E}xpenditure and income",
  author =       "J. B. Ramsey and C. Lampart",
  journal =      "Studies in Nonlinear Dynamics and Econometrics",
  volume =       "3",
  number =       "1",
  year =         "1998",
  pages =        "23--42",
  keywords =     "permanent income consumption hypothesis",
  abstract =     "Economists have long known that time scale matters, in
                 that the structure of decisions as to the relevant time
                 horizon, degree of time aggregation, strength of
                 relationship, and even the relevant variables differ by
                 time scale. Unfortunately, until recently it was
                 difficult to decompose economic time series into
                 orthogonal time-scale components except for the short
                 and long run, in which the former is dominated by
                 noise. This paper uses wavelets to produce an
                 orthogonal decomposition of some economic variables by
                 time scale over six different time scales. The
                 relationship of interest is the permanent income
                 hypothesis. We confirm that time-scale decomposition is
                 very important for analyzing economic relationships and
                 that a number of anomalies previously noted in the
                 literature are explained by these means. The analysis
                 indicates the importance of recognizing variations in
                 phase between variables when investigating the economic
                 relationships.",
}

@Article{ram-usi-zas:us-stock,
  title =        "An analysis of {U.S.} Stock Price Behavior Using
                 Wavelets",
  author =       "James B. Ramsey and Daniel Uskinov and George M.
                 Zaslavsky",
  journal =      "Fractals",
  volume =       "3",
  number =       "2",
  year =         "1995",
  pages =        "377--389",
}

@Article{ram-zei:fBm,
  title =        "On the wavelet transform of fractional {B}rownian
                 motion",
  author =       "J. Ramanathan and O. Zeitouni",
  journal =      IEEETIT,
  volume =       "37",
  number =       "4",
  year =         "1991",
  pages =        "1156--1158",
  keywords =     "wavelet transform, fractional Brownian motion,
                 covariance structure, Gaussian processes",
  abstract =     "A theorem characterizing fractional Brownian motion by
                 the covariance structure of its wavelet transform is
                 established. The authors examine whether there are
                 alternate Gaussian processes whose wavelet transforms
                 have a natural covariance structure. In addition, the
                 authors examine if there are any Gaussian processes
                 whose wavelet transform is stationary with respect to
                 the affine group (i.e. the statistics of the wavelet
                 transform do not depend on translations and dilations
                 of the process).",
}

@Article{ram-zha:analysis,
  title =        "The analysis of foreign exchange data using waveform
                 dictionaries",
  author =       "James B. Ramsey and Zhifeng Zhang",
  journal =      "Journal of Empirical Finance",
  volume =       "4",
  year =         "1997",
  pages =        "341--372",
}

@InCollection{ram-zha:application,
  title =        "The application of wave form dictionaries to stock
                 market index data",
  author =       "J. B. Ramsey and Z. F. Zhang",
  booktitle =    "Predictability of Dynamical Systems",
  editor =       "Y. A. Kravstov and J. B. Kadtke",
  publisher =    "Springer Verlag",
  address =      NY,
  volume =       "69",
  year =         "1996",
  pages =        "189--205",
}

@Article{ram:contribution,
  title =        "The contribution of wavelets to the anlaysis of
                 economic and financial data",
  author =       "James B. Ramsey",
  journal =      PTRSLA,
  volume =       "357",
  number =       "1760",
  year =         "1999",
  pages =        "2593--2606",
}

@Unpublished{ram:regression,
  title =        "Regression over Time Scale Decompositions: {A}
                 Sampling Analysis of Distributional Properties",
  author =       "James B. Ramsey",
  year =         "1998",
  note =         "New York University",
}

@Article{rei-etal:multifractal,
  title =        "A multifractal wavelet model with application to
                 network traffic",
  author =       "R. H. Riedi and M. S. Crouse and V. J. Ribeiro and R.
                 G. Baraniuk",
  journal =      IEEETIT,
  volume =       "45",
  number =       "3",
  year =         "1999",
  pages =        "992--1018",
  keywords =     "long-range dependence multifractals network traffic
                 positive 1/f noise wavelets",
  abstract =     "In this paper, we develop a new multiscale modeling
                 framework for characterizing positive-valued data with
                 long-range-dependent correlations (1/f noise). Using
                 the Haar wavelet transform and a special multiplicative
                 structure on the wavelet and scaling coefficients to
                 ensure positive results, the model provides a rapid
                 O(N) cascade algorithm for synthesizing N-point data
                 sets. We study both the second-order and multifractal
                 properties of the model, the latter after a tutorial
                 overview of multifractal analysis. We derive a scheme
                 for matching the model to real data observations and,
                 to demonstrate its effectiveness, apply the model to
                 network traffic synthesis. The flexibility and accuracy
                 of the model and fitting procedure result in a close
                 fit to the real data statistics (variance-time plots
                 and moment scaling) and queuing behavior, Although for
                 illustrative purposes we focus on applications in
                 network traffic modeling, the multifractal wavelet
                 model could be useful in a number of other areas
                 involving positive data, including image processing,
                 finance, and geophysics.",
}

@InProceedings{rib-etal:simulating,
  title =        "Simulation of non{G}aussian Long-Range Dependent
                 Traffic using Wavelets",
  author =       "V. J. Ribeiro and R. H. Riedi and M. S. Crouse and R.
                 G. Baraniuk",
  booktitle =    "ACM SIGMETRICS Conference on the Measurement and
                 Modeling of Computer Systems",
  year =         "1999",
  note =         "1-4 May 1999, Atlanta, Georgia",
  abstract =     "In this paper, we develop a simple and powerful
                 multiscale model for the synthesis of nonGaussian,
                 long-range dependent (LRD) network traffic. Although
                 wavelets effectively decorrelate LRD data,
                 wavelet-based models have generally been restricted by
                 a Gaussianity assumption that can be unrealistic for
                 traffic. Using a multiplicative superstructure on top
                 of the Haar wavelet transform, we exploit the
                 decorrelating properties of wavelets while
                 simultaneously capturing the positivity and
                 ``spikiness'' of nonGaussian traffic. This leads to a
                 swift O(N) algorithm for fitting and synthesizing
                 N-point data sets. The resulting model belongs to the
                 class of multifractal cascades, a set of processes with
                 rich statistical properties. We elucidate our model's
                 ability to capture the covariance structure of real
                 data and then fit it to real traffic traces. Queueing
                 experiments demonstrate the accuracy of the model for
                 matching real data. Our results indicate that the
                 nonGaussian nature of traffic has a significant effect
                 on queuing.",
}

@Unpublished{rid-den:aeromagnetic,
  title =        "The wavelet transform in aeromagnetic processing",
  author =       "T. A. Ridsdill-Smith and M. C. Dentith",
  journal =      "GEOPHYSICS",
  volume =       "64",
  number =       "4",
  year =         "1999",
  pages =        "1067--1078",
  url =          "http://geolpc42.geol.uwa.edu.au/papers/wavemag.zip",
  abstract =     "The phase-shift method of wavefield extrapolation
                 applies a phase shift in the Fourier domain to deduce a
                 scalar wavefield at one depth level given its value at
                 another. The phase-shift operator varies with frequency
                 and wavenumber, and assumes constant velocity across
                 the extrapolation step. We use nonstationary filter
                 theory to generalize this method to nonstationary phase
                 shift (NSPS), which allows the phase shift to vary
                 laterally depending upon the local propagation
                 velocity. For comparison, we derive an analytic form
                 for the popular phase shift plus interpolation (PSPI)
                 method in the limit of an exhaustive set of reference
                 velocities. NSPS and this limiting form of PSPI can be
                 written as generalized Fourier integrals which reduce
                 to ordinary phase shift in the constant velocity limit.
                 In the (x, omega) domain, these processes are the
                 transpose of each other; however, only NSPS has the
                 physical interpretation of forming the scaled, linear
                 superposition of laterally-variable impulse responses
                 (i.e., Huygen's wavelets).The difference between NSPS
                 and PSPI is clear when they are compared in the case of
                 a piecewise constant velocity variation. Define a set
                 of windows such that the jth window is unity when the
                 propagation velocity is the jth distinct velocity and
                 is zero otherwise. NSPS can be computed by applying the
                 window set to the input data to create a set of
                 windowed wavefields, which are individually phase-shift
                 extrapolated with the corresponding constant velocity,
                 and the extrapolated set is superimposed. PSPI proceeds
                 by phase-shift extrapolating the input data for each
                 distinct velocity, applying the jth window to the jth
                 extrapolation, and superimposing. Though neither
                 process is fully correct, PSPI has the unphysical limit
                 that discontinuities in the lateral velocity variation
                 cause discontinuities in the wavefield, whereas NSPS
                 shows the expected wavefront ``healing.'' We then
                 formulate a finite aperture compensation for NSPS which
                 has the practical result of absorbing lateral
                 boundaries for all incidence angles. Wavefield
                 extrapolation can be regarded as the crosscorrelation
                 of the wavefield with the expected response of a point
                 diffractor at the new depth level. Aperture
                 compensation simply applies a laterally varying window
                 to the infinite, theoretical diffraction response. The
                 crosscorrelation becomes spatially variant, even for
                 constant velocity, and hence is a nonstationary filter.
                 The nonstationary effects of aperture compensation can
                 be simultaneously applied with the NSPS extrapolation
                 through a laterally variable velocity field.",
}

@Article{rid:separating,
  title =        "Separation filtering of aeromagnetic data using
                 filter-banks",
  author =       "T. A. Ridsdill-Smith",
  journal =      "Exploration Geophysics",
  volume =       "29",
  number =       "3-4",
  year =         "1998",
  pages =        "577--583",
  url =          "http://geolpc42.geol.uwa.edu.au/papers/aseg98trs.zip",
}

@Article{rie-sid:adaptive,
  title =        "Adaptive smoothing of the log-spectrum with multiple
                 tapering",
  author =       "Kurt S. Riedel and Alexander Sidorenko",
  journal =      IEEETSP,
  volume =       "44",
  number =       "7",
  year =         "1996",
  pages =        "1794--1800",
  abstract =     "A hybrid estimator of the log-spectral density of a
                 stationary time series is proposed, First, a multiple
                 taper estimate is performed, followed by kernel
                 smoothing the log-multiple taper estimate, This
                 procedure reduces the expected mean square error by
                 (pi(2)/4)(4/5) over simply smoothing the log tapered
                 periodogram, A data-adaptive implementation of a
                 variable-bandwidth kernel smoother is given.",
}

@Article{rie-etal:multifractal-wavelet,
  title =        "A Multifractal Wavelet Model with Application to
                 Network Traffic",
  author =       "R. H. Riedi and M. S. Crouse and V. J. Ribeiro and R.
                 G. Baraniuk",
  journal =      IEEETIT,
  volume =       "45",
  number =       "4",
  year =         "1999",
  pages =        "992--1018",
  url =          "http://www-dsp.rice.edu/~riedi/cv_frame.html",
  keywords =     "Multifractals, long-range dependence, positive 1/f
                 noise, wavelets, network traffic",
  abstract =     "In this paper, we develop a new multiscale modeling
                 framework for characterizing positive-valued data with
                 long-range-dependent correlations (1/f noise). Using
                 the Haar wavelet transform and a special multiplicative
                 structure on the wavelet and scaling coefficients to
                 ensure positive results, the model provides a rapid
                 O(N) cascade algorithm for synthesizing N-point data
                 sets. We study both the second-order and multifractal
                 properties of the model, the latter after a tutorial
                 overview of multifractal analysis. We derive a scheme
                 for matching the model to real data observations and,
                 to demonstrate its effectiveness, apply the model to
                 network traffic synthesis. The flexibility and accuracy
                 of the model and fitting procedure result in a close
                 fit to the real data statistics (variance-time plots
                 and moment scaling) and queuing behavior. Although for
                 illustrative purposes we focus on applications in
                 network traffic modeling, the multifractal wavelet
                 model could be useful in a number of other areas
                 involving positive data, including image processing,
                 finance, and geophysics.",
}

@InProceedings{rie:geophysics,
  title =        "Multifractals and Wavelets: {A} potential tool in
                 Geophysics",
  author =       "R. H. Riedi",
  booktitle =    "Society of Exploration Geophysicists Annual Meeting",
  address =      "New Orleans",
  year =         "1998",
  pages =        "???--???",
  url =          "http://www-dsp.rice.edu/~riedi/cv_frame.html",
}

@TechReport{rie:introduction,
  title =        "Introduction to Multifractals",
  author =       "R. H. Riedi",
  number =       "99-06",
  institution =  "ECE Department, Rice University",
  year =         "1999",
}

@Article{rio-fla:time-scale,
  title =        "Time-Scale Energy Distributions: {A} General Class
                 Extending Wavelet Transforms",
  author =       "Olivier Rioul and Patrick Flandrin",
  journal =      IEEETSP,
  volume =       "40",
  number =       "7",
  year =         "1992",
  pages =        "1746--1757",
  abstract =     "A proposed theoretical framework for time-scale energy
                 representation is based on local frequency which is
                 covariant under modulations and time scaling which is
                 covariant under dilations or contractions. The
                 frameworks seeks to illustrate the relationship between
                 scalograms and spectrograms. Results show that, from
                 the Wigner-Ville distribution, it is possible to shift
                 continuously to either a scalogram or a spectrogram.
                 The approach simultaneously maintains a balance between
                 time-frequency resolution and cross-terms reduction in
                 both time-scale and time-frequency representations.",
}

@Article{rio-vet:wavelets,
  title =        "Wavelets and Signal Processing",
  author =       "Olivier Rioul and Martin Vetterli",
  journal =      IEEESPM,
  volume =       "8",
  number =       "4",
  year =         "1991",
  pages =        "14--38",
  abstract =     "A simple, nonrigorous, synthetic view of wavelet
                 theory is presented for both review and tutorial
                 purposes. The discussion includes nonstationary signal
                 analysis, scale versus frequency, wavelet analysis and
                 synthesis, scalograms, wavelet frames and orthonormal
                 bases, the discrete-time case, and applications of
                 wavelets in signal processing. The main definitions and
                 properties of wavelet transforms are covered, and
                 connections among the various fields where results have
                 been developed are shown.",
}

@TechReport{rio-vid:random,
  title =        "Wavelet-Based Random Densities",
  author =       "David Insua Rios and Brani Vidakovi\'{c}",
  institution =  "Institute of Statisics and Decision Sciences, Duke
                 University",
  year =         "1997",
  note =         "Discussion Paper 97-05",
  url =          "ftp://ftp.isds.duke.edu/pub/WorkingPapers/97-05.ps",
}

@Article{rob-par-alv:extraction,
  title =        "Extraction of impulse response data via wavelet
                 transform for structural system identification",
  author =       "A. N. Robertson and K. C. Park and K. F. Alvin",
  journal =      JVA,
  volume =       "120",
  number =       "1",
  year =         "1998",
  pages =        "252--260",
  keywords =     "vibration",
  abstract =     "This paper presents a wavelet transform-based method
                 of extracting the impulse response characteristics from
                 the measured disturbances and response histories of
                 linear structural dynamic systems. The proposed method
                 is found to be effective in determining the impulse
                 response functions for systems subjected to harmonic
                 (narrow frequency-band) input signals and signals with
                 sharp discontinuities, thus alleviating the Gibbs
                 phenomenon encountered in FFT methods. When the system
                 is subjected to random burst input signals for which
                 the FFT methods are known to perform well, the proposed
                 wavelet method performs equally well with a fewer
                 number of ensembles than FFT-based methods. For
                 completely random input signals, both the wavelet and
                 FFT methods experience difficulties, although the
                 wavelet method appears to perform somewhat better in
                 tracing the fundamental response modes.",
}

@Article{rob-par-alv:identification,
  title =        "Identification of structural dynamics models using
                 wavelet-generated impulse response data",
  author =       "A. N. Robertson and K. C. Park and K. F. Alvin",
  journal =      JVA,
  volume =       "120",
  number =       "1",
  year =         "1998",
  pages =        "261--266",
  keywords =     "vibration",
}

@InProceedings{rom-cho-bar:bayesian,
  title =        "{B}ayesian Tree-Structured Image Modeling using
                 Wavelet-domain Hidden {M}arkov Models",
  author =       "J. K. Romberg and H. Choi and R. G. Baraniuk",
  booktitle =    "SPIE Technical Conference on Mathematical Modeling,
                 Bayesian Estimation, and Inverse Problems",
  volume =       "3816",
  year =         "1999",
  pages =        "31--44",
  email =        "jrom@rice.edu, choi@ece.rice.edu, richb@rice.edu",
  url =          "http://www-dsp.rice.edu/publications/pub/jrom99spie.ps.Z",
  abstract =     "Wavelet-domain hidden Markov models have proven to be
                 useful tools for statistical signal and image
                 processing. The hidden Markov tree model captures the
                 key features of the joint density of the wavelet
                 coefficients of real-world data. One potential drawback
                 to the HMT framework is the need for computationally
                 expensive iterative training. In this paper, we prose
                 two reduced-parameter HMT models that capture the class
                 of real-world images. In the image HMT (iHMT) model we
                 use the fact that for a large class of images the
                 structure of the HMT is self-similar across scale. This
                 allows us to reduce the complexity of the iHMT to just
                 nine easily trained parameters. In the universal HMT
                 (uHMT) we take a Bayesian approach and fix these nine
                 parameters. The uHMT requires no training of any kind.
                 While simple, we show using a series of image
                 estimation/denoising experiments that these two new
                 models retain nearly all of the key structure modeled
                 by the full HMT. Finally, we propose a fast
                 shift-invariant HMT estimation algorithm that
                 outperforms all other wavelet- based estimators in the
                 current literature, both in mean- square error and
                 visual metrics.",
}

@InProceedings{rom-cho-bar:bayesian2,
  title =        "{B}ayesian Wavelet Domain Image Modeling using Hidden
                 {M}arkov Trees",
  author =       "J. K. Romberg and H. Choi and R. G. Baraniuk",
  booktitle =    "Proceedings of the IEEE International Conference on
                 Image Processing",
  year =         "1999",
  pages =        "???--???",
  email =        "jrom@rice.edu, choi@ece.rice.edu, richb@rice.edu",
  url =          "http://www-dsp.rice.edu/publications/pub/jrom-icip99.ps.Z",
}

@InProceedings{rom-cho-bar:shift-invariant,
  title =        "Shift-Invariant Denoising using Wavelet-Domain Hidden
                 {M}arkov Trees",
  author =       "J. K. Romberg and H. Choi and R. G. Baraniuk",
  booktitle =    "Conference Record of The Thirty-Third Asilomar
                 Conference on Signals, Systems and Computers",
  year =         "1999",
  pages =        "???--???",
  email =        "jrom@rice.edu, choi@ece.rice.edu, richb@rice.edu",
  url =          "http://www-dsp.rice.edu/publications/pub/jrom-asilomar99.ps.Z",
}

@Unpublished{rou-vei:measuring,
  title =        "Measuring Long-Range Dependence Under Changing Traffic
                 Conditions",
  author =       "Matthew Roughan and Darryl Veitch",
  year =         "1999",
  note =         "preprint",
}

@InProceedings{rou-vei-abr:on-line,
  title =        "On-line estimation of the parameters of long-range
                 dependence",
  author =       "Matthew Roughan and Darryl Veitch and Patrice Abry",
  booktitle =    "Proceedings Globecom '98",
  address =      "Sydney",
  volume =       "6",
  year =         "1998",
  pages =        "3716--3721",
}

@Article{rug-vid:bayesian,
  title =        "A Bayesian decision theoretic approach to the choice
                 of thresholding parameter",
  author =       "F. Ruggeri and B. Vidakovic",
  journal =      SSin,
  volume =       "9",
  number =       "1",
  year =         "1999",
  pages =        "183--197",
  keywords =     "Bayes rule hard-thresholding wavelets",
  abstract =     "Thresholding rules recently became of considerable
                 interest when Donoho and Johnstone applied them in the
                 wavelet shrinkage context. Analytically simple, such
                 rules are very efficient in data denoising and data
                 compression problems. In this paper we find hard
                 thresholding decision rules that minimize Bayes risk
                 for broad classes of underlying models. Standard
                 Donoho-Johnstone test signals are used to evaluate
                 performance of such rules. We show that an optimal
                 Bayesian decision theoretic (BDT) hard thresholding
                 rule can achieve smaller mean squared error than some
                 standard wavelet thresholding methods, if the prior
                 information on the noise level is precise.",
}

@Book{rus-etal:wavelets,
  title =        "Wavelets and Their Applications",
  booktitle =    "Wavelets and Their Applications",
  editor =       "Mary Beth Ruskai and Gregory Beylkin and Ronald
                 Coifman and Ingrid Daubechies and Stephane Mallat and
                 Yves Meyer and Louise Raphael",
  publisher =    "Jones and Bartlett Publishers",
  year =         "1992",
  pages =        "474",
  url =          "http://www.jbpub.com/catalog/Detail.CFM?titles__ISBN=0867202254",
  loc =          "QA 403.3 .W385 1992",
  ISBN =         "0-86720-225-4",
}

@Article{rus-lab-les:commodity,
  title =        "Wavelet Analysis of Commodity Price Behavior",
  author =       "Russell Davidson and Walter C. Labys and Jean-Baptiste
                 Lesourd",
  journal =      CE,
  volume =       "11",
  number =       "1-2",
  year =         "1998",
  pages =        "103--128",
  abstract =     "We propose a form of semi-nonparametric regression
                 based on wavelet analysis. Traditional time series
                 methods usually involve either the time or the
                 frequency domain, but wavelets can combine the
                 information from both of these. While wavelet
                 transforms are typically restricted to equally spaced
                 observations an integer power of 2 in number, we show
                 how to go beyond these constraints. We use our methods
                 to construct ``patios'' for twenty-one important
                 international commodity price series. These graph the
                 magnitude of the variations in the series at different
                 time scales for various subperiods of the full
                 sample.",
}

@Article{sac-pra:coherent,
  title =        "Coherent modes in multiscale variability of streamflow
                 over the {U}nited {S}tates",
  author =       "P. Saco and P. Kumar",
  journal =      WRR,
  volume =       "36",
  number =       "4",
  year =         "2000",
  pages =        "1049--1067",
  abstract =     "Motivated by the need to understand large-scale
                 hydrologic response, significant research has been
                 directed toward the identification of coherent regions
                 using characteristics of streamflow variability.
                 Typically, these regions are delineated using principal
                 component analysis on streamflow. This method does not
                 account for differences in temporal scales of
                 fluctuations embedded in the time series. To capture
                 this, we use wavelet spectral analysis. Wavelet spectra
                 from the specific streamflow series are obtained for
                 outflow binned at 3 degrees-length segments along the
                 border of the conterminous United States. Rotated
                 principal component analysis is performed on the
                 wavelet spectra to obtain clusters of segments that
                 exhibit similar distribution of variability across
                 scales. Three physically distinct modes explain over
                 89% of the variability. Two of the modes identified are
                 associated with high variability at seasonal scales,
                 and the third is associated with high variability at
                 small timescales. The runoff generation mechanisms
                 underlying the observed modes of multiscale variability
                 of various regions are also discussed. Each of these
                 coherent modes of multiscale variability indicate the
                 existence of regions with similar scales of
                 fluctuations that are located geographically apart, as
                 well as regions located geographically close with
                 dissimilar scales of fluctuations.",
}

@Article{sai-bey:autocorrelation,
  title =        "Multiresolution representations using the
                 autocorrelation functions of compactly supported
                 wavelets",
  author =       "Naoki Saito and Gregory Beylkin",
  journal =      IEEETSP,
  volume =       "41",
  number =       "12",
  year =         "1993",
  pages =        "3584--3590",
  url =          "http://math.ucdavis.edu/~saito/publications/miniframe.html",
  abstract =     "Proposes a shift-invariant multiresolution
                 representation of signals or images using dilations and
                 translations of the autocorrelation functions of
                 compactly supported wavelets. Although these functions
                 do not form an orthonormal basis, their properties make
                 them useful for signal and image analysis. Unlike
                 wavelet-based orthonormal representations, the present
                 representation has (1) symmetric analyzing functions,
                 (2) shift-invariance, (3) associated iterative
                 interpolation schemes, and (4) a simple algorithm for
                 finding the locations of the multiscale edges as
                 zero-crossings. The authors also develop a noniterative
                 method for reconstructing signals from their
                 zero-crossings (and slopes at these zero-crossings) in
                 their representation. This method reduces the
                 reconstruction problem to that of solving a system of
                 linear algebraic equations.",
}

@InProceedings{sai:asilomar98,
  title =        "The least statistically-dependent basis and its
                 applications",
  author =       "Naoki Saito",
  booktitle =    "Conference Record of The Thirty-Second Asilomar
                 Conference on Signals, Systems and Computers",
  year =         "1998",
  pages =        "732--736",
  url =          "http://math.ucdavis.edu/~saito/publications/asilomar98.html",
}

@Unpublished{sai:image,
  title =        "Image approximation and modeling via least
                 statistically-dependent bases",
  author =       "Naoki Saito",
  note =         "Submitted to {\em Pattern Recognition}",
  year =         "1999",
  abstract =     "Statistical independence is one of the most desirable
                 properties of a coordinate system for representing and
                 modeling images. In reality, however, truly independent
                 coordinates may not exist for a given set of images, or
                 it may be too difficult to compute them in practice.
                 Therefore, it makes sense to obtain the least
                 statistically-dependent coordinate system efficiently.
                 To achieve this goal, we use the best-basis algorithm
                 with new criterion that can rapidly select the least
                 statistically-dependent basis (LSDB) from a basis
                 dictionary (e.g., the local cosine or wavelet packet
                 dictionaries) containing a huge number of orthonormal
                 (or biorthogonal) bases. Our new basis selection
                 criterion is minimization of the mutual information of
                 the distributions of the basis coefficients as a
                 measure of statistical dependence, which in turn is
                 equivalent to minimization of the sum of the
                 differential entropy of each coordinate in the basis
                 dictionary. We show that this criterion, combined with
                 the best-basis algorithm, can find the coordinates
                 closest to the statistical independence from all
                 possible bases searchable in a basis dictionary with
                 O(n [log n]^p), where n is the dimensionality of the
                 image (the number of pixels in each image), and p=1 for
                 the wavelet packet dictionaries, and p=2 for the local
                 cosine/sine dictionaries. In this sense, we can view
                 this LSDB algorithm as the best-basis version of the
                 Independent Component Analysis (ICA), which is
                 increasingly gaining popularity. This criterion is
                 different from that of the Joint Best Basis (JBB)
                 proposed by Wickerhauser, which can be viewed as the
                 best-basis version of the Karhunen-Loeve basis (KLB).
                 We demonstrate the application of the LSDB to image
                 approximation and modeling and compare its performance
                 with that of KLB and JBB using a collection of real
                 geophysical acoustic waveforms and an image database of
                 human faces. For these datasets, the LSDB provides the
                 best approximation in terms of the average relative l^2
                 errors among various bases including the KLB, JBB, DCT,
                 and wavelet basis. For image modeling, we propose two
                 simple stochastic models for a given class of signals
                 or images based on the LSDB coordinates. The first
                 model is to assume the statistical independence among
                 the LSDB coordinates, which allows us to sample typical
                 coefficients of each coordinate separately using the
                 empirical distribution estimated from the available
                 training coefficients of that coordinate, which in turn
                 easily allows us to simulate new images at our
                 disposal. For the geophysical acoustic waveforms, this
                 first model turned out to be good enough. The second
                 model is based on the ``second rotation'' by the KLB
                 computed from the top m LSDB coordinates. This model
                 gives us the decorrelated coordinates built on top of
                 the LSDB coordinates. The simulation results on the
                 human face database using the second model suggest that
                 this second rotation can further reduce the statistical
                 dependency among the coordinates, and allows better
                 modeling for a class of complicated images.",
}

@InProceedings{sai:least,
  title =        "Least statistically-dependent basis and its
                 applications to image modeling",
  author =       "Naoki Saito",
  pages =        "24--37",
  crossref =     "lai-uns-ald:wavelet6",
  url =          "http://math.ucdavis.edu/~saito/publications/lsdb_spie2.html",
}

@PhdThesis{sai:thesis,
  title =        "Local Feature Extraction and Its Applications Using a
                 Library of Bases",
  author =       "Naoki Saito",
  school =       "Yale University",
  year =         "1994",
  url =          "http://math.ucdavis.edu/~saito/publications/saito_phd.html",
}

@Article{sak:pseudo,
  title =        "Pseudodiagonalization of the autocorrelation of a
                 stochastic process by an over-complete wavelet system",
  author =       "F. Sakaguchi",
  journal =      ECJ3,
  volume =       "78",
  number =       "4",
  year =         "1995",
  pages =        "16--27",
  note =         "Translated from Denshi Joho Tsushin Gakkai Ronbunshi,
                 Vol. 77-A, No. 8, August 1994, pp. 1065--1074",
  abstract =     "If a stochastic process can be regarded as a
                 superposition of the wavelets which arise randomly and
                 independently of one another, the random-wavelet
                 picture of a stochastic process is intuitive and
                 convenient. This paper investigates theoretically in
                 what case the picture can be used; i.e., in what case
                 the autocorrelation of the stochastic process can be
                 diagonalized by using the over-complete wavelet system.
                 A general method for calculating the pseudodiagonal
                 form from an arbitrarily given autocorrelation function
                 using the operator algebra is proposed. Next, some
                 properties of stationary wavelet-diagonal processes are
                 investigated where it is shown that the power spectra
                 of these processes are related to the spectral
                 estimates under the circumstances in which the number
                 of the time points are constrained to a constant finite
                 number.",
}

@Article{sar-brz:shift-invariant,
  title =        "A Shift-Invariant Discrete Wavelet Transform",
  author =       "Hamed Sari-Sarraf and Dragana Brzakovic",
  journal =      IEEETSP,
  volume =       "45",
  number =       "10",
  year =         "1997",
  pages =        "2621--2626",
  abstract =     "This correspondence presents a unifying approach to
                 the derivation and implementation of a shift-invariant
                 wavelet transform of one-and two-dimensional (1-D and
                 2-D) discrete signals, Starting with Mallat's
                 multiresolution wavelet representation (MRWAR), the
                 correspondence presents an analytical process through
                 which a shift-invariant, orthogonal, discrete wavelet
                 transform called the multiscale wavelet representation
                 (MSWAR) is obtained, The coefficients in MSWAR are
                 shown to be inclusive of those in MRWAR with the
                 implication that the derived representation is
                 invertible. The computational complexity of MSWAR is
                 quantified in terms of the required convolutions, and
                 its implementation is shown to be equivalent to the
                 filter upsampling technique.",
}

@Article{sar-etal:unequal,
  title =        "Wavelet DeNoising for Unequally Spaced Data",
  author =       "Sylvain Sardy and Donald B. Percival and Andrew G.
                 Bruce and Hong-Ye Gao and Werner Stuetzle",
  journal =      SC,
  volume =       "9",
  number =       "1",
  year =         "1999",
  pages =        "65--75",
  url =          "ftp://ftp.statsci.com/pub/WAVELETS/papers/unequal.ps.gz",
  keywords =     "Nonparametric regression; Wavelet transform;
                 WaveShrink",
  abstract =     "Wavelet shrinkage (WaveShrink) is a relatively new
                 technique for nonparametric function estimation that
                 has been shown to have asymptotic near-optimality
                 properties over a wide class of functions. As
                 originally formulated by Donoho and Johnstone,
                 WaveShrink assumes equally spaced data. Because so many
                 statistical applications (e.g., scatterplot smoothing)
                 naturally involve unequally spaced data, we investigate
                 in this paper how WaveShrink can be adapted to handle
                 such data. Focusing on the Haar wavelet, we propose
                 four approaches that extend the Haar wavelet transform
                 to the unequally spaced case. Each approach is
                 formulated in terms of continuous wavelet basis
                 functions applied to a piecewise constant interpolation
                 of the observed data, and each approach leads to
                 wavelet coefficients that can be computed via a matrix
                 transform of the original data. For each approach, we
                 propose a practical way of adapting WaveShrink. We
                 compare the four approaches in a Monte Carlo study and
                 find them to be quite comparable in performance. The
                 computationally simplest approach (isometric wavelets)
                 has an appealing justification in terms of a weighted
                 mean square error criterion and readily generalizes to
                 wavelets of higher order than the Haar.",
}

@Article{sar:minimax,
  title =        "Minimax threshold for denoising complex signals with
                 waveshrink",
  author =       "Sylvain Sardy",
  journal =      IEEETSP,
  volume =       "48",
  number =       "4",
  year =         "2000",
  pages =        "1023--1028",
  url =          "http://dmawww.epfl.ch/~sardy/PS/article-minimax.ps",
  abstract =     "For the problem of signal extraction from noisy data,
                 Waveshrink has proven to be a powerful tool, both from
                 an empirical and an asymptotic point of view.
                 Waveshrink is especially efficient at estimating
                 spatially inhomogeneous signals, A key step of the
                 procedure is the selection of the threshold parameter.
                 Donoho and Johnstone propose a selection of the
                 threshold based on a minimax principle, Their
                 derivation is specifically for real signals and real
                 wavelet transforms. In this paper, we propose to extend
                 the use of Waveshrink to denoising complex signals with
                 complex wavelet transforms. We illustrate the problem
                 of denoising complex signals with an electronic
                 surveillance application.",
}

@Unpublished{sar-tse-bru:robust,
  title =        "Robust Wavelet Denoising",
  author =       "S. Sardy and P. Tseng and A. G. Bruce",
  year =         "1998",
  note =         "Submitted to {\em Journal of the American Statistical
                 Association}",
  url =          "http://dmawww.epfl.ch/~sardy/PS/article-robust.ps",
}

@Article{sca-etal:quasi,
  title =        "{T}he quasi-periodic oscillations and very low
                 frequency noise of {S}corpius {X}-1 as transient chaos:
                 a dripping handrail?",
  journal =      "Astrophysical Journal Letters",
  volume =       "411",
  number =       "2",
  year =         "1993",
  pages =        "91--94",
  author =       "J. D. Scargle and T. {Steiman, Cameron} and K. Young
                 and D. L. Donoho and J. P. Crutchfield and J. Imamura",
  abstract =     "The authors present evidence that the quasi-periodic
                 oscillations (QPO) and very low frequency noise (VLFN)
                 characteristic of many accretion sources are different
                 aspects of the same physical process. They analyzed a
                 long, high time resolution EXOSAT observation of the
                 low-mass X-ray binary (LMXB) Sco X-1. The X-ray
                 luminosity varies stochastically on time scales from
                 milliseconds to hours. The nature of this
                 variability-as quantified with both power spectrum
                 analysis and a new wavelet technique, the
                 scalegram-agrees well with the dripping handrail
                 accretion model, a simple dynamical system which
                 exhibits transient chaos. In this method both the QPO
                 and VLFN are produced by radiation from blobs with a
                 wide size distribution, resulting from accretion and
                 subsequent diffusion of hot gas, the density of which
                 is limited by an unspecified instability to lie below a
                 threshold.",
  keywords =     "V818 Sco. 4U 1617-15. variable star. quasi-periodic
                 oscillations. very low frequency noise. transient
                 chaos. accretion sources. low-mass X-ray binary. Sco
                 X-1. X-ray luminosity. power spectrum analysis. wavelet
                 technique. scalegram. dripping handrail accretion
                 model. blobs. size distribution. diffusion. hot gas.
                 density. instability.",
}

@InCollection{sca:astronomical,
  title =        "Wavelet Methods in Astronomical Time Series Analysis",
  author =       "Jeffrey D. Scargle",
  email =        "jeffrey@sunshine.arc.nasa.gov",
  pages =        "226--248",
  crossref =     "rao-pri-les:applications",
}

@InProceedings{sca:astronomical2,
  title =        "Astronomical Time Series Analysis: {N}ew Methods for
                 Studying Periodic and Aperiodic Systems",
  author =       "Jeffrey D. Scargle",
  booktitle =    "The Weise Observatory 25th Anniversary Symposium:
                 Astronomical Time Series",
  email =        "jeffrey@sunshine.arc.nasa.gov",
  year =         "1996",
}

@InCollection{sca:detection,
  title =        "Detection and modeling of chaotic dynamics using
                 wavelet techniques",
  author =       "Jeffrey D. Scargle",
  email =        "jeffrey@sunshine.arc.nasa.gov",
  crossref =     "szu:wavelet1",
  abstract =     "Powerful new data analysis techniques based on
                 wavelets are proving extremely useful in the reduction
                 and interpretation of time series data. The goals of
                 these methods include denoising, characterizing,
                 modeling, and compressing of time series data. The
                 multi-scale nature of wavelet analysis makes it
                 especially useful for detection and characterization of
                 self-similar or 'scaling' behavior, such as is common
                 for chaotic processes. This paper describes how wavelet
                 techniques led to a transient-chaos model for a rapidly
                 fluctuating celestial X-ray source. The methods
                 described here are freely available in a new software
                 package called TeachWave, developed by David Donoho and
                 Iain Johnstone of Stanford University (anonymous ftp to
                 playfair.stanford.edu; the software is in directory
                 /pub/software/wavelets, and a number of related
                 technical papers are in /pub/reports).",
}

@InProceedings{sch-swe:sphere,
  author =       "Peter Schr{\"o}der and Wim Sweldens",
  title =        "Spherical Wavelets: {E}fficiently Representing
                 Functions on the Sphere",
  booktitle =    "Computer Graphics Proceedings (SIGGRAPH 95)",
  year =         "1995",
  publisher =    "ACM Siggraph",
  pages =        "161--172",
  url =          "http://cm.bell-labs.com/who/wim/papers/sphere.ps.gz",
  abstract =     "Wavelets have proven to be powerful bases for use in
                 numerical analysis and signal processing. Their power
                 lies in the fact that they only require a small number
                 of coefficients to represent general functions and
                 large data sets accurately. This allows compression and
                 efficient computations. Classical constructions have
                 been limited to simple domains such as intervals and
                 rectangles. In this paper we present a wavelet
                 construction for scalar functions defined on the
                 sphere. We show how biorthogonal wavelets with custom
                 properties can be constructed with the lifting scheme.
                 The bases are extremely easy to implement and allofw
                 fully adaptive subdivisions. We give examples of
                 functions defined on the sphere, such as topographic
                 data, bi-directional reflection distribution functions,
                 and illumination, and show how they can be efficiently
                 represented with spherical wavelets.",
}

@Book{sch-web:recent,
  title =        "Recent Advances in Wavelet Analysis",
  booktitle =    "Recent Advances in Wavelet Analysis",
  editor =       "Larry L. Schumaker and Glenn Webb",
  volume =       "3",
  series =       "Wavelet Analysis and its Applications",
  year =         "1993",
  publisher =    "Academic Press, Inc.",
  ISBN =         "0-12-632370-4",
  abstract =     "Recent Advances in Wavelet Analysis is the third
                 volume in the WAVELET ANALYSIS AND ITS APPLICATIONS
                 series. This edited volume features ten timely and
                 important articles authored by various experts in their
                 respective fields, including such notable contributors
                 as David L. Donoho, Ingrid Daubechies (MacArthur grant
                 awardees in ‘91 and ‘92, respectively), Phillippe
                 Tchamitchian, Patrick Flandrin (both featured speakers
                 at the ‘92 International Wavelets Conference in
                 Toulouse), Charles Chui, and Bjorn Jawerth (one of the
                 editors of the Wavelet Digest). This book covers recent
                 advances in wavelet analysis and applications in areas
                 including wavelets on bounded intervals, wavelet
                 decomposition of special interest to statisticians,
                 wavelets approach to differential and integral
                 equations, analysis of subdivision operators, and
                 wavelets related to problems in engineering and
                 physics. Anyone interested in the ever-evolving field
                 of wavelets will find this book an excellent addition
                 to the series and to the literature overall.",
}

@Article{sch:investigation,
  title =        "On the investigation of hidden periodicities with
                 application to a supposed 26-day period of
                 meterological phenomena",
  author =       "A. Schuster",
  journal =      "Terrestrial Magnetism",
  volume =       "3",
  year =         "1898",
  pages =        "13--41",
}

@Article{sch:optimal,
  title =        "Fast and statistically optimal period search in uneven
                 sampled observations",
  author =       "A. Schwarzenberg-Czerny",
  journal =      ApJ,
  volume =       "460",
  number =       "2",
  year =         "1996",
  pages =        "107--110",
  url =          "http://www.journals.uchicago.edu/ApJ/journal/issues/ApJL/v460n2/5758/5758.html",
  abstract =     "The classical methods for searching for a periodicity
                 in uneven sampled observations suffer from a poor match
                 of the model and true signals and/or use of a statistic
                 with poor properties. We present a new method employing
                 periodic orthogonal polynomials to fit the observations
                 and the analysis of variance (ANOVA) statistic to
                 evaluate the quality of the fit. The orthogonal
                 polynomials constitute a flexible and numerically
                 efficient model of the observations. Among all popular
                 statistics, ANOVA has optimum detection properties as
                 the uniformly most powerful test. Our recurrence
                 algorithm for expansion of the observations into the
                 orthogonal polynomials is fast and numerically stable.
                 The expansion is equivalent to an expansion into
                 Fourier series. Aside from its use of an inefficient
                 statistic, the Lomb-Scargle power spectrum can be
                 considered a special case of our method. Tests of our
                 new method on simulated and real light curves of
                 nonsinusoidal pulsators demonstrate its excellent
                 performance. In particular, dramatic improvements are
                 gained in detection sensitivity and in the damping of
                 alias periods.",
}

@Article{sch:translation-invariant,
  author =       "D. J. Scholl",
  title =        "Translation-invariant data visualization with
                 orthogonal discrete wavelets",
  journal =      IEEETSP,
  volume =       "46",
  number =       "7",
  year =         "1998",
  pages =        "2031--2034",
  abstract =     "Orthogonal discrete wavelet transforms, can be made
                 translation-invariant by adding redundant wavelet
                 coefficients through repeated shifting operations.
                 Othogonality is lost, but isometry and compact time
                 support can be preserved. The practical application to
                 data visualization of scalograms based on such
                 transforms is discussed and illustrated with measured
                 transient signals.",
}

@Article{sel:balanced,
  title =        "Balanced multiwavelet bases based on symmetric {FIR}
                 filters",
  author =       "Ivan W. Selesnick",
  journal =      IEEETSP,
  volume =       "48",
  number =       "1",
  year =         "2000",
  pages =        "184--191",
  abstract =     "This paper describes a basic difference between
                 multiwavelets and scalar wavelets that explains,
                 without using zero moment properties, why certain
                 complications arise in the implementation of discrete
                 multiwavelet transforms. Assuming we wish to avoid the
                 use of prefilters in implementing the discrete
                 multiwavelet transform, it is suggested that the
                 behavior of the iterated filter bank associated with a
                 multiwavelet basis of multiplicity r is more fully
                 revealed by an expanded set of r(2) scaling functions
                 phi(i,j). This paper also introduces new K-balanced
                 orthogonal multiwavelet bases based on symmetric FIR
                 filters. The nonlinear design equations arising in this
                 work are solved using the Grobner basis. The
                 minimal-length K-balanced multiwavelet bases based on
                 even-length symmetric FIR filters are better behaved
                 than those based on odd-length symmetric FIR filters,
                 as illustrated by special relations they satisfy and by
                 examples constructed.",
}

@Article{sel:interpolating,
  title =        "Interpolating multiwavelet bases and the sampling
                 theorem",
  author =       "Ivan W. Selesnick",
  journal =      IEEETSP,
  volume =       "47",
  number =       "6",
  year =         "1999",
  pages =        "1615--1621",
  email =        "seles@taco.poly.edu",
  keywords =     "filter banks multiwavelet bases sampling wavelet
                 transforms",
  abstract =     "This paper considers the classical sampling theorem in
                 multiresolution spaces with scaling functions as
                 interpolants. As discussed by Xia and Zhang, for an
                 orthogonal scaling function to support such a sampling
                 theorem, the scaling function must be cardinal
                 (interpolating). They also showed that the only
                 orthogonal scaling function that is both cardinal and
                 of compact support is the Haar function, which is not
                 continuous, This paper addresses the same question, but
                 in the multiwavelet context, where the situation is
                 different. This paper presents the construction of
                 compactly supported orthogonal multiscaling functions
                 that are continuously differentiable and cardinal. The
                 scaling functions thereby support a Shannon-like
                 sampling theorem, Such wavelet bases are appealing
                 because the initialization of the discrete wavelet
                 transform (prefiltering) is the identity operator.",
}

@Article{sel:slantlet,
  title =        "The Slantlet transform",
  author =       "Ivan W. Selesnick",
  journal =      IEEETSP,
  volume =       "47",
  number =       "5",
  year =         "1999",
  pages =        "1304--1313",
  email =        "seles@taco.poly.edu",
  keywords =     "wavelet transform bases L(2)",
  abstract =     "The discrete wavelet transform (DWT) is usually
                 carried out by filterbank iteration; however, for a
                 fixed number of zero moments, this does not yield a
                 discrete-time basis that is optimal with respect to
                 time localization. This paper discusses the
                 implementation and properties of an orthogonal DWT,
                 with two zero moments and with improved time
                 localization. The basis is not based on filterbank
                 iteration; instead, different filters are used for each
                 scale. For coarse scales, the support of the
                 discrete-time basis functions approaches two thirds
                 that of the corresponding functions obtained by
                 filterbank iteration, This basis, which is a special
                 case of a class of bases described by Alpert, retains
                 the octave-hand characteristic and is piecewise linear
                 (but discontinuous). Closed-form expressions for the
                 filters are given, an efficient implementation of the
                 transform is described, and improvement in a denoising
                 example is shown. This basis, being piecewise linear,
                 is reminiscent of the slant transform, to which it is
                 compared.",
}

@Article{ser-wal-per:properties,
  title =        "Statistical Properties of the Wavelet Variance
                 Estimator for Non-{G}aussian/Non-Linear time series",
  author =       "Abdeslam Serroukh and Andrew T. Walden and Donald B.
                 Percival",
  journal =      JASA,
  volume =       "95",
  number =       "449",
  year =         "2000",
  pages =        "184--196",
  url =          "http://www.ma.ic.ac.uk/~atw/Wavar.ps.gz",
}

@Article{ser-wal:bivariate1,
  title =        "Wavelet scale analysis of bivariate time series {I}:
                 {M}otivation and estimation",
  author =       "Abdeslam Serroukh and Andrew T. Walden",
  journal =      JNS,
  year =         "2000",
  note =         "to appear",
}

@Article{ser-wal:bivariate2,
  title =        "Wavelet scale analysis of bivariate time series {II}:
                 {S}tatistical properties for linear processes",
  author =       "Abdeslam Serroukh and Andrew T. Walden",
  journal =      JNS,
  year =         "2000",
  note =         "to appear",
}

@Article{ses-cso-ste:exponential,
  title =        "Tests for the Exponential Distribution using
                 {K}olmogorov-type Statistics",
  author =       "V. Seshadri and M. Cs{\"o}rg{\H o} and M. A.
                 Stephens",
  journal =      JRSSB,
  volume =       "31",
  number =       "3",
  year =         "1969",
  pages =        "499--509",
}

@Article{sha-hou:on-line,
  title =        "An on-line wavelet transform for de-noising of high
                 performance liquid chromatograms",
  author =       "Xueguang Shao and Shunquan Hou",
  journal =      "Analytical Letters",
  volume =       "32",
  number =       "12",
  year =         "1999",
  pages =        "2507--2520",
}

@Article{sha-xia:wavelet,
  title =        "The Wavelet Analysis Method of Stationary Random
                 Processes",
  author =       "Luo Shaoming and Zhang Xiangwei",
  journal =      "Applied Mathematics and Mechanics",
  volume =       "19",
  number =       "10",
  year =         "1998",
  pages =        "929--935",
  note =         "English Edition",
}

@Article{sha-yen:exact,
  title =        "On the exact values of orthonormal scaling
                 coefficients of lengths 8 and 10",
  author =       "W. C. Shann and C. C. Yen",
  journal =      ACHA,
  volume =       "6",
  number =       "1",
  year =         "1999",
  pages =        "109--112",
  abstract =     "We show the exact values of the scaling coefficients
                 of length 8 and 10 for Daubechies' orthonormal scaling
                 functions.",
}

@Article{she-rob-szu:optical,
  title =        "Optical Wavelet Transform",
  author =       "Yunlong Sheng and Donny Roberge and Harold H. Szu",
  journal =      OE,
  volume =       "31",
  number =       "9",
  year =         "1992",
  pages =        "1840--1845",
  abstract =     "The wavelet transform is implemented using an optical
                 multichannel correlator with a bank of wavelet
                 transform filters. This approach provides a
                 shift-invariant wavelet transform with continuous
                 translation and discrete dilation parameters. The
                 wavelet transform filters can be in many cases simply
                 optical transmittance masks. Experimental results show
                 detection of the frequency transition of the input
                 signal by the optical wavelet transform.",
}

@Article{she-str:asymptotics,
  title =        "Asymptotics of {D}aubechies filters, scaling
                 functions, and wavelets",
  author =       "J. H. Shen and G. Strang",
  journal =      ACHA,
  volume =       "5",
  number =       "3",
  year =         "1998",
  pages =        "312--331",
  abstract =     "We study the asymptotic form as p --> infinity of the
                 Daubechies orthogonal minimum phase filter h(p)[n],
                 scaling function phi(p)(t), and wavelet w(p)(t). Kateb
                 and Lemarie calculated the leading term in the phase of
                 the frequency response H-p(omega). The infinite product
                 <(phi)over cap>(p)(omega) = Pi H-p(omega/2(k)) leads us
                 to a problem in stationary phase, for an oscillatory
                 integral with parameter t. The leading terms change
                 form with tau = t/p and we find three regions for
                 phi(p)(tau): (1) An Airy function up to near tau(0):
                 root 42 pi/p Ai(-root 42 pi p(2)(tau - tau(0))) +
                 o(p(-1/3)) (2) An oscillating region root 2/pi
                 pG'(omega(tau))cos [p(G((-1))(omega(tau)) -
                 G(omega(tau))omega(tau)) + pi/4] + o(p(-1/2)) (3) A
                 rapid decay after tau(1): (1/p pi)(1/(tau -
                 tau(1)))sin[p(G((-1))(pi) - tau pi)] + o(p(-1)) The
                 numbers tau(0) similar or equal to 0.1817 and tau(1)
                 similar or equal to 0.3515 are known constants. The
                 function G and its integral G((-1)) are independent of
                 p. Regions 1 and 2 are matched over the interval
                 p(-2/3) much less than tau - tau(0) much less than 1.
                 The wavelets have a simpler asymptotic expression
                 because the Airy wavefront is removed by the highpass
                 filter. We also find the asymptotics of the impulse
                 response h(p)[n] -a different function g(omega)
                 controls the three regions. The difficulty throughout
                 is to estimate the phase.",
}

@Article{she:dwt,
  title =        "The discrete wavelet transform: {W}edding the \`{a}
                 trous and {M}allat algorithms",
  author =       "Mark J. Shensa",
  journal =      IEEETSP,
  volume =       "40",
  number =       "10",
  year =         "1992",
  pages =        "2464--2482",
  abstract =     "Two separately motivated implementations of the
                 wavelet transform are brought together. It is observed
                 that these algorithms are both special cases of a
                 single filter bank structure, the discrete wavelet
                 transform, the behavior of which is governed by the
                 choice of filters. In fact, the a trous algorithm is
                 more properly viewed as a nonorthonormal
                 multiresolution algorithm for which the discrete
                 wavelet transform is exact. Moreover, it is shown that
                 the commonly used Lagrange a trous filters are in
                 one-to-one correspondence with the convolutional
                 squares of the Daubechies filters for orthonormal
                 wavelets of compact support. A systematic framework for
                 the discrete wavelet transform is provided, and
                 conditions are derived under which it computes the
                 continuous wavelet transform exactly. Suitable filter
                 constraints for finite energy and boundedness of the
                 discrete transform are also derived. Relevant signal
                 processing parameters are examined, and it is observed
                 that orthonormality is balanced by restrictions on
                 resolution.",
}

@Article{she:inverse,
  title =        "Discrete inverses for nonorthogonal wavelet
                 transforms",
  author =       "M. J. Shensa",
  journal =      IEEETSP,
  volume =       "44",
  number =       "4",
  year =         "1996",
  pages =        "798--807",
  url =          "ftp://ftp.nosc.mil/pub/Shensa/WTinverse_TR1621.ps.Z",
  keywords =     "discrete inverses, nonorthogonal wavelet transforms,
                 signal processing, resolution, standard inversion
                 procedure, finite expansion, algorithms, Morlet
                 wavelets",
  abstract =     "Discrete nonorthogonal wavelet transforms play an
                 important role in signal processing by offering finer
                 resolution in time and scale than their orthogonal
                 counterparts. The standard inversion procedure for such
                 transforms is a finite expansion in terms of the
                 analyzing wavelet. While this approximation works quite
                 well for many signals, it fails to achieve good
                 accuracy or requires an excessive number of scales for
                 others. This paper proposes several algorithms that
                 provide more adequate inversion and compares them in
                 the case of Morlet wavelets. In the process, both
                 practical and theoretical issues for the inversion of
                 nonorthogonal wavelet transforms are discussed.",
}

@Article{shu-fed:shannon,
  title =        "Analysis and synthesis of $1/f$ processes via Shannon
                 wavelets",
  author =       "E. Shusterman and M. Feder",
  journal =      IEEETSP,
  volume =       "46",
  number =       "6",
  year =         "1998",
  pages =        "1698--1702",
  keywords =     "nonstationary processes 1/f noise spectral analysis
                 wavelets",
  abstract =     "1/f processes can he very useful in modeling processes
                 with long-term correlation. We propose analysis and
                 synthesis procedures to express these processes in
                 terms of the Shannon wavelet. Unlike previous
                 techniques, our analysis procedure generates
                 uncorrelated decomposition coefficients for the 1/f
                 process. This is done hy taking onto account, and then
                 removing, the residual correlation between the wavelet
                 components. The analysis procedure is the major
                 contribution of this work. The proposed synthesis
                 algorithm, which is a byproduct of the proposed
                 analysis algorithm, is competitive with other
                 techniques.",
}

@Article{sim-fre-ade-hee:shiftable,
  title =        "Shiftable multiscale transforms",
  author =       "Eero P. Simoncelli and William T. Freeman and Edward
                 H. Adelson and David J. Heeger",
  journal =      IEEETIT,
  volume =       "38",
  number =       "2",
  year =         "1992",
  pages =        "587--607",
  url =          "ftp://ftp.cis.upenn.edu/pub/eero/simoncelli91.ps.Z",
  keywords =     "scale domain. orientation domain. signal analysis.
                 multiscale transforms. orthogonal wavelet transforms.
                 translation invariance. wavelet subbands. shiftability.
                 spatial domain. sampling theorem. shiftable transforms.
                 1-D transform. jointly shiftable. scale-space analysis.
                 stereo disparity measurement. image enhancement",
  abstract =     "One of the major drawbacks of orthogonal wavelet
                 transforms is their lack of translation invariance: the
                 content of wavelet subbands is unstable under
                 translations of the input signal. Wavelet transforms
                 are also unstable with respect to dilations of the
                 input signal and, in two dimensions, rotations of the
                 input signal. The authors formalize these problems by
                 defining a type of translation invariance called
                 shiftability. In the spatial domain, shiftability
                 corresponds to a lack of aliasing; thus, the conditions
                 under which the property holds are specified by the
                 sampling theorem. Shiftability may also be applied in
                 the context of other domains, particularly orientation
                 and scale. Jointly shiftable transforms that are
                 simultaneously shiftable in more than one domain are
                 explored. Two examples of jointly shiftable transforms
                 are designed and implemented: a 1-D transform that is
                 jointly shiftable in position and scale, and a 2-D
                 transform that is jointly shiftable in position and
                 orientation. The usefulness of these image
                 representations for scale-space analysis, stereo
                 disparity measurement, and image enhancement is
                 demonstrated.",
}

@InProceedings{sim-fre:steerable,
  title =        "The Steerable Pyramid: {A} Flexible Architecture for
                 Multi-Scale Derivative Computation",
  author =       "Eero P. Simoncelli and William T. Freeman",
  booktitle =    "International Conference on Image Processing",
  volume =       "3",
  address =      "23-26 Oct. 1995, Washington, DC, USA",
  month =        oct,
  year =         "1995",
  pages =        "444--447",
  url =          "ftp://ftp.cis.upenn.edu/pub/eero/simoncelli95b.ps.Z",
  keywords =     "flexible architecture multiscale derivative
                 computation steerable pyramid linear image
                 decomposition orientation subbands scale subbands basis
                 functions directional derivative operators transform
                 filters Fourier domain",
  abstract =     "We describe an architecture for efficient and accurate
                 linear decomposition of an image into scale and
                 orientation subbands. The basis functions of this
                 decomposition are directional derivative operators of
                 any desired order. We describe the construction and
                 implementation of the transform.",
}

@Article{sim-han-nes:determination,
  title =        "Determination of the Hurst exponent by use of wavelet
                 transforms",
  author =       "I. Simonsen and A. Hansen and O. M. Nes",
  journal =      PRE,
  volume =       "58",
  number =       "3",
  year =         "1998",
  pages =        "2779--2787",
  keywords =     "inverse fractal problem surfaces roughness growth",
  abstract =     "We propose a method for (global) Hurst exponent
                 determination based on wavelets. Using this method, we
                 analyze synthetic data with predefined Hurst exponents,
                 fracture surfaces, and data from economy. The results
                 are compared to those obtained with Fourier spectral
                 analysis. When many samples are available, the wavelet
                 and Fourier methods are comparable in accuracy.
                 However, when one or only a few samples are available,
                 the wavelet method outperforms the Fourier method by a
                 large margin.",
}

@TechReport{sli-etal:intraseasonal,
  title =        "Intraseasonal oscillations in 15 atmospheric general
                 circulation models (results from an {AMIP} diagnostic
                 subproject)",
  author =       "J. M. Slingo and K. R. Sperber and J. S. Boyle and
                 J.-P. Ceron and M. Dix and B. Dugas and W. Ebisuzaki
                 and J. Fyfe and D. Gregory and J.-F. Gueremy and J.
                 Hack and A. Harzallah and P. Inness and A. Kitoh and W.
                 K.-M. Lau and B. McAvaney and R. Madden and A. Matthews
                 and T. N. Palmer and C.-K. Park and D. Randell and N.
                 Renno",
  number =       "661",
  institution =  "World Meteorological Organization",
  year =         "1995",
}

@Article{son-wu:multiscale,
  title =        "Multiscale interrelations between air temperature in
                 southeast {C}hina and {E}l {N}ino: {W}avelet analysis",
  author =       "D. M. Sonechkin and H. B. Wu",
  journal =      "Izvestiya Akademii Nauk Fizika Atmosfery I Okeana",
  volume =       "35",
  number =       "2",
  year =         "1999",
  pages =        "250--258",
  keywords =     "seasonal cycle oscillation transform chaos",
  abstract =     "Multiscale manifestations of the El Nino-Southern
                 Oscillation in the dynamics of air temperature in
                 various regions of the earth were examined, using
                 southeast China as an example. The wavelet transforms
                 of surface air temperature time series observed in
                 Guangzhou (southeast China) and sea surface temperature
                 time series observed in the Nine 1 + 2 and Nino 3
                 regions were analyzed. An intense interdecadal
                 oscillation was revealed in these time series. The
                 subsequent correlation of the transformed series
                 separately for each time scale, which is a new
                 technique designed to analyze interrelations of
                 nonstationary stochastic processes, showed that the
                 interrelations between these series are complex in
                 character. This manifests itself in positive and
                 negative correlations between the series on interannual
                 and interdecadal scales, respectively. Since the
                 interdecadal variability is determined. by a sequence
                 of extremely intense El Nino events, it follows that
                 the response of the Guangzhou temperature to intense El
                 Nino is other than that to routine El Nino.",
  note =         "In Russian",
}

@Article{spo:adaptive,
  title =        "Adaptive hypothesis testing using wavelets",
  author =       "V. G. Spokoiny",
  journal =      AofS,
  volume =       "24",
  number =       "6",
  year =         "1996",
  pages =        "??--??",
}

@Article{sta-zee:filter-banks,
  title =        "Two-dimensional orthogonal filter banks and wavelets
                 with linear phase",
  author =       "D. Stanhill and Y. Y. Zeevi",
  journal =      IEEETSP,
  volume =       "46",
  number =       "1",
  year =         "1998",
  pages =        "183--190",
  keywords =     "filter banks linear phase symmetry 2-D wavelets",
  url =          "ftp://ftp.technion.ac.il/pub/supported/ee/Signal_processing/2dlp.ps.gz",
  abstract =     "Two-dimensional (2-D) compactly supported, orthogonal
                 wavelets and filter banks having linear phase are
                 presented, Two cases are discussed: wavelets with
                 two-fold symmetry (centrosymmetric) and wavelets with
                 four-fold symmetry that are symmetric (or
                 anti-symmetric) about the vertical and horizontal axes.
                 We show that imposing the requirement of linear phase
                 in the case of order-factorable wavelets imposes a
                 simple constraint on each of its polynomial order-1
                 factors, We thus obtain a simple and complete method of
                 constructing orthogonal order-factorable wavelets with
                 linear phase, This method is exemplified by design in
                 the case of four-band separable sampling. An
                 interesting result that is similar to the one
                 well-known in the one-dimensional (1-D) case is
                 obtained: Orthogonal order-factorable wavelets cannot
                 be both continuous and have four-fold symmetry.",
}

@Article{sta-zee:wavelets,
  title =        "Two-dimensional orthogonal wavelets with vanishing
                 moments",
  author =       "D. Stanhill and Y. Y. Zeevi",
  journal =      IEEETSP,
  volume =       "44",
  number =       "10",
  year =         "1996",
  pages =        "2579--2590",
  keywords =     "reconstruction filter banks regularity matrices
                 design",
  url =          "ftp://ftp.technion.ac.il/pub/supported/ee/Signal_processing/2dvm.ps.gz",
  abstract =     "We investigate a very general subset of 2-D,
                 orthogonal, compactly supported wavelets, This subset
                 includes all the wavelets with a corresponding wavelet
                 (polyphase) matrix that can be factored as a product of
                 factors of degree-1 in one variable. In this paper, we
                 consider, in particular, wavelets with vanishing
                 moments, The number of vanishing moments that can be
                 achieved increases with the increase in the McMillan
                 degrees of the wavelet matrix. We design wavelets with
                 the maximal number of vanishing moments for given
                 McMillan degrees by solving a set of nonlinear
                 constraints on the free parameters defining the wavelet
                 matrix and discuss their relation to regular, smooth
                 wavelets, Design examples are given for two fundamental
                 sampling schemes: the quincunx and the four-band
                 separable sampling, The relation of the wavelets to the
                 well-known 1-D Daubechies wavelets with vanishing
                 moments is discussed.",
}

@InProceedings{sta-mur-bij:multi,
  title =        "Multiresolution and Astronomical Image Processing",
  author =       "J. L. Stark and F. Murtagh and A. Bijaoui",
  booktitle =    "Astronomical Data Analysis Software and Systems IV",
  editor =       "R. A. Shaw and H. E. Payne and J. J. E. Hayes",
  series =       "ASP Conference Series",
  volume =       "77",
  year =         "1995",
  pages =        "279--288",
  url =          "http://http.hq.eso.org/~fmurtagh/adass-jls.ps",
  abstract =     "We present several wavelet transform algorithms and
                 their applications in astronomical image processing
                 (restoration, object detection, compression, etc.).",
}

@Article{sta-sie-gre:spectral,
  title =        "Spectral analysis using the wavelet transform",
  author =       "Starck J. L. and Siebenmorgen R. and Gredel R.",
  journal =      ApJ,
  volume =       "482",
  number =       "2",
  pages =        "1011--1020",
  year =         "1997",
  url =          "http://www.journals.uchicago.edu/ApJ/cgi-bin/resolve?1997ApJ...482.1011SMPS",
  keywords =     "infrared, stars. methods, observational. stars,
                 individual (HH 100). stars, pre-main-sequence.
                 techniques, spectroscopic.",
  abstract =     "We introduce a new signal processing technique to
                 analyze noisy spectra. The method is based on the
                 wavelet transform and employs the a trous algorithm.
                 Noise determination and detection criteria are
                 discussed in detail, together with pitfalls related to
                 the use of wavelets in the analysis of spectra.
                 Simulations are presented to demonstrate the power and
                 the shortcomings of our method. We apply our technique
                 to the case of continuum sources that show superposed
                 interstellar or circumstellar absorption or emission
                 bands that are shallow and broad. In particular, we
                 analyze an L-band spectrum of the Herbig-Haro energy
                 source HH 100 IRS. The analysis indicates the presence
                 of a shallow emission band near 3.51 mu m that is
                 tentatively assigned to arise from aliphatic (CH2)
                 vibrations.",
}

@Article{ste-pav-boj:nao,
  title =        "Is the {N}orth {A}tlantic {O}scillation a random
                 walk?",
  author =       "D. B. Stephenson and V. Pavan and R. Bojariu",
  journal =      IJC,
  volume =       "20",
  number =       "1",
  year =         "2000",
  pages =        "1--18",
  abstract =     "The North Atlantic Oscillation (NAO) is a major mode
                 of large-scale climate variability which contains a
                 broad spectrum of variations. There are substantial
                 contributions from short-term 2-5 year variations,
                 which have clearly marked teleconnections. Decadal
                 trends are also apparent in the historical record of
                 the NAO and may be due to either stochastic or
                 deterministic processes. Evidence is presented that
                 suggests the NAO exhibits 'long-range' dependence
                 having winter values residually correlated over many
                 years. Several simple stochastic models have been used
                 to fit the NAO SLP (sea-level pressure) wintertime
                 index over the period 1864-1998, and their performance
                 at predicting the following year has been assessed.
                 Long-range fractionally integrated noise provides a
                 better fit than does either stationary red noise or a
                 non-stationary random walk.",
}

@Article{ste:edf,
  title =        "{EDF} Statistics for Goodness of Fit and Some
                 Comparisons",
  author =       "M. A. Stephens",
  journal =      JASA,
  volume =       "69",
  number =       "347",
  pages =        "730--737",
  year =         "1974",
  keywords =     "Normal distribution; Exponential distribution; Power;
                 Anderson-Darling statistic; Cram{\'e}r-von Mises test;
                 Kolmogorov-Smirnov test; EDF = empirical distribution
                 function",
}

@Article{ste:estimation,
  title =        "Estimation of the mean of a multivariate normal
                 distribution",
  author =       "Charles M. Stein",
  journal =      AofS,
  volume =       "9",
  number =       "6",
  year =         "1981",
  pages =        "1135--1151",
}

@InCollection{ste:tests-edf,
  title =        "Tests Based on {EDF} Statistics",
  author =       "Michael A. Stephens",
  pages =        "97--193",
  crossref =     "dag-ste:goodness",
}

@InCollection{ste:tests-exp,
  title =        "Tests for the Exponential Distribution",
  author =       "Michael A. Stephens",
  pages =        "421--459",
  crossref =     "dag-ste:goodness",
}

@Article{ste:use,
  title =        "Use of the {K}olmogorov--{S}mirnov, {C}ram{\'e}r--von
                 {M}ises and related statistics without extensive
                 tables",
  author =       "Michael A. Stephens",
  journal =      JRSSB,
  volume =       "32",
  number =       "1",
  year =         "1970",
  pages =        "115--122",
}

@Article{sto-lan-ngy:practical,
  title =        "Practical synthesis of accurate fractal images",
  author =       "M. A. Stosik and R. G. Lane and D. T. Nguyen",
  journal =      "Graphical Models and Image Processing",
  volume =       "57",
  number =       "3",
  year =         "1995",
  pages =        "206--219",
  abstract =     "This paper compares the synthesis of fractal images
                 using both wavelets and a modified form of the random
                 midpoint displacement algorithm. The accuracy of the
                 generated fractal is investigated by an analysis of its
                 second-order temporal statistics. It is shown that,
                 although wavelets can be used to produce a good
                 approximation to fractional Brownian motion, a
                 technique based on the random midpoint displacement
                 algorithm is in practice much simpler to implement,
                 faster to generate, and results in a comparable
                 accuracy. Furthermore the proposed method is shown to
                 be considerably more efficient computationally.",
}

@Unpublished{sto:remarks,
  title =        "Remarks on the Unsubsampled Wavelet Transform and the
                 Lifting Scheme",
  author =       "Alexander Stoffel",
  year =         "1998",
  note =         "Submitted to {\em Signal Processing}",
}

@Unpublished{str-etal:multiwavelet,
  title =        "The Application of Multiwavelet Filter Banks to Image
                 Processing",
  author =       "V. Strela and P. N. Heller and G. Strang and P.
                 Topiwala and C. Heil",
  year =         "1995",
  note =         "Submitted to {\em IEEE Transactions on Image
                 Processing}",
  url =          "http://www-math.mit.edu/~gs/papers/mw_journal.ps.gz",
}

@Article{str-hah:mammograms,
  title =        "Wavelet Transforms for Detecting Microcalcifications
                 in Mammograms",
  author =       "Robin N. Strickland and Hee Il Hahn",
  journal =      IEEETMI,
  volume =       "15",
  number =       "2",
  year =         "1996",
  pages =        "218--229",
  email =        "strickland@ece.arizona.edu",
  abstract =     "Clusters of fine, granular microcalcifications in
                 mammograms may be an early sign of disease. Individual
                 grains are difficult to detect and segment due to size
                 and shape variability and because the background
                 mammogram texture is typically inhomogeneous. We
                 develop a two-stage method based on wavelet transforms
                 for detecting and segmenting calcifications. The first
                 stage is based on an undecimated wavelet transform,
                 which is simply the conventional filter bank
                 implementation without downsampling, so that the
                 low-low (LL), low-high (LH), high-low (HL), and
                 high-high (HH) sub-bands remain at full size. Detection
                 takes place in HH and the combination LH+HL. Four
                 octaves are computed with two inter- octave voices for
                 finer scale resolution. By appropriate selection of the
                 wavelet basis the detection of microcalcifications in
                 the relevant size range can be nearly optimized. In
                 fact, the filters which transform the input image into
                 HH and LH+HL are closely related to prewhitening
                 matched filters for detecting Gaussian objects
                 (idealized microcalcifications) in two common forms of
                 Markov (background) noise. The second stage is designed
                 to overcome the limitations of the simplistic Gaussian
                 assumption and provides an accurate segmentation of
                 calcification boundaries. Detected pixel sites in HH
                 and LH+HL are dilated then weighted before computing
                 the inverse wavelet transform. Individual
                 microcalcifications are greatly enhanced in the output
                 image, to the point where straightforward thresholding
                 can be applied to segment them. FROC curves are
                 computed from tests using a freely distributed database
                 of digitized mammograms.",
}

@Book{str-ngu:book,
  author =       "Gilbert Strang and Truong Nguyen",
  title =        "Wavelets and Filter Banks",
  publisher =    "Wellesley-Cambridge Press",
  year =         "1996",
  address =      "Wellesley, MA",
  url =          "http://saigon.ece.wisc.edu/~waveweb/Tutorials/overview.html",
  abstract =     "This new textbook by Gilbert Strang and Truong Nguyen
                 offers a clear and easy-to-understand introduction to
                 two central ideas -- filter banks for discrete signals,
                 and wavelets. The connections are fully explained --
                 the wavelet is determined by a choice of filter
                 coefficients. All important wavelet properties
                 (orthogonality or biorthogonality, symmetry, accuracy
                 of approximation, and smoothness) come from specific
                 properties of the filters. The text shows how to
                 construct those filters and wavelets. The applications
                 are very widespread -- and they continue to develop
                 rapidly. The book gives a direct approach to signal
                 processing and image processing through filter banks
                 that iterate on the lowpass filter (this is the wavelet
                 idea). Blocking and ringing artifacts are analyzed,
                 along with many MATLAB applications. Wavelets and
                 Filter Banks is written for the very broad audience
                 that uses these ideas: Digital Signal Processing and
                 Speech Processing, Image Processing including Medical
                 Imaging, Scientific and Engineering Applications,
                 Students and Professionals (wanting to understand
                 wavelets!)",
}

@InCollection{str-sie:haar,
  title =        "The {H}aar Wavelet Transform in the Time Series
                 Similarity Paradigm",
  author =       "Z. R. Struzik and A. P. J. M. Siebes",
  booktitle =    "Principles of Data Mining and Knowledge Discovery",
  editor =       "J. M. Zytkow and J. Rauch",
  publisher =    "Springer-Verlag",
  address =      "Berlin",
  pages =        "12--22",
  year =         "1999",
  email =        "Zbigniew.Struzik@cwi.nl",
  abstract =     "Similarity measures play an important role in many
                 data mining algorithms. To allow the use of such
                 algorithms on non-standard databases, such as databases
                 of financial time series, their similarity measure has
                 to be defined. We present a simple and powerful
                 technique which allows for the rapid evaluation of
                 similarity between time series in large data bases. It
                 is based on the orthonormal decomposition of the time
                 series into the Haar basis. We demonstrate that this
                 approach is capable of providing estimates of the local
                 slope of the time series in the sequence of
                 multi-resolution steps. The Haar representation and a
                 number of related represenations derived from it are
                 suitable for direct comparison, e.g. evaluation of the
                 correlation product. We demonstrate that the distance
                 between such representations closely corresponds to the
                 subjective feeling of similarity between the time
                 series. In order to test the validity of subjective
                 criteria, we test the records of currency exchanges,
                 finding convincing levels of correlation.",
}

@InProceedings{str-sie:iwoss99,
  title =        "Measuring Time Series' Similarity through Large
                 Singular Features Revealed with Wavelet
                 Transformation",
  author =       "Z. R. Struzik and A. P. J. M. Siebes",
  booktitle =    "Proceedings of the International Workshop on Database
                 and Expert Systems Application",
  month =        sep,
  publisher =    "IEEE Computer Society Press",
  address =      "Florence, Italy",
  year =         "1999",
  pages =        "162--166",
  abstract =     "For the majority of data mining applications, there
                 are no models of data which would facilitate the task
                 of comparing records of time series. We propose a
                 generic approach to comparing noise time series using
                 the largest deviations from consistent statistical
                 behaviour. For this purpose we use a powerful framework
                 based on wavelet decomposition, which allows filtering
                 polynomial bias, while capturing the essential singular
                 behaviour. In addition, we are able to reveal
                 scale-wise ranking of singular events including their
                 scale free characteristic: the Hoelder exponent.",
}

@InProceedings{str-sie:pakdd98,
  title =        "Wavelet Transform in Similarity Paradigm",
  author =       "Z. R. Struzik and A. P. J. M. Siebes",
  booktitle =    "Proceedings of the Pacific-Asia Conference on
                 Knowledge Discovery and Data Mining",
  series =       "Lecture Notes in Artificial Intelligence",
  volume =       "1394",
  month =        apr,
  pages =        "295--309",
  year =         "1998",
  address =      "Melbourne, Australia",
  abstract =     "Searching for similarity in time series finds still
                 broader applications in data mining. However, due to
                 the very broad spectrum of data involved, there is no
                 possibility of defining one single notion of similarity
                 suitable to serve all applications. We present a
                 powerful framework based on wavelet decomposition,
                 which allows designing and implementing a variety of
                 criteria for the evaluation of similarity between time
                 series. As an example, two main classes of similarity
                 measures are considered. One is the global, statistical
                 similarity, which uses the wavelet transform derived
                 Hurst exponent to classify time series according to
                 their global scaling properties. The second measure
                 estimates similarity locally using the scale-position
                 bifurcation representation.",
}

@TechReport{str-sie:paradigm1,
  title =        "Wavelet transform in similarity paradigm {I}",
  author =       "Zbigniew R. Struzik and Arno P. J. M. Siebes",
  number =       "INS-R9802",
  institution =  "CWI, Amsterdam, The Netherlands",
  year =         "1998",
  abstract =     "Searching for similarity in time series finds still
                 broader applications in data mining. However, due to
                 the very broad spectrum of data involved, there is no
                 possibility of defining one single notion of similarity
                 suitable to serve all applications.",
}

@TechReport{str-sie:paradigm2,
  title =        "Wavelet transform in similarity paradigm {II}",
  author =       "Zbigniew R. Struzik and Arno P. J. M. Siebes",
  number =       "INS-R9815",
  institution =  "CWI, Amsterdam, The Netherlands",
  year =         "1998",
  abstract =     "For the majority of data mining applications, there
                 are no models of data which would facilitate the tasks
                 of comparing records of time series, thus leaving one
                 with `noise' as the only description. We propose a
                 generic approach to comparing noise time series using
                 the largest deviations from consistent statistical
                 behaviour. For this purpose we use a powerful framework
                 based on wavelet decomposition, which allows filtering
                 polynomial bias, while capturing the essential singular
                 behaviour. In particular we are able to reveal
                 scale-wise ranking of singular events including their
                 scale-free characteristic: the H{\"o}lder exponent. We
                 use such characteristics to design a compact
                 representation of the time series suitable for direct
                 comparison, e.g. evaluation of the correlation product.
                 We demonstrate that the distance between such
                 representations closely corresponds to the subjective
                 feeling of similarity between the time series. In order
                 to test the validity of subjective criteria, we test
                 the records of currency exchanges, finding convincing
                 levels of (local) correlation.",
}

@Article{str-str:multiwavelets,
  title =        "Orthogonal multiwavelets with vanishing moments",
  author =       "Gilbert Strang and Vasily Strela",
  journal =      OE,
  volume =       "33",
  number =       "7",
  year =         "1994",
  pages =        "2104--2107",
  email =        "gs@math.mit.edu",
  keywords =     "vanishing moments dilation equation scaling function
                 low-pass filter high-pass filter matrices vectors
                 translation finite energy matrix coefficients piecewise
                 linear orthogonal wavelets orthogonal multiwavelets",
  abstract =     "A scaling function is the solution to a dilation
                 equation Phi(t)= Sigma c/sub k/ Phi (2t-k), in which
                 the coefficients come from a low-pass filter. The
                 coefficients in the wavelet W(t)= Sigma d/sub k/ Phi
                 (2t-k) come from a high-pass filter. When these
                 coefficients are matrices, Phi and W are vectors: there
                 are two or more scaling functions and an equal number
                 of wavelets. By dilation and translation of the
                 wavelets, we have an orthogonal basis W/sub ijk/=W/sub
                 i/(2/sup j/t-k) for all functions of finite energy.
                 These ``multiwavelets'' open new possibilities. They
                 can be shorter, with more vanishing moments, than
                 single wavelets. They can be symmetric, which is
                 impossible for scalar wavelets (except for Haar's). We
                 determine the conditions to impose on the matrix
                 coefficients c/sub k/ in the design of multiwavelets,
                 and we construct a new pair of piecewise linear
                 orthogonal wavelets with two vanishing moments.",
}

@TechReport{str-wal:denoising,
  title =        "Signal and Image denoising via wavelet thresholding:
                 {O}rthogonal and biorthogonal, scalar and multiple
                 wavelet transforms",
  author =       "Vasily Strela and Andrew T. Walden",
  number =       "TR-98-01",
  institution =  "Statistics Section, Department of Mathematics,
                 Imperial College of Science, Technology \& Medicine",
  year =         "1998",
}

@InProceedings{str-wal:orthogonal,
  title =        "Orthogonal and biorthogonal multiwavelets for signal
                 denoising and image compression",
  author =       "Vasily Strela and Andrew T. Walden",
  crossref =     "szu:wavelet5",
}

@Article{str:brief,
  title =        "Wavelets and Dilation Equations: {A} Brief
                 Introduction",
  author =       "Gilbert Strang",
  journal =      SIREV,
  volume =       "31",
  number =       "4",
  year =         "1989",
  pages =        "614--627",
  url =          "http://www-math.mit.edu/~gs/papers/siamrev.ps.gz",
  abstract =     "This is an introduction to the construction of
                 wavelets from the solution to a dilation equation. It
                 discusses the approximation and orthogonal properties
                 of wavelets and describes the recursive algorithms that
                 decompose and reconstruct a function. The object of
                 wavelets is to localize as far as possible in both time
                 and frequency, with efficient algorithms.",
}

@Unpublished{str:creating,
  title =        "Creating and Comparing Wavelets",
  author =       "Gilbert Strang",
  year =         "1996",
  note =         "Department of Mathematics, Massachusetts Institute of
                 Technology",
  url =          "http://www-math.mit.edu/~gs/papers/dundee.ps.gz",
  email =        "gs@math.mit.edu",
}

@InCollection{str:ftae99,
  title =        "Local Effective {H}{\"o}der Exponent Estimation on the
                 Wavelet Transform Maxima Tree",
  author =       "Z. R. Struzik",
  booktitle =    "Fractals: Theory and Applications in Engineering",
  editor =       "Michel Dekking and Jacques L\'{e}vy V\'{e}hel and
                 Evelyne Lutton and Claude Tricot",
  address =      NY,
  publisher =    "Springer-Verlag",
  pages =        "93--112",
  year =         "1999",
  abstract =     "We present a robust method of estimating an effective
                 Holder exponent locally at an arbitrary resolution. The
                 method is motivated by the multiplicative cascade
                 paradigm, and implemented on the hierarchy of
                 singularities revealed with the wavelet transform
                 modulus maxima tree. In addition, we illustrate the
                 possibility of the direct estimation of the scaling
                 spectrum of the effective Holder exponent, and we link
                 it to the established partition functions based
                 multifractal formalism. We motivate both the local and
                 the global multifractal analysis by showing examples of
                 computer generated and real life time series.",
}

@Article{str:make,
  title =        "How to Make Wavelets",
  author =       "Robert S. Strichartz",
  journal =      AMM,
  volume =       "100",
  number =       "6",
  year =         "1993",
  pages =        "539--557",
  keywords =     "Fourier analysis, Matrices, Norms, Matrix mechanics",
  abstract =     "Wavelet bases where Haar functions are constructed
                 from a single function by dyadic dilations and integer
                 translations are considered as approximate definitions
                 of a wavelet expansion. First, a scaling function and
                 associated multiresolution analysis are chosen. The
                 orthonormality conditions should be satisfied by
                 generation of a multiresolution analysis of the
                 function. The wavelets are then constructed by solving
                 two algebraic identities and establishing the
                 properties of the wavelet functions.",
}

@PhdThesis{str:thesis,
  title =        "Multiwavelets: Theory and Applications",
  author =       "Vasily Strela",
  school =       "Massachusetts Institute of Technology",
  year =         "1996",
  url =          "http://pascal.dartmouth.edu/~strela/vvthmain.ps",
}

@Article{str:versus,
  title =        "Wavelet transforms versus {F}ourier transforms",
  author =       "Gilbert Strang",
  journal =      BAMathS,
  volume =       "28",
  number =       "2",
  year =         "1993",
  pages =        "288--305",
  abstract =     "An orthogonal basis for piecewise constant functions
                 is constructed by dilation and translation. The
                 wavelength transform maps each function to its
                 coefficients with respect to this basis. The
                 approximation is found to be poor and is improved by
                 dilation equations. Higher-order wavelets are
                 constructed and indirect and recursive methods are used
                 to compute them. The practicality of the wavelet
                 transform and Fourier transform in signal processing
                 are discussed.",
}

@Article{str:wavelets,
  title =        "Wavelets",
  author =       "G. Strang",
  journal =      "American Scientist",
  volume =       "82",
  year =         "1994",
  pages =        "250--255",
  url =          "http://www-math.mit.edu/~gs/papers/amsci.ps.gz",
  abstract =     "The transformation of signals into a sum of small,
                 overlapping waves offers a new method for analyzing,
                 storing and transmitting information. The author
                 discusses: Fourier and wavelet transforms; choosing the
                 best basis; higher dimensions; fast wavelet transform;
                 Daubechies wavelets; high-definition television; the
                 future of fingerprints.",
}

@Unpublished{swe-sch:building,
  title =        "Building Your Own Wavelets at Home",
  author =       "Wim Sweldens and Peter Schr{\"o}der",
  year =         "1996",
  note =         "In ``Wavelets in Computer Graphics'', ACM SIGGRAPH
                 Course Notes",
  url =          "http://cm.bell-labs.com/who/wim/papers/athome.ps.gz",
  abstract =     "We give an practical overview of three simple
                 techniques to construct wavelets under general
                 circumstances: interpolating subdivision, average
                 interpolation, and lifting. We include examples
                 concerning the construction of wavelets on an interval,
                 weighted wavelets, and wavelets adapted to irregular
                 samples.",
}

@Article{swe:future,
  author =       "W. Sweldens",
  title =        "Wavelets: {W}hat Next?",
  journal =      "Proc. IEEE",
  volume =       "84",
  number =       "4",
  pages =        "680--685",
  year =         "1996",
  url =          "http://cm.bell-labs.com/who/wim/papers/future.ps",
  abstract =     "In this concluding article, we want to look ahead and
                 see what the future can bring to wavelet research. We
                 try to find a common denominator for ``wavelets'' and
                 identify promising research directions and challenging
                 problems.",
}

@Article{swe:lift1,
  author =       "W. Sweldens",
  title =        "The lifting scheme: {A} custom-design construction of
                 biorthogonal wavelets",
  journal =      "Appl. Comput. Harmon. Anal.",
  volume =       "3",
  number =       "2",
  pages =        "186--200",
  year =         "1996",
  url =          "http://cm.bell-labs.com/who/wim/papers/lift1.ps",
  abstract =     "We present the lifting scheme, a new idea of
                 constructing compactly supported wavelets with
                 compactly supported duals. The lifting scheme provides
                 a simple relationship between all multiresolution
                 analyses with the same scaling function. It isolates
                 the degrees of freedom remaining after fixing the
                 biorthogonality relations. Then one has full control
                 over these degrees of freedom to custom-design the
                 wavelet for a particular application. It also leads to
                 a faster implementation of the fast wavelet transform.
                 We illustrate the use of the lifting scheme in the
                 construction of wavelets with interpolating scaling
                 functions.",
}

@TechReport{swe:lift2,
  author =       "W. Sweldens",
  title =        "The lifting scheme: {A} construction of second
                 generation wavelets",
  institution =  "Department of Mathematics, University of South
                 Carolina",
  number =       "1995:6",
  year =         "1995",
  url =          "http://cm.bell-labs.com/who/wim/papers/lift2.ps",
  abstract =     "We present the lifting scheme, a simple construction
                 of second generation wavelets, wavelets that are not
                 necessarily translates and dilates of one fixed
                 function. Such wavelets can be adapted to intervals,
                 domains, surfaces, weights, and irregular samples. We
                 show how the lifting scheme leads to a faster, in-place
                 calculation of the wavelet transform. Several examples
                 are included.",
}

@InProceedings{swe:spie95,
  author =       "W. Sweldens",
  title =        "The Lifting Scheme: {A} New Philosophy in Biorthogonal
                 Wavelet Constructions",
  pages =        "68--79",
  crossref =     "lai-uns:wavelet3",
  url =          "http://cm.bell-labs.com/who/wim/papers/spie95.ps",
  abstract =     "In this paper we present the basic idea behind the
                 lifting scheme, a new construction of biorthogonal
                 wavelets which does not use the Fourier transform. In
                 contrast with earlier papers we introduce lifting
                 purely from a wavelet transform point of view and only
                 consider the wavelet basis functions in a later stage.
                 We show how lifting leads to a faster, fully in-place
                 implementation of the wavelet transform. Moreover, it
                 can be used in the construction of second generation
                 wavelets, wavelets that are not necessarily translates
                 and dilates of one function. A typical example of the
                 latter are wavelets on the sphere.",
}

@Article{sza-gal-kis:application2,
  title =        "{A}pplication of wavelet analysis in variable star
                 research. {II}. {T}he semiregular star {V} {B}ootis",
  journal =      AandA,
  volume =       "308",
  number =       "3",
  year =         "1996",
  pages =        "791--8",
  author =       "K. Szatmary and J. Gal and L. L. Kiss",
  abstract =     "For pt.I see Astron. Astrophys. Suppl. Ser., vol.108,
                 no.2, p.377-94 (1994). Light curve analysis of the
                 SRa-type variable V Boo is presented and discussed. The
                 periods are determined and the stability of these
                 periods as well as their amplitudes are investigated
                 with wavelet analysis. The amplitude decrease is
                 studied with the so-called ridge procedure, which shows
                 that the amplitude of the longer period strongly
                 decreased while the amplitude of the shorter period
                 seems to remain stable. The possible interpretations of
                 this effect are discussed. Using theoretical models and
                 observational relations physical parameters and
                 pulsational modes of V Boo are also estimated.",
  keywords =     "wavelet analysis, variable star research, light curve
                 analysis, sra type variable, periods, period stability,
                 period amplitudes, amplitude decrease, ridge procedure,
                 interpretations, theoretical models, observational
                 relations, physical parameters, pulsational modes.",
}

@Article{sza-vin-gal:application1,
  title =        "{A}pplication of wavelet analysis in variable star
                 research. {I}. {P}roperties of the wavelet map of
                 simulated variable star light curves",
  journal =      "AASS",
  volume =       "108",
  number =       "2",
  year =         "1994",
  pages =        "377--394",
  author =       "K. Szatmary and J. Vinko and J. Gal",
  email =        "K.Szatmary@physx.u-szeged.hu,
                 vinko@physx.u-szeged.hu",
  abstract =     "A type of the relatively new time-frequency method,
                 the wavelet analysis is studied. Some results of
                 testing this method are presented. The test data series
                 were defined so that they show similarities with the
                 light variations of variable stars. The effects of
                 observational noise and irregularities in data sampling
                 are pointed out. The wavelet analysis seems to be a
                 suitable method for detecting the local behaviour of
                 the light curves, e.g. phase jump or mode switching.
                 The investigation of time-dependent phenomena, e.g.
                 amplitude or frequency modulation, is more available
                 than in the case of standard Fourier analysis. In order
                 to interpret the real wavelet maps of variable stars it
                 is necessary to take into account the properties of the
                 method presented by similar tests.",
  keywords =     "stellar photometry, measurement technique, variable
                 star light curve, wavelet analysis, variable star,
                 wavelet map, light curve, time-frequency method,
                 observational noise, irregularities, method.",
}

@Article{szi-kat-par-alb-cah:local,
  title =        "The local effect of intermittency on the inertial
                 subrange energy spectrum of the atmospheric surface
                 layer",
  author =       "Jozsef Szilagyi and Gabriel G. Katul and Marc B.
                 Parlange and John D. Albertson and Anthony T. Cahill",
  journal =      BLM,
  volume =       "79",
  number =       "1--2",
  year =         "1996",
  pages =        "35--50",
  abstract =     "Orthonormal wavelet expansions are applied to
                 atmospheric surface layer velocity measurements. The
                 effect of intermittent events on the energy spectrum of
                 the inertial subrange is investigated through analysis
                 of wavelet coefficients. The local nature of the
                 orthonormal wavelet transform in physical space makes
                 it possible to identify a relationship between the
                 inertial subrange slope of the local wavelet spectrum
                 and a simple indicator (i.e. the local variance of the
                 signal) of local intermittency buildup. The slope of
                 the local wavelet energy spectrum in the inertial
                 subrange is shown to be sensitive to the presence of
                 intermittent events. During well-developed intermittent
                 events (coherent structures), the slope of the energy
                 spectrum is somewhat steeper than -5/3, while in less
                 active regions the slope is found to be flatter than
                 -5/3. When the slopes of local wavelet spectra are
                 ensemble averaged, a slope of -5/3 is recovered for the
                 inertial subrange.",
}

@Article{tac:differentiation,
  title =        "The differentiation by a wavelet and its application
                 to the estimation of a transfer function",
  author =       "Y. Tachibana",
  journal =      IEICETFECCS,
  volume =       "E81A",
  number =       "6",
  year =         "1998",
  pages =        "1194--1200",
  keywords =     "wavelet digital filter differential filters digital
                 signal processing identification parameters estimation
                 step response",
  abstract =     "This paper deals with a set of differential operators
                 for calculating the differentials of an observed signal
                 by the Daubechies wavelet and its application for the
                 estimation of the transfer function of a linear system
                 by using non-stationary step-like signals. The
                 differential operators are constructed by iterative
                 projections of the differential of the scaling function
                 for a multiresolution analysis into a dilation
                 subspace. By the proposed differential operators we can
                 extract the arbitrary order differentials of a signal.
                 We propose a set of identifiable filters constructed by
                 the sum of multiple filters with the first order lag
                 characteristics. Using the above differentials and the
                 identifiable filters we propose an identification
                 method for the transfer function of a linear system. In
                 order to ensure the appropriateness and effectiveness
                 of the proposed method some numerical simulations are
                 presented.",
}

@InProceedings{tas:near-best,
  title =        "Near-best basis selection algorithms with non-additive
                 information cost functions",
  author =       "C. Taswell",
  booktitle =    "Proceedings of the IEEE-SP International Symposium on
                 Time- Frequency and Time-Scale Analysis",
  editor =       "M. G. Amin",
  publisher =    "IEEE Press",
  address =      "Philadelphia, PA",
  year =         "1994",
  pages =        "13--16",
  url =          "http://www.wavebox.com/NBBSA94.ps",
  keywords =     "near-best basis selection algorithms non-additive
                 information cost functions search algorithms signal
                 decomposition decision criteria wavelet packet
                 transforms additive information costs matching pursuit
                 decomposition time- frequency analysis data
                 compression",
  abstract =     "Search algorithms for finding signal decompositions
                 called near-best bases using decision criteria called
                 non-additive information costs are proposed for
                 selecting bases in wavelet packet transforms. These new
                 methods are compared with the best bases and additive
                 information costs of Coifman and Wickerhauser (see IEEE
                 Trans. Information Theory, vol.38, p.713-18, 1992). All
                 near-best and best bases were also compared with the
                 matching pursuit decomposition of Mallat and Zhang (see
                 IEEE Trans. Signal Processing, vol.41, p.3397-3415,
                 1993). Preliminary experiments suggest that for the
                 application of time-frequency analysis, a wide variety
                 of results can be obtained with the different methods,
                 and that for the application of data compression, the
                 near-best basis selected with non-additive costs may
                 outperform the best basis selected with additive
                 costs.",
}

@Article{tas:satisficing,
  title =        "Satisficing search algorithms for selecting near-best
                 bases in adaptive tree-structured wavelet transforms",
  author =       "C. Taswell",
  journal =      IEEETSP,
  volume =       "44",
  number =       "10",
  year =         "1996",
  pages =        "2423--2438",
  url =          "http://www.wavebox.com/SSANBB96.ps",
  keywords =     "image compression speech",
  abstract =     "Satisficing search algorithms are proposed for
                 adaptively selecting near-best basis and near-best
                 frame decompositions in redundant tree-structured
                 wavelet transforms, Any of a variety of additive or
                 nonadditive information cost functions can be used as
                 the decision criterion for comparing and selecting
                 nodes when searching through the tree,The algorithms
                 are applicable to tree-structured transforms generated
                 by any kind of wavelet whether orthogonal,
                 biorthogonal, or nonorthogonal, These satisficing
                 search algorithms implement suboptimizing rather than
                 optimizing principles, and acquire the important
                 advantage of reduced computational complexity with
                 significant savings in memory, flops, and time, Despite
                 the suboptimal approach, top-down tree-search
                 algorithms with additive or nonadditive costs that
                 yield near-best bases can be considered, in certain
                 important and practical situations, better than
                 bottom-up tree-search algorithms with additive costs
                 that yield best bases, Here, ''better than'' means
                 that, effectively, the same level of performance can be
                 attained for a relative fraction of the computational
                 work, Experimental results comparing the various
                 information cost functions and basis selection methods
                 are demonstrated for both data compression of real
                 speech and time- frequency analysis of artificial
                 transients.",
}

@InCollection{tas:top-down,
  title =        "Top-Down and Bottom-Up Tree Search Algorithms for
                 Selecting Bases in Wavelet Packet Transforms",
  author =       "Carl Taswell",
  crossref =     "ant-opp:wavelets",
  pages =        "???--???",
  url =          "http://www.wavebox.com/TDBUTSA94.ps",
  abstract =     "Search algorithms for finding signal decompositions
                 called near-best bases using decision criteria called
                 non-additive information costs have recently been
                 proposed by Taswell for selecting bases in wavelet
                 packet transforms represented as binary trees. These
                 methods are extended here to distinguish between
                 top-down and bottom-up tree searches. Other new
                 non-additive information cost functions are also
                 proposed. In particular, the near-best basis with the
                 non-additive cost of the Shannon entropy on
                 probabilities is compared against the best basis with
                 the additive cost of the Coifman-Wickerhauser entropy
                 on energies. All wavelet packet basis decompositions
                 are also compared with the nonorthogonal matching
                 pursuit decomposition of Mallat and Zhang and the
                 orthogonal matching pursuit decomposition of Pati et
                 al. Monte Carlo experiments using a constant-bit-rate
                 variable-distortion paradigm for lossy compression
                 suggest that the statistical performance of top-down
                 near-best bases with non-additive costs is superior to
                 that of bottom-up best bases with additive costs.
                 Top-down near-best bases provide a significant increase
                 in computational efficiency with reductions in memory,
                 flops, and time while nevertheless maintaining similar
                 coding efficiency with comparable reconstruction errors
                 measured by l^p-norms. Finally, a new compression
                 scheme called parameterized model coding is introduced
                 and demonstrated with results showing better
                 compression than standard scalar quantization coding at
                 comparable levels of distortion.",
}

@Book{teo:computational,
  title =        "Computational Signal Processing with Wavelets",
  author =       "A. Teolis",
  publisher =    "Springer-Verlag",
  year =         "1997",
  pages =        "332",
  keywords =     "Introduction * Mathematical Preliminaries * Signal
                 Representation and Frames * Continuous Wavelet
                 Transform * Discrete Wavelet Transform * Non-orthogonal
                 Wavelet Transform * Wavelet Signal Processing * World
                 Wide Web Access",
  abstract =     "Computational Signal Processing with Wavelets examines
                 both theoretical and practical aspects of computational
                 signal processing using wavelets. Theoretically, an
                 emphasis is placed on balancing the accessibility of
                 the material with the level of mathematical rigor which
                 sacrifices as little as possible of both.
                 Computationally, wavelet signal processing algorithms
                 are presented and applied to signal compression, noise
                 suppression, and signal identification. Numerical
                 illustrations of these computational techniques are
                 further provided with interactive software (MATLAB) via
                 an internet accessible WEB site. Starting from basic
                 principles of signal representation with atomic
                 functions, a mathematically well founded theory of the
                 discretization of analog signals is developed. General
                 families are specialized to wavelet families and the
                 discrete representation are specialized to generally
                 non-orthogonal wavelet transforms. The theory leads
                 naturally to the computer implementation of the
                 non-orthogonal wavelet transform. Specific topics
                 covered include general signal representation,
                 continuous and discrete Fourier transforms, orthonormal
                 and biorthogonal bases, frames, wavelet frames and
                 frame reconstruction, discrete wavelet transform,
                 multi-resolution analysis, orthonormal wavelets,
                 continuous wavelet transform, non-orthogonal wavelet
                 transform, and wavelet based signal processing
                 algorithms for compression, noise suppression, and
                 identification. The discussion is at the level of a
                 senior or beginning graduate student level and is
                 accessible to signal processing professionals and
                 practicioners. Dissemination of the material is
                 provided by a hybrid combination of traditional (text)
                 and non-traditional (internet and electronic) media.",
}

@Article{tet-kri:ocean,
  title =        "{SAR} Ocean Image Representation Using Wavelets",
  author =       "Joseph G. Teti and H. N. Kritikos",
  journal =      IEEETGRS,
  volume =       "30",
  number =       "5",
  year =         "1992",
  pages =        "1089--1094",
  abstract =     "The utility of wavelet analysis as a tool for
                 geophysical research is examined using both continuous
                 and discrete versions of the wavelet transform. In both
                 cases, waveform decomposition and reconstruction is
                 possible using somewhat different computational
                 procedures. The theoretical background of each
                 procedure is briefly described and applied using a
                 specific 'wavelet'. The wavelet used is based on a
                 Gaussian function, and provides simultaneous
                 time-frequency (or space-wavenumber) localization that
                 meets the lower limit of the uncertainty principle. A
                 representation of this type is ideally suited for the
                 analysis of waveforms that arise from nonstationary
                 processes. The properties of wavelet analysis are
                 examined by expanding an FM-chirp waveform and azimuth
                 cuts taken from two different SAR ocean images. The
                 performance and ease of implementation are compared for
                 the continuous and discrete formulations, and the
                 effects of filtering in wavelet phase space using the
                 discrete case are also examined.",
}

@Article{tew-kim:correlation,
  title =        "Correlation Structure of the Discrete Wavelet
                 Coefficients of Fractional {B}rownian Motion",
  author =       "A. H. Tewfik and M. Kim",
  journal =      IEEETIT,
  volume =       "38",
  number =       "2",
  year =         "1992",
  pages =        "904--909",
  abstract =     "It is shown that the discrete wavelet coefficients of
                 fractional Brownian motion at different scales are
                 correlated and that their auto- and cross-correlation
                 functions decay hyperbolically fast at a rate much
                 faster than that of the autocorrelation of the
                 fractional Brownian motion itself. The rate of decay of
                 the correlation function in the wavelet domain is
                 primarily determined by the number of vanishing moments
                 of the analyzing wavelet.",
}

@Book{tit:book,
  title =        "The Theory of Functions",
  author =       "E. C. Titchmarsh",
  publisher =    "Oxford University Press",
  address =      "Oxford",
  edition =      "2",
  year =         "1939",
  pages =        "454",
}

@Article{tor-com:practical,
  title =        "A Practical Guide to Wavelet Analysis",
  author =       "Christopher Torrence and Gilbert P. Compo",
  journal =      BAMetS,
  volume =       "79",
  number =       "1",
  year =         "1998",
  pages =        "61--78",
  url =          "http://paos.colorado.edu/research/wavelets/",
  abstract =     "A practical step-by-step guide to wavelet analysis is
                 given, with examples taken from time series of the El
                 Nino-Southern Oscillation (ENSO). The guide includes a
                 comparison to the windowed Fourier transform, the
                 choice of an appropriate wavelet basis function, edge
                 effects due to finite-length time series, and the
                 relationship between wavelet scale and Fourier
                 frequency. New statistical significance tests for
                 wavelet power spectra are developed by deriving
                 theoretical wavelet spectra for white and red noise
                 processes and using these to establish significance
                 levels and confidence intervals. It is shown that
                 smoothing in time or scale can be used to increase the
                 confidence of the wavelet spectrum. Empirical formulas
                 are given for the effect of smoothing on significance
                 levels and confidence intervals. Extensions to wavelet
                 analysis such as filtering, the power Hovm{\"o}ller,
                 cross-wavelet spectra, and coherence are described. The
                 statistical significance tests are used to give a
                 quantitative measure of changes in ENSO variance on
                 interdecadal timescales. Using new datasets that extend
                 back to 1871, the Nino3 sea surface temperature and the
                 Southern Oscillation index show significantly higher
                 power during 1880-1920 and 1960-90, and lower power
                 during 1920-60, as well as a possible 15-yr modulation
                 of variance. The power Hovm{\"o}ller of sea level
                 pressure shows significant variations in 2--8-yr
                 wavelet power in both longitude and time.",
}

@Unpublished{tor-web:interdecadal,
  title =        "Interdecadal Changes in the {ENSO}-Monsoon System",
  author =       "Christopher Torrence and Peter J. Webster",
  journal =      JC,
  volume =       "12",
  number =       "8",
  year =         "1999",
  pages =        "2679--2690",
  url =          "http://www.cgd.ucar.edu/~torrence/interdec/",
  abstract =     "The El Nino-Southern Oscillation (ENSO) and Indian
                 monsoon are shown to have undergone significant
                 interdecadal changes in variance and coherency over the
                 last 125 years. Wavelet analysis is applied to indexes
                 of equatorial Pacific sea surface temperature (Nino3
                 SST), the Southern Oscillation index, and all-India
                 rainfall. Time series of 2-7-yr variance indicate
                 intervals of high ENSO-monsoon variance (1875-1920 and
                 1960-90) and an interval of low variance (1920-60). The
                 ENSO-monsoon variance also contains a modulation of
                 ENSO-monsoon amplitudes on a 12-20-yr timescale.The
                 annual-cycle (1 yr) variance time series of Nino3 SST
                 and Indian rainfall is negatively correlated with the
                 interannual ENSO signal. The 1-yr variance is larger
                 during 1935-60, suggesting a negative correlation
                 between annual-cycle variance and ENSO variance on
                 interdecadal timescales.The method of wavelet coherency
                 is applied to the ENSO and monsoon indexes. The Nino3
                 SST and Indian rainfall are found to be highly
                 coherent, especially during intervals of high variance.
                 The Nino3 SST and Indian rainfall are approximately 180
                 degrees out of phase and show a gradual increase in
                 phase difference versus Fourier period. All of the
                 results are shown to be robust with respect to
                 different datasets and analysis methods.",
}

@Article{tor-web:persistence,
  title =        "The Annual Cycle of Persistence in the {E}l
                 {N}i\~no-{S}outhern {O}scillation",
  author =       "Christopher Torrence and Peter J. Webster",
  journal =      QJRMS,
  volume =       "125",
  year =         "1998",
  pages =        "1985--2004",
  url =          "http://www.cgd.ucar.edu/~torrence/barrier/",
  keywords =     "El Ni\~no-Southern Oscillation, Predictability,
                 Interdecadal Variability",
  abstract =     "A spring `predictability barrier' exists in both data
                 and models of the El Ni\~no-Southern Oscillation (ENSO)
                 phenomenon. In statistical analyses this barrier
                 manifests itself as a drop-off in monthly persistence
                 (lagged correlation) while in coupled ocean-atmosphere
                 models it appears as a decrease in forecast skill. The
                 persistence barrier for ENSO indices is investigated
                 using historical sea surface temperature and sea level
                 pressure data. Simple statistical models are used to
                 show that the persistence barrier occurs because the
                 boreal spring is the transition time from one climate
                 state to another, when the `signal-to-noise' of the
                 system is lowest and the system is most susceptible to
                 perturbations. The strength of the persistence barrier
                 is shown to depend on the degree of phase locking of
                 the ENSO to the annual cycle. The phase locking of the
                 ENSO to the annual cycle, as well as the ENSO variance,
                 is shown to vary on interdecadal time scales. During
                 1871--1920 and 1960--1990 the ENSO variance was high,
                 while during 1920--1950 the ENSO variance was low.
                 Using wavelet analysis, this interdecadal variability
                 in ENSO is shown to be correlated with changes in
                 Indian summer monsoon strength. Finally, the change in
                 persistence barrier strength between 1960--1979 and
                 1980--1995 is related to changes in the phase locking
                 of ENSO to the annual cycle. These changes in
                 persistence and phase locking appear to be related to
                 the increased forecast skill seen in recent coupled
                 ocean-atmosphere models.",
}

@PhdThesis{tor:thesis,
  title =        "The El Ni\~no-Southern Oscillation: Interannual
                 Predictability and Interdecadal Variability",
  author =       "Christopher Torrence",
  school =       "University of Colorado at Boulder",
  year =         "1997",
}

@Article{tre-and:turbulence,
  title =        "On wavelet analysis of nonstationary turbulence",
  author =       "Beorge Trevi{\~n}o and Edgar L. Andreas",
  journal =      BLM,
  volume =       "81",
  number =       "3-4",
  year =         "1996",
  pages =        "271--288",
  keywords =     "coherent structures, forest canopy, transforms,
                 cascade, motions",
  abstract =     "Wavelets are new tools for turbulence analysis that
                 are yielding important insights into boundary-layer
                 processes. Wavelet analysis, however, has some as yet
                 undiscussed limitations: failure to recognize these can
                 lead to misinterpretation of wavelet analysis results.
                 Here we discuss some limitations of wavelet analysis
                 when applied to nonstationary turbulence. Our main
                 point is that the analysis wavelet must be carefully
                 matched to the phenomenon of interest, because wavelet
                 coefficients obscure significant information in the
                 signal being analyzed. For example, a wavelet that is a
                 second-difference operator can provide no information
                 on the linear trend in a turbulence signal. Wavelet
                 analysis also yields no meaningful information about
                 nonlinear behavior in a signal - contrary to claims in
                 the literature - because, at any instant, a wavelet is
                 a single-scale operator, while nonlinearity involves
                 instantaneous interactions among many scales.",
}

@InCollection{tri:adaptive,
  title =        "Adaptive Density Estimation",
  author =       "K. Tribouley",
  pages =        "385--395",
  crossref =     "ant-opp:wavelets",
}

@Article{tri:practical,
  title =        "Practical estimation of multivariate densities using
                 wavelet methods",
  author =       "K. Tribouley",
  journal =      SN,
  volume =       "49",
  number =       "1",
  year =         "1995",
  pages =        "41--62",
  abstract =     "This paper describes a practical method for estimating
                 multivariate densities using wavelets. As in kernel
                 methods, wavelet methods depend on two types of
                 parameters. On the one hand we have a functional
                 parameter: the wavelet [phi] (comparable to the kernel
                 K) and on the other hand we have a smoothing parameter:
                 the resolution index (comparable to the bandwidth h).
                 Classically, we determine the resolution index with a
                 cross-validation method. The advantage of wavelet
                 methods compared to kernel methods is that we have a
                 technique for choosing the wavelet [phi] among a fixed
                 family. Moreover, the wavelets method simplifies
                 significantly both the theoretical and the practical
                 computations.",
  keywords =     "Density estimation cross validation wavelet
                 orthonormal bases Besov spaces",
}

@Article{tso-kum-els-tso:dna,
  journal =      PRE,
  volume =       "53",
  number =       "2",
  year =         "1997",
  pages =        "1828--1834",
  title =        "{W}avelet analysis of {DNA} sequences",
  author =       "A. A. Tsonis and P. Kumar and J. B. Elsner and P. A.
                 Tsonis",
  abstract =     "In this paper we use wavelet analysis in order to
                 probe the localized structure of DNA sequences. We
                 demonstrate that, unlike other conventional approaches,
                 wavelets are able to decompose seemingly homogeneous
                 regions in noncoding sequences into smaller distinct
                 regions that obey their own repetition and construction
                 rules. The significance of this result to gene
                 evolution is discussed.",
  keywords =     "coding sequences, sampling theory, evolution,
                 propagation, gene",
}

@Article{tur-hal:interpolation,
  title =        "Interpolation Methods for Nonlinear Wavelet Regression
                 with Irregularly Spaced Design",
  author =       "Berwin A. Turlach and Peter Hall",
  journal =      "AS",
  volume =       "25",
  number =       "5",
  year =         "1997",
  email =        "berwin@alphasun.anu.edu.au",
  abstract =     "We suggest and discuss interpolation methods that
                 enable nonlinear wavelet estimators to be employed with
                 stochastic design, or non-dyadic regular design, in
                 problems of nonparametric regression. This approach
                 allows relatively rapid computation, involving dyadic
                 approximations to wavelet-after-interpolation
                 techniques. New types of interpolation are described,
                 enabling first-order variance reduction at the expense
                 of second-order increases in bias. The effect of
                 interpolation on threshold choice is addressed, and
                 appropriate thresholds are suggested for error
                 distributions with as few as four finite moments. A
                 concise account of mean squared error properties is
                 given for interpolation-based wavelet estimators
                 applied to piecewise-smooth functions.",
}

@Article{uns-ald:biomedical,
  journal =      PIEEE,
  volume =       "84",
  number =       "4",
  year =         "1996",
  pages =        "626--638",
  title =        "{A} review of wavelets in biomedical applications",
  author =       "M. Unser and A. Aldroubi",
  abstract =     "In this paper we present an overview of the various
                 uses of the wavelet transform (WT) in medicine and
                 biology. We start by describing the wavelet properties
                 that are the most important for biomedical
                 applications. In particular, we provide an
                 interpretation of the continuous wavelet transform
                 (CWT) as a prewhitening multiscale matched filter. Me
                 also briefly indicate the analogy between the WT and
                 some of the biological processing that occurs in the
                 early components of the auditory and visual system. We
                 then review the rises of the WT for the analysis of 1-D
                 physiological signals obtained by phonocardiography,
                 electrocardiography (ECC), and electroencephalography
                 (EEG), including evoked response Next, we provide a
                 survey of recent wavelet developments in medical
                 imaging. These include biomedical image processing
                 algorithms (e.g., noise reduction, image enhancement,
                 and detection of microcalcifications in mammograms),
                 image reconstruction and acquisition schemes
                 (tomography, and magnetic resonance imaging (MRI)), and
                 multiresolution methods for the registration and
                 statistical analysis of functional images of the brain
                 (positron emission tomography (PET) and functional MRI
                 (fMRI)). In each case, we provide the reader with some
                 general background information and a brief explanation
                 of how the methods work.",
}

@Article{uns-the-ald:shift,
  title =        "Shift-orthogonal wavelet bases",
  author =       "M. Unser and P. Thevenaz and A. Aldroubi",
  journal =      IEEETSP,
  volume =       "46",
  number =       "7",
  year =         "1998",
  pages =        "1827--1836",
  keywords =     "multiresolution approximations ondelettes spaces",
  abstract =     "Shift-orthogonal wavelets are a new type of
                 multiresolution wavelet bases that are orthogonal with
                 respect to translation (or shifts) within one level but
                 not with respect to dilations across scales. In this
                 paper, we characterize these wavelets and investigate
                 their main properties by considering two general
                 construction methods. In the first approach, we start
                 by specifying the analysis and synthesis function
                 spaces and obtain the corresponding shift-orthogonal
                 basis functions by suitable orthogonalization. In the
                 second approach, we take the complementary view and
                 start from the digital filterbank. We present several
                 illustrative examples, including a hybrid version of
                 the Battle-Lemarie spline wavelets. We also provide
                 filterbank formulas for the fast wavelet algorithm. A
                 shift-orthogonal wavelet transform is closely related
                 to an orthogonal transform that uses the same primary
                 scaling function; both transforms have essentially the
                 same approximation properties. One experimentally
                 confirmed benefit of relaxing the interscale
                 orthogonality requirement is that we can design
                 wavelets that decay faster than their orthogonal
                 counterpart.",
}

@TechReport{uyt-bul:red-black,
  title =        "The Red-Black Wavelet Transform",
  author =       "Geert Uytterhoeven and Adhemar Bultheel",
  number =       "271",
  institution =  "Department of Computer Science, Katholieke
                 Universiteit Leuven",
  year =         "1997",
  url =          "http://www.cs.kuleuven.ac.be/publicaties/rapporten/tw/TW271.ps.gz",
}

@TechReport{van-bro-fea:long-memory,
  title =        "Wavelet Analysis of Long-memory Processes",
  author =       "Marina Vannucci and Philip J. Brown and Tom Fearn",
  institution =  "Institute of Mathematics and Statistics, University of
                 Kent at Canterbury",
  note =         "UKC/IMS/98/22",
  year =         "1998",
  email =        "M.Vannucci@ukc.ac.uk",
}

@Article{van-cor:covariance,
  title =        "Covariance Structure of Wavelet Coefficients: {T}heory
                 and Models in a Bayesian Perspective",
  author =       "Marina Vannucci and Fabio Corradi",
  journal =      JRSSB,
  volume =       "?",
  number =       "?",
  year =         "1999",
  pages =        "???--???",
  email =        "mvannucci@stat.tamu.edu, corradi@stat.ds.unifi.it",
  url =          "http://stat.tamu.edu/~mvannucci/webpages/papers/wjrssb.ps",
}

@InCollection{van-cor:dependence,
  title =        "Modeling Dependence in the Wavelet Domain",
  author =       "Marina Vannucci and Fabio Corradi",
  pages =        "???--???",
  crossref =     "mul-vid:biwbm",
  url =          "http://stat.tamu.edu/~mvannucci/webpages/papers/deprior.ps",
}

@Article{van-vid:preventing,
  title =        "Preventing the {D}irac disaster: {W}avelet based
                 density estimation",
  author =       "Marina Vannucci and Brani Vidakovic",
  journal =      JISS,
  volume =       "6",
  number =       "2",
  year =         "1999",
  pages =        "???--???",
  url =          "http://stat.tamu.edu/~mvannucci/webpages/paper/wjiss.ps",
}

@PhdThesis{van:thesis,
  title =        "On the Application of Wavelets in Statistics",
  author =       "Marina Vannucci",
  school =       "Dipartimento di Statistica ``G. Parenti'', University
                 of Florence, Italy",
  year =         "1996",
  postscript =   "http://www.isds.duke.edu/~brani/wp/marina.ps",
  note =         "In Italian",
}

@Unpublished{vei-abr:constancy,
  title =        "A Statistical Test for the Time Constancy of Scaling
                 Exponents",
  author =       "Darryl Veitch and Patrice Abry",
  year =         "1999",
  note =         "Submitted for publication",
  url =          "http://www.serc.rmit.edu.au/~darryl/A4.ps",
}

@Article{vei-abr:joint,
  title =        "A wavelet based joint estimator of the parameters of
                 long-range dependence",
  author =       "Darryl Veitch and Patrice Abry",
  journal =      IEEETIT,
  volume =       "45",
  number =       "3",
  year =         "1999",
  pages =        "878--897",
  url =          "http://www.serc.rmit.edu.au/~darryl/A3.ps",
  keywords =     "Hurst parameter long-range dependence packet traffic
                 parameter estimation telecommunications networks
                 time-scale analysis wavelet decomposition",
  abstract =     "A joint estimator is presented for the two parameters
                 that define the long-range dependence phenomenon in the
                 simplest case. The estimator is based on the
                 coefficients of a discrete wavelet decomposition,
                 improving a recently proposed wavelet-based estimator
                 of the scaling parameter [4], as well as extending it
                 to include the associated power parameter. An important
                 feature is its conceptual and practical simplicity,
                 consisting essentially in measuring the slope and the
                 intercept of a linear fit after a discrete wavelet
                 transform is performed, a very fast (O(n)) operation.
                 Under well-justified technical idealizations the
                 estimator is shown to be unbiased and of minimum or
                 close to minimum variance for the scale parameter, and
                 asymptotically unbiased and efficient for the second
                 parameter. Through theoretical arguments and numerical
                 simulations it is shown that in practice, even for
                 small data sets, the bias is very small and the
                 variance close to optimal for both parameters.
                 Closed-form expressions are given for the covariance
                 matrix of the estimator as a function of data length,
                 and are shown by simulation to be very accurate even
                 when the technical idealizations are not satisfied,
                 Comparisons are made against two maximum-likelihood
                 estimators. In terms of robustness and computational
                 cost the wavelet estimator is found to be clearly
                 superior and statistically its performance is
                 comparable, We apply the tool to the analysis of
                 Ethernet teletraffic data, completing an earlier study
                 on the scaling parameter alone.",
}

@Article{vel-ulr:annealing,
  title =        "Simulated annealing wavelet estimation via
                 fourth-order cumulant matching",
  author =       "D. R. Velis and T. J. Ulrych",
  journal =      "Geophysics",
  volume =       "61",
  number =       "6",
  year =         "1996",
  pages =        "1939--1948",
  keywords =     "deconvolution, coefficients, gaussianity, phase",
  abstract =     "The fourth-order cumulant matching method has been
                 developed recently for estimating a mixed-phase wavelet
                 from a convolutional process. Matching between the
                 trace cumulant and the wavelet moment is done in a
                 minimum mean-squared error sense under the assumption
                 of a non-Gaussian, stationary, and statistically
                 independent reflectivity series. This leads to a highly
                 nonlinear optimization problem, usually solved by
                 techniques that require a certain degree of
                 linearization, and that invariably converge to the
                 minimum closest to the initial model. Alternatively, we
                 propose a hybrid strategy that makes use of a simulated
                 annealing algorithm to provide reliability of the
                 numerical solutions by reducing the risk of being
                 trapped in local minima. Beyond the numerical aspect,
                 the reliability of the derived wavelets depends
                 strongly on the amount of data available. However, by
                 using a multidimensional taper to smooth the trace
                 cumulant, we show that the method can be used even in a
                 trace-by-trace implementation, which is very important
                 from the point of view of stationarity and consistency.
                 We demonstrate the viability of the method under
                 several reflectivity models. Finally, we illustrate the
                 hybrid strategy using marine and held real data
                 examples. The consistency of the results is very
                 encouraging because the improved cumulant matching
                 strategy we describe can be effectively used with a
                 limited amount of data.",
}

@Book{vet-kov:wavelets,
  title =        "Wavelets and Subband Coding",
  author =       "Martin Vetterli and Jelena Kova{\v{c}}evi{\'c}",
  year =         "1995",
  publisher =    "Prentice Hall PTR",
  address =      "New Jersey",
  url =          "http://www.prenhall.com/allbooks/ptr_0130970808.html",
  keywords =     "discrete-time case, or filter banks; development of
                 wavelets; continuous wavelet and local Fourier
                 transforms; efficient algorithms for filter banks and
                 wavelet computations; and signal compression",
}

@TechReport{vid-kat-alb:multiscale,
  title =        "Multiscale Denoising of Self Similar Processes",
  author =       "Brani Vidakovic and Gabriel Katul and John Albertson",
  number =       "00-02",
  institution =  "Institute of Statisics and Decision Sciences, Duke
                 University",
  year =         "2000",
  url =          "http://ftp.isds.duke.edu/WorkingPapers/00-02.ps",
  abstract =     "A practical limitation to investigating
                 self-similarity in geophysical phenomena from their
                 measured state variables is that measured signals are
                 typically convolved with instrumentation noise at
                 multiple scales. This study develops and tests a
                 multiscale Bayesian model (BEFE) for separating a
                 $1/f$-like signal from inherent instrumentation noise
                 and contrasts its performance to the Wiener-type (WAS)
                 and Fourier amplitude (FAS) shrinkage methods. The
                 novel feature in BEFE is that the separation is
                 performed in the wavelet domain and involves the use of
                 a Bayesian inference approach guided by existing
                 theoretical power-laws in the filtered signal energy
                 spectrum. We contrast the performance of all three
                 methods for synthetic fractional Brownian motion ({\it
                 fBm}) signals and turbulent velocity time series
                 collected in the atmospheric boundary layer. A
                 discussion on the advantages and disadvantages of each
                 method is also presented, particularly when the process
                 is not exactly an {\it fBm}.",
}

@Article{vid-loz:time-dependent,
  title =        "On time-dependent wavelet denoising",
  author =       "B. Vidakovic and C. B. Lozoya",
  journal =      IEEETSP,
  volume =       "46",
  number =       "9",
  year =         "1998",
  pages =        "2549--2554",
  keywords =     "denoising image processing wavelet shrinkage",
  abstract =     "In this correspondence, we address the shrinkage of
                 wavelet coefficients and induced denoising in the time
                 domain by taking into consideration the `time' behavior
                 of a noisy signal. We illustrate our time adaptation
                 paradigm in a thresholding procedure utilizing Bayesian
                 hypothesis tests. Both one-dimensional (1-D) and
                 two-dimensional (2-D) signals are considered in
                 examples to motivate and implement our method.",
}

@Unpublished{vid-mul:kids,
  title =        "Wavelets for Kids: Tutorial Introduction",
  author =       "Brani Vidakovi{\'c} and Peter M{\"u}ller",
  note =         "Institute of Statisics and Decision Sciences, Duke
                 University",
  year =         "1994",
  email =        "brani@isds.duke.edu, pm@isds.duke.edu",
  url =          "http://www.isds.duke.edu/~brani/papers/wav4kidsA.ps",
}

@Article{vid:bayes,
  title =        "Nonlinear wavelet shrinkage with {B}ayes rules and
                 {B}ayes factors",
  author =       "Brani Vidakovic",
  journal =      JASA,
  volume =       "93",
  number =       "441",
  year =         "1998",
  pages =        "173--179",
  url =          "http://www.isds.duke.edu/~brani/papers/WavShrinkBF.ps",
  keywords =     "Bayes model denoising thresholding wavelet
                 regression",
  abstract =     "Wavelet shrinkage, the method proposed by the seminal
                 work of Donoho and Johnstone is a disarmingly simple
                 and efficient way of denoising data. Shrinking wavelet
                 coefficients was proposed from several optimality
                 criteria. In this article a wavelet shrinkage by
                 coherent Bayesian inference in the wavelet domain is
                 proposed. The methods are tested on standard Donoho-
                 Johnstone test functions.",
}

@Book{vid:book,
  title =        "Statistical Modeling by Wavelets",
  author =       "Brani Vidakovic",
  publisher =    "John Wiley \& Sons",
  address =      NY,
  year =         "1999",
  pages =        "381",
  ISBN =         "0471293652",
  url =          "http://www.isds.duke.edu/~brani/Wiley.html",
}

@Article{von-nas-kro:adaptive,
  title =        "Wavelet processes and adaptive estimation of the
                 evolutionary wavelet spectrum",
  author =       "Rainier {von Sachs} and Guy P. Nason and Gerald
                 Kroisandt",
  journal =      JRSSB,
  volume =       "62",
  number =       "2",
  year =         "2000",
  pages =        "271--292",
  url =          "http://www.stats.bris.ac.uk:81/pub/reports/Wavelets/StanTechRep516.ps.gz",
}

@InCollection{von-nas-kro:spectral,
  title =        "Spectral representation and estimation for locally
                 stationary wavelet processes",
  author =       "Rainier {von Sachs} and Guy P. Nason and Gerald
                 Kroisandt",
  booktitle =    "Spline Functions and the Theory of Wavelets",
  editor =       "S. Dubuc and G. Deslauriers",
  series =       "CRM Proceedings \& Lecture Notes",
  publisher =    "American Mathematical Society",
  address =      "Montreal, Canada",
  volume =       "18",
  year =         "1999",
  pages =        "381--397",
  url =          "http://playfair.Stanford.EDU/reports/rvs/vSNK.ps.gz",
}

@Article{von-neu:stationarity,
  title =        "A Wavelet-based Test for Stationarity",
  author =       "Rainier {von Sachs} and Michael H. Neumann",
  journal =      JTSA,
  year =         "2000",
  pages =        "--",
  url =          "http://playfair.Stanford.EDU/reports/rvs/Stattest.ps.gz",
}

@Article{von-sch:evolutionary,
  title =        "Wavelet smoothing of evolutionary spectra by
                 non-linear thresholding",
  author =       "Rainier {von Sachs} and Kai Shneider",
  journal =      ACHA,
  volume =       "3",
  year =         "1996",
  pages =        "268--282",
  url =          "http://www.mathematik.uni-kl.de/~wwwtecm/preprints/reports/report_106.ps.gz",
  abstract =     "We consider wavelet estimation of the time-dependent
                 (evolutionary) power spectrum of a locally stationary
                 time series in a model which was recently introduced by
                 Dahlhaus [2]. Allowing for departures from stationary
                 proves useful for modelling, e.g., transient phenomena,
                 quasi-oscillating behaviour or spectrum modulation. In
                 contrast to classical parametric and nonparametric
                 (linear) approaches we use nonlinear thresholding of
                 the empirical wavelet coefficients of the evolutionary
                 spectrum. We show how these techniques allow for both
                 adaptively reconstructing the local structure in the
                 time-frequency plane and for denoising the resulting
                 estimates. To this end a threshold choice is derived
                 which is motivated by minimax properties w.r.t. the
                 integrated mean squared error. Our approach is based on
                 a 2-d orthogonal wavelet transform modified by using a
                 cardinal Lagrange interpolation function on the finest
                 scale. As an example, we apply our procedure to a
                 time-varying spectrum motivated from mobile radio
                 propagation.",
}

@Article{von:modelling,
  title =        "Modelling and Estimation of the Time-varying Structure
                 of Nonstationary Time Series",
  author =       "Rainier {von Sachs}",
  journal =      "Brazilian Journal of Probability and Statistics",
  volume =       "10",
  number =       "2",
  year =         "1996",
  pages =        "181--204",
  url =          "http://playfair.Stanford.EDU/reports/rvs/brazilpaper.ps.gz",
}

@TechReport{von:nonparametric,
  title =        "Nonparametric Wavelet Methods for Nonstationary Time
                 Series",
  author =       "Rainier {von Sachs}",
  number =       "98/19",
  year =         "1998",
  institution =  "Institut de Statistique, Universit{\'e} Catholique de
                 Louvain",
  url =          "http://www.stat.ucl.ac.be/dp/dp98/9819.ps",
}

@Article{wal-con:matching,
  title =        "Matching pursuit by undecimated discrete wavelet
                 transform for non-stationary time series of arbitrary
                 length",
  author =       "Andrew T. Walden and A. Contreras Cristan",
  journal =      SC,
  volume =       "8",
  number =       "3",
  year =         "1998",
  pages =        "205--219",
  url =          "http://www.ma.ic.ac.uk/statistics/links/atw.link/matching-pursuit-TR-96-02.ps",
}

@Article{wal-con:shock,
  title =        "The phase-corrected undecimated discrete wavelet
                 packet transform and the recurrence of high latitude
                 interplanetary shock waves",
  author =       "Andrew T. Walden and Alberto Contreras Cristan",
  journal =      PRSLA,
  volume =       "454",
  number =       "1976",
  year =         "1998",
  pages =        "2243--2266",
  keywords =     "wavelet packet transform wavelet phase non-stationary
                 time series Ulysses spacecraft solar magnetic field
                 heliospheric magnetic-field fourier-analysis
                 representation algorithms ulysses.",
  url =          "http://www.ma.ic.ac.uk/statistics/links/atw.link/phase-corrected-TR-97-03.ps",
  abstract =     "This paper is concerned with the development and
                 application of the phase-corrected maximal overlap
                 discrete wavelet packet transform (MODWPT). The
                 discrete cyclic filtering steps of the MODWPT are fully
                 explained. Energy preservation is proven. With filter
                 coefficients chosen from Daubechies's least asymmetric
                 class, the optimum time shifts to apply to ensure
                 approximate zero phase filtering at every level of the
                 MODWPT are studied, and applied to the wavelet packet
                 coefficients to give phase corrections which ensure
                 alignment with the original time series. Also, the time
                 series values at each time are decomposed into details
                 associated with each frequency band, and these line up
                 perfectly with features in the original time series
                 since the details are shown to arise through exact zero
                 phase filtering. The phase-corrected MODWPT is applied
                 to a non-stationary time series of hourly averaged
                 Southern Hemisphere solar magnetic field magnitude data
                 acquired by the Ulysses spacecraft. The occurrence
                 times of the shock waves previously determined via
                 manual pattern matching on the raw data match those
                 times in the time-frequency plot where a broadband
                 spectrum is obtained; in other words, the
                 phase-corrected MODWPT provides an approach to picking
                 the location of complicated events. We demonstrate the
                 superiority of the MODWPT in interpreting timing
                 information over two competing methods, namely the
                 cosine packet transform (or 'local cosine transform'),
                 and the short-time Fourier transform.",
}

@Article{wal-per-mcc:multitaper,
  title =        "Spectrum Estimation by Wavelet Thresholding of
                 Multitaper Estimators",
  author =       "Andrew T. Walden and Donald B. Percival and Emma J.
                 McCoy",
  journal =      IEEETSP,
  volume =       "46",
  number =       "12",
  pages =        "3153--3165",
  year =         "1998",
  abstract =     "Current methods for power spectrum estimation by
                 wavelet thresholding use the empirical wavelet
                 coefficients derived from the log periodogram.
                 Unfortunately, the periodogram is a very poor estimate
                 when the true spectrum has a high dynamic range and/or
                 is rapidly varying. In addition, because the
                 distribution of the log periodogram is markedly
                 non-Gaussian, special wavelet-dependent thresholding
                 schemes are needed. These difficulties can be bypassed
                 by starting with a multitaper spectrum estimator. The
                 logarithm of this estimator is close to Gaussian
                 distributed if a moderate number (greater than or equal
                 to 5) of tapers are used. In contrast to the log
                 periodogram, log multitaper estimates are not
                 approximately pairwise uncorrelated at the Fourier
                 frequencies, but the form of the correlation can be
                 accurately and simply approximated. For
                 scale-independent thresholding, the correlation acts in
                 accordance with the wavelet shrinkage paradigm to
                 suppress small-scale `noise spikes' while leaving
                 informative coarse scale coefficients relatively
                 unattenuated. This simple approach to spectrum
                 estimation is demonstrated to work very well in
                 practice. Additionally, the progression of the variance
                 of wavelet coefficients with scale can be accurately
                 calculated, allowing the use of scale-dependent
                 thresholds. This more involved approach also works well
                 in practice but is not uniformly preferable to the
                 scale-independent approach.",
}

@Book{wal:orthogonal,
  title =        "Wavelets and Other Orthogonal Systems with
                 Applications",
  author =       "Gilbert G. Walter",
  publisher =    "CRC Press Inc.",
  address =      "Boca Raton",
  pages =        "272",
  year =         "1994",
  url =          "http://www.crcpress.com/prods/7878.htm",
  abstract =     "This book makes accessible to both mathematicians and
                 engineers important elements of the theory,
                 construction, and application of orthogonal wavelets.
                 It is integrated with more traditional orthogonal
                 series, such as Fourier series and orthogonal
                 polynomials. It treats the interaction of both with
                 generalized functions (delta functions), which have
                 played an important part in engineering theory but
                 whose rules are often vaguely presented. Unlike most
                 other books that are excessively technical, this
                 text/reference presents the basic concepts and examples
                 in a readable form. Much of the material on wavelets
                 has not appeared previously in book form. Applications
                 to statistics, sampling theorems, and stochastic
                 processes are given. In particular, the close affinity
                 between wavelets and sampling theorems is explained and
                 developed.",
}

@Unpublished{wan-cav-son:self-similarity,
  title =        "Self-similarity index estimation via wavelets for
                 locally self-similar processes",
  author =       "Yazhen Wang and Joseph E. Cavanaugh and Changyong
                 Song",
  year =         "1997",
  note =         "Department of Statistics, University of Missouri",
}

@Article{wan-zho:aseismic,
  title =        "Aseismic designs based on artificial simulations -
                 {H}ow to achieve chirplet-based signal approximation
                 with a strong earthquake ground-model",
  author =       "Jun-Jie Wang and Jing Zhou",
  journal =      IEEESPM,
  volume =       "16",
  number =       "2",
  month =        mar,
  year =         "1999",
  pages =        "94--99",
  keywords =     "motion",
}

@Unpublished{wan:change-curve,
  title =        "Change curve estimation via wavelets",
  author =       "Yazhen Wang",
  institution =  "Department of Statistics, University of Missouri",
  year =         "1997",
  note =         "{\em Journal of the American Statistical Association},
                 to be published in 1998",
}

@Article{wan:indirect,
  title =        "Change-points via wavelets for indirect data",
  author =       "Yazhen Wang",
  journal =      SSin,
  volume =       "9",
  number =       "1",
  year =         "1999",
  pages =        "103--117",
  abstract =     "This article studies change-points of a function for
                 noisy data observed from a transformation of the
                 function. The proposed method uses a wavelet-vaguelette
                 decomposition to extract information about the wavelet
                 transformation of the function from the data and then
                 detect and estimate change-points by the wavelet
                 transformation. Asymptotic theory for the detection and
                 estimation is established. A simulated example is
                 carried out to illustrate the method.",
}

@Article{wan:jump,
  title =        "Jump and sharp cusp detection by wavelets",
  author =       "Yazhen Wang",
  journal =      BKA,
  volume =       "82",
  number =       "2",
  year =         "1995",
  pages =        "385--397",
  abstract =     "A method proposed to detect jumps and sharp cusps in a
                 function which is observed with noise, by checking if
                 the wavelet transformation of the data has
                 significantly large absolute values across fine scales.
                 Asymptotic theory is established and practical
                 implementation is discussed. The method is tested on
                 simulated examples, and applied to stock market return
                 data.",
}

@Article{wan:long-range,
  title =        "Function estimation via wavelet shrinkage for
                 long-memory data",
  author =       "Yazhen Wang",
  journal =      AofS,
  volume =       "24",
  number =       "2",
  year =         "1996",
  pages =        "466--484",
}

@Article{wei-bov:enhancement,
  title =        "Enhancement of compressed images by optimal
                 shift-invariant wavelet packet basis",
  author =       "D. Wei and A. C. Bovik",
  journal =      JVCIR,
  volume =       "9",
  number =       "1",
  year =         "1998",
  pages =        "15--24",
  keywords =     "compactly supported wavelets coded images transform
                 reduction algorithms bases",
  abstract =     "A novel postprocessing method based on the optimal
                 shift-invariant wavelet packet (SIWP) representation
                 and wavelet shrinkage is proposed to enhance compressed
                 images. At the encoder, the optimal (in the mean square
                 error sense) SIWP basis is searched using a fast
                 optimization algorithm and the location of the best
                 basis in the entire SIWP library is transmitted as
                 overhead information to the decoder. The selected basis
                 is jointly optimal in terms of both the time-frequency
                 tiling and the relative time-domain offset (or shift)
                 between a signal and its wavelet packet representation.
                 After the decoder reconstructs the compressed image,
                 the postprocessor performs wavelet shrinkage using the
                 optimal basis. Due to its powerful adaptability, the
                 method is shown to achieve a better trade-off between
                 enhancement performance and decoder complexity than
                 both the orthonormal wavelet transform and the
                 undecimated wavelet transform-based methods.",
}

@Article{wei-dix:underwater,
  journal =      JAcSA,
  volume =       "101",
  number =       "1",
  year =         "1997",
  pages =        "377--383",
  title =        "{W}avelet-based denoising of underwater acoustic
                 signals",
  author =       "L. G. Weiss and T. L. Dixon",
  abstract =     "Underwater environmental measurements of the ocean
                 require signals that are free from unwanted backscatter
                 and clutter. Removing these unwanted signal components
                 usually amounts to applying some form of filtering
                 technique such as a high pass filter, a bandpass
                 filter, a Wiener filter, etc. These approaches however
                 are limited in their abilities to remove acoustic
                 returns that vary spectrally. This paper presents a
                 multiresolution approach to removing unwanted
                 backscatter from high-frequency underwater acoustic
                 signals and compares it to high pass filtering of the
                 same signals. The filtering approach presented applies
                 wavelet transforms for signal recovery and denoising of
                 high-frequency acoustic signals. It is shown that by
                 computing a wavelet transform of the returned signals,
                 applying a denoising technique, and then reconstructing
                 the signal, additional unwanted backscatter can be
                 removed.",
  keywords =     "scattering",
}

@Unpublished{wei:invariance,
  title =        "Translation Invariance and the Wavelet Transform",
  author =       "John Weiss",
  year =         "1993",
  note =         "Applied Mathematics Group",
  url =          "http://www.tiac.net/users/nurit/trep3/trep3.html",
  keywords =     "wavelet transform, translation invariance, best basis,
                 transient detection",
  abstract =     "A translation invariant wavelet transform algorithm is
                 defined. The algorithm is an extension of the best
                 basis approach and can be used to define translation
                 invariant best bases and wavelet transforms. The
                 computational cost is a factor of $m$ greater than the
                 usual algorithms, where $m$ is the multiplier of the
                 wavelet system. Some applications to transient
                 detection are presented. A general form of an invariant
                 wavelet transform is presented. This transform is shown
                 to be invariant under a large group of symmetries
                 described, most naturally, by the g-circulant
                 transformations. The symmetries include translation and
                 time-reversal of a periodic data vector. In our
                 construction the expansion coefficients of g-circulant
                 transformations of a data vector areshown to be simply
                 related by periodic shifts of their expansion
                 coefficients. Therefore, under g-circulant
                 transformations the numerical values and ordering are
                 invariant.",
}

@InCollection{wey-war:de-noising,
  title =        "De-noising using wavelets and cross validation",
  author =       "N. Weyrich and G. T. Warhola",
  booktitle =    "Recent Developments in Approximation Theory, Wavelets
                 and Applications",
  editor =       "S. P. Singh",
  publisher =    "Kluwar",
  address =      "Boston, MA",
  year =         "1995",
  pages =        "523--532",
}

@Article{wey-war:shrinkage,
  title =        "Wavelet shrinkage and generalized cross validation for
                 image denoising",
  author =       "N. Weyrich and G. T. Warhola",
  journal =      IEEETIP,
  volume =       "7",
  number =       "1",
  pages =        "82--90",
  year =         "1998",
  abstract =     "We present a denoising method based on wavelets and
                 generalized cross validation and apply these methods to
                 image denoising, We describe the method of modified
                 wavelet reconstruction and show that the related
                 shrinkage parameter vector can be chosen without prior
                 knowledge of the noise variance by using the method of
                 generalized cross validation, By doing so, we obtain an
                 estimate of the shrinkage parameter vector and, hence,
                 the image, which is very close to the best achievable
                 mean-squared error result-that given by complete
                 knowledge of the underlying clean image.",
}

@Unpublished{whi-etal:lmwnr,
  title =        "Testing for Homogeneity of Variance in Time Series:
                 {L}ong Memory, Wavelets and the {N}ile {R}iver",
  author =       "Brandon Whitcher and Simon D. Byers and Peter Guttorp
                 and Donald B. Percival",
  year =         "1998",
  note =         "Submitted for publication",
  url =          "http://www.eurandom.tue.nl/whitcher/papers/nile.ps",
  keywords =     "Cumulative sum of squares; Discrete wavelet transform,
                 Fractional difference process; Variance change",
  abstract =     "We consider the problem of testing for homogeneity of
                 variance in a time series that has long memory
                 structure. We demonstrate that a test whose null
                 hypothesis is designed to be white noise can in fact be
                 applied, on a scale by scale basis, to the discrete
                 wavelet transform of long memory processes. In
                 particular, we show that evaluating a normalized
                 cumulative sum of squares test statistic using critical
                 levels appropriate for the null hypothesis of white
                 noise yields approximately the same null hypothesis
                 rejection rates when applied to the discrete wavelet
                 transform of samples from a fractional difference
                 process. The point at which the test statistic, using
                 the maximal overlap discrete wavelet transform,
                 achieves its maximum value can be used to estimate the
                 time of the unknown variance change. We apply our
                 proposed test statistic on a time series of Nile River
                 yearly minimum water levels covering the years 622 to
                 1284 AD. The test confirms an inhomogeneity of variance
                 at short scales and identifies the change point around
                 720 AD, which coincides closely with the construction
                 of a new device in 715 AD for measuring Nile River
                 water levels.",
}

@TechReport{whi-gut-per:background,
  title =        "Mathematical Background for Wavelet Estimators for
                 Cross-Covariance and Cross-Correlation",
  author =       "Brandon Whitcher and Peter Guttorp and Donald B.
                 Percival",
  institution =  "National Research Center for Statistics and the
                 Environment",
  number =       "38",
  year =         "1999",
  url =          "http://www.eurandom.tue.nl/whitcher/papers/background.ps",
}

@Article{whi-gut-per:covariance,
  title =        "Wavelet Analysis of Covariance with Application to
                 Atmospheric Time Series",
  author =       "Brandon Whitcher and Peter Guttorp and Donald B.
                 Percival",
  journal =      JGRA,
  year =         "2000",
  note =         "to appear",
  url =          "http://www.eurandom.tue.nl/whitcher/papers/wavecov.ps",
  keywords =     "Confidence intervals; Cross-correlation;
                 Cross-covariance; Madden-Julian oscillation; Maximal
                 overlap discrete wavelet transform; Southern
                 Oscillation Index",
  abstract =     "Multi-scale analysis of univariate time series has
                 appeared in the literature at an ever increasing rate.
                 Here we introduce the multi-scale analysis of
                 covariance between two time series using the discrete
                 wavelet transform. The wavelet covariance and wavelet
                 correlation are defined and applied to this problem as
                 an alternative to traditional cross-spectrum analysis.
                 The wavelet covariance is shown to decompose the
                 covariance between two stationary processes on a scale
                 by scale basis. Asymptotic normality is established for
                 estimators of the wavelet covariance and correlation.
                 Both quantities are generalized into the wavelet
                 cross-covariance and cross-correlation in order to
                 investigate possible lead/lag relationships. A thorough
                 analysis of El-Ni\~no--Southern Oscillation events and
                 the Madden--Julian oscillation is performed using a 35+
                 year record. We show how potentially complicated
                 patterns of cross-correlation are easily decomposed
                 using the wavelet cross-correlation on a scale by scale
                 basis, where each wavelet cross-correlation series is
                 associated with a specific physical time scale.",
}

@Article{whi-jen:aseg2000,
  title =        "Wavelet Estimation of a Local Long Memory Parameter",
  author =       "Brandon Whitcher and Mark J. Jensen",
  journal =      "Exploration Geophysics",
  volume =       "31",
  number =       "1 \& 2",
  year =         "2000",
  pages =        "89--98",
  url =          "http://www.eurandom.tue.nl/whitcher/papers/ASEG2000.pdf",
  keywords =     "discrete wavelet transform, least-squares regression,
                 long-range dependence, time series, wavelet variance.",
  abstract =     "Physical processes often exhibit long-range dependence
                 that vary and evolve over time. Various techniques
                 already exist in order to estimate global long-range
                 dependence. That is, these methods assume the level of
                 dependence does not vary over time and hence, fail to
                 adapt to any potential change in the level of
                 long-range dependence. The discrete wavelet transform
                 is well-localized in time-scale space and thus, enables
                 us to consistently estimate a local measure of
                 long-range dependence and the time interval over which
                 this estimate is constant. We utilize the so-called
                 `cone of influence' (level-dependent support of the
                 wavelet filter) induced by the wavelet transform to
                 define an estimator of local variability - the
                 time-dependent wavelet variance. Using a fractionally
                 integrated autoregressive, moving average model, whose
                 differencing parameter changes over time, we estimate
                 the local differencing parameter at time $t$ using a
                 log-log linear relationship between the time-dependent
                 wavelet variance whose support contains $t$ and the
                 scale parameter of the wavelet transform. Simulation
                 studies demonstrate the estimation procedure for a
                 variety of time-varying fractionally integrated
                 autoregressive, moving average processes and we also
                 apply it to a geophysical process.",
}

@Unpublished{whi-gut-per:multiple,
  title =        "Multiscale Detection and Location of Multiple Variance
                 Changes in the Presence of Long Memory",
  author =       "Brandon Whitcher and Peter Guttorp and Donald B.
                 Percival",
  year =         "1999",
  note =         "{\em Journal of Statistical Computation and
                 Simulation}, to appear",
  url =          "http://www.eurandom.tue.nl/whitcher/papers/multiple.ps",
}

@Unpublished{whi:simulating,
  title =        "Simulating {G}aussian Stationary Processes with
                 Unbounded Spectra",
  author =       "Brandon Whitcher",
  year =         "1999",
  note =         "Tentatively accepted for publication in the {\em
                 Journal of Computational and Graphical Statistics}",
  url =          "http://www.eurandom.tue.nl/whitcher/papers/sim.ps",
}

@PhdThesis{whi:thesis,
  title =        "Assessing Nonstationary Time Series Using Wavelets",
  author =       "Brandon Whitcher",
  school =       "University of Washington",
  year =         "1998",
  postscript =   "http://www.eurandom.tue.nl/whitcher/papers/thesis.ps.gz",
  abstract =     "The discrete wavelet transform has be used extensively
                 in the field of statistics, mostly in the area of
                 ``denoising signals'' or nonparametric regression. This
                 thesis provides a new application for the discrete
                 wavelet transform, assessing nonstationary events in
                 time series -- especially long memory processes. Long
                 memory processes are those which exhibit substantial
                 correlations between events separated by a long period
                 of time. Departures from stationarity in these heavily
                 autocorrelated time series, such as an abrupt change in
                 the variance at an unknown location or ``bursts'' of
                 increased variability, can be detected and accurately
                 located using discrete wavelet transforms -- both
                 orthogonal and overcomplete. A cumulative sum of
                 squares method, utilizing a Kolomogorov--Smirnov-type
                 test statistic, and an information criterion method are
                 investigated. By analyzing a time series on a scale by
                 scale basis, each scale corresponding to a range of
                 frequencies, the ability to detect and locate a sudden
                 change in the variance in the time series is
                 introduced. Using this same procedure to detect a
                 change in the long memory parameter is also
                 investigated. Applications involve the Nile River
                 minimum water levels and vertical ocean shear
                 measurements. In the atmospheric sciences, broadband
                 features in the spectrum of recorded time series have
                 been hypothesized to be nonstationary events; e.g., the
                 Madden--Julian oscillation. The Madden--Julian
                 oscillation is a result of large-scale circulation
                 cells oriented in the equatorial plane from the Indean
                 Ocean to the central Pacific. The oscillation has been
                 noted to have higher frequencies during warm events in
                 El Nino--Southern Oscillation (ENSO) years. The
                 concepts of wavelet covariance and wavelet correlation
                 are introduced and applied to this problem as an
                 alternative to cross-spectrum analysis. The wavelet
                 covariance is shown to decompose the covariance between
                 two stationary processes on a scale by scale basis.
                 Asymptotic normality of estimators of the wavelet
                 covariance and correlation is shown in order to
                 construct approximate confidence intervals. Both
                 quantities are generalized into the wavelet
                 cross-covariance and cross-correlation in order to
                 investigate possible lead/lag relations in bivariate
                 time series. Atmospheric measurements (such as station
                 pressure and zonal wind speeds) from a single station
                 at Canton Island (2.8S, 171.7W) are analyzed and nicely
                 replicate the results found in Madden and Julian
                 (1971). To highlight that the wavelet methods can
                 provide insight over and above traditional spectral
                 methods (including multitaper techniques) a daily
                 ``Southern Oscillation Index'' and station pressure
                 series from Truk Island (7.4N, 151.8W) are analyzed.
                 The wavelet cross-covariance nicely decomposes the
                 usual cross-covariance into scales which are more
                 easily associated with physical phenomena. The
                 time-varying wavelet covariance is used to show the
                 increase in positive correlation between the SOI and
                 Truk Island station pressure in the first half of each
                 year versus latter half.",
}

@Book{wic:adapted,
  title =        "Adapted Wavelet Analysis from Theory to Software",
  author =       "Mladen Victor Wickerhauser",
  publisher =    "A K Peters",
  ISBN =         "1-56881-041-5",
  year =         "1994",
  address =      "Wellesley, Massachusetts",
  abstract =     "This detail-oriented text is intended for engineers
                 and applied mathematicians who must write computer
                 programs to perform wavelet and related analyses on
                 real data. It should also be useful to the pure
                 mathematician with questions about wavelet theory
                 applications and to the instructor or student as a
                 textbook in the mathematics and latest techniques in
                 transient signal analysis and processing. Beginning
                 with an overview of mathematical prerequisites,
                 successive chapters rigorously examine the properties
                 of waveforms used in adapted wavelet analysis: discrete
                 ``fast'' Fourier transforms, orthogonal and
                 biorthogonal wavelets, wavelet packets, and localized
                 trigonometric or lapped orthogonal functions. Other
                 chapters discuss the ``best-basis''
                 method,time-frequency analysis, and combinations of
                 these algorithms useful for signal analysis,
                 de-noising, and data compression. Each chapter
                 discusses the technical aspects of implementation
                 giving examples in pseudocode backed up with a Standard
                 C source code (on optional diskette) and closes with a
                 list of worked exercises.",
}

@Unpublished{wic:theory-applications,
  title =        "Wavelet Theory and Applications",
  author =       "Mladen Victor Wickerhauser",
  year =         "1997",
  note =         "Department of Mathematics, Washington University of
                 St. Louis",
}

@Unpublished{won-ip-lua-xie:detection,
  title =        "Wavelet Detection of Jump Points and an Application to
                 Exchange Rates",
  author =       "Heung Wong and Wai-Cheung Ip and Yihui Luan and
                 Zhongjie Xie",
  year =         "1996",
  note =         "The Hong Kong Polytechnic University, Hong Kong",
}

@Article{won:harmonizable,
  title =        "Wavelet decomposition of harmonizable random
                 processes",
  author =       "P. W. Wong",
  journal =      IEEETIT,
  volume =       "39",
  number =       "1",
  year =         "1993",
  pages =        "7--18",
  keywords =     "pointwise convergence, signal analysis, discrete
                 wavelet decomposition, second-order harmonizable random
                 processes, deterministic wavelet decomposition, complex
                 exponential, bounded convergence, stochastic wavelet
                 decomposition, linear operations, addition,
                 differentiation, linear filtering",
  abstract =     "The discrete wavelet decomposition of second-order
                 harmonizable random processes is considered. The
                 deterministic wavelet decomposition of a complex
                 exponential function is examined, where its pointwise
                 and bounded convergence to the function is proved. This
                 result is then used for establishing the stochastic
                 wavelet decomposition of harmonizable processes. The
                 similarities and differences between the wavelet
                 decompositions of general harmonizable processes and a
                 subclass of processes having no spectral mass at zero
                 frequency, e.g., those that are wide-sense stationary
                 and have continuous power spectral densities, are also
                 investigated. The relationships between the
                 harmonization of a process and that of its wavelet
                 decomposition are examined. Finally, certain linear
                 operations such as addition, differentiation, and
                 linear filtering on stochastic wavelet decompositions
                 are considered. It is shown that certain linear
                 operations can be performed term by term with the
                 decomposition.",
}

@Article{wor-opp:self-similar,
  title =        "Wavelet-based representations for a class of
                 self-similar signals with application to fractal
                 modulation",
  author =       "Gregory W. Wornell and Alan V. Oppenheim",
  journal =      IEEETIT,
  volume =       "38",
  number =       "2",
  year =         "1992",
  pages =        "785--800",
  keywords =     "spectral characteristics, wavelet transforms,
                 self-similar signals, fractal modulation, deterministic
                 scale-invariance characterization, orthonormal wavelet
                 bases, dy-homogeneous signals, communications-based
                 context, multiple time-scales, multirate modulation
                 strategy, noisy channels",
  abstract =     "A potentially important family of self-similar signals
                 based upon a deterministic scale-invariance
                 characterization is introduced. These signals, which
                 are referred to as 'dy-homogeneous' signals because
                 they generalize the well-known homogeneous functions,
                 have highly convenient representations in terms of
                 orthonormal wavelet bases. In particular, wavelet
                 representations can be exploited to construct
                 orthonormal self-similar bases for these signals. The
                 spectral and fractal characteristics of dy-homogeneous
                 signals make them appealing candidates for use in a
                 number of applications. As one potential example, their
                 use in a communications-based context is considered.
                 Specifically, a strategy for embedding information into
                 a dy-homogeneous waveform on multiple time-scales is
                 developed. This multirate modulation strategy, called
                 fractal modulation, is potentially well-suited for use
                 with noisy channels of simultaneously unknown duration
                 and bandwidth.",
}

@Book{wor:book,
  title =        "Signal Processing with Fractals: {A} Wavelet Based
                 Approach",
  author =       "Gregory W. Wornell",
  publisher =    "Prentice Hall",
  address =      NJ,
  year =         "1996",
  url =          "http://www.prenhall.com/books/ptr_013120999x.html",
  keywords =     "Wavelet Transformations, Statistically Self-Similar,
                 Detection and Estimation with Fractal Processes,
                 Deterministically Self-Similar Signals, Fractal
                 Modulation, Linear Self-Similar Systems",
  abstract =     "Fractal signals, derived from wavelet theory, are
                 ideally suited for use in many engineering
                 applications, ranging from communications to remote
                 sensing. This book provides an introduction to wavelet
                 theory from a signal processing perspective, and
                 details fractal signals and a collection of practical
                 wavelet-based techniques for representing and
                 manipulating fractal signals in various applications.",
}

@Article{wor:karhunen-loeve,
  title =        "A {K}arhunen-{L}o\'{e}ve-like expansion for $1/f$
                 processes via wavelets",
  author =       "Gregory W. Wornell",
  journal =      IEEETIT,
  volume =       "36",
  number =       "4",
  year =         "1990",
  pages =        "859--861",
  keywords =     "orthonormal wavelet bases, Karhunen-Loeve-like
                 expansion, 1/f processes, scaling processes,
                 uncorrelated random variables",
  abstract =     "While so-called 1/f or scaling processes emerge
                 regularly in modeling a wide range of natural
                 phenomena, as yet no entirely satisfactory framework
                 has been described for the analysis of such processes.
                 Orthonormal wavelet bases are used to provide a new
                 construction for nearly 1/f processes from a set of
                 uncorrelated random variables.",
}

@Article{wor:representations,
  title =        "Wavelet-based representations for the $1/f$ family of
                 fractal processes",
  author =       "G. W. Wornell",
  journal =      PIEEE,
  volume =       "81",
  number =       "10",
  year =         "1993",
  pages =        "1428--1450",
  keywords =     "signal detection, 1/f family, fractal processes,
                 orthonormal wavelet bases, frequency-domain
                 characterization, Karhunen-Loeve-type expansion,
                 estimation problems",
  abstract =     "It is demonstrated that 1/f fractal processes are, in
                 a broad sense, optimally represented in terms of
                 orthonormal wavelet bases. Specifically, via a useful
                 frequency-domain characterization for 1/f processes,
                 the wavelet expansion's role as a Karhunen-Loeve-type
                 expansion for 1/f processes is developed. As an
                 illustration of potential, it is shown that
                 wavelet-based representations naturally lead to highly
                 efficient solutions to some fundamental detection and
                 estimation problems involving 1/f processes.",
}

@InProceedings{wu-su:relationship,
  title =        "On the relationship between the self-similarities of
                 fractal signals and wavelet transforms",
  author =       "Bing-Fei Wu and Yu-Lin Su",
  booktitle =    "International Symposium on Signal Processing and its
                 Applications",
  editor =       "B. Boashash and N. Harle and A. A. Zoubir",
  year =         "1996",
  pages =        "736--739",
  email =        "bwu@haeshiuh.cn.nctu.edu.tw",
  keywords =     "fractal signals. wavelet transforms. stochastic
                 processes. correlation functions. power spectra.
                 fractal dimensions. probability measure function.
                 variance function. time series function. time-averaging
                 autocorrelation function. ensemble-averaging
                 autocorrelation function. time-averaging power
                 spectrum. average power spectrum. distribution
                 functions. stationary processes. nonstationary
                 processes. one-dimensional self-similarity. continuous
                 wavelet transform. discrete wavelet transform.
                 quadrature mirror filter structure. fractional Brownian
                 motion process",
  abstract =     "Since many natural phenomena are occasionally defined
                 as stochastic processes and the corresponding fractal
                 characteristics are hidden from their correlation
                 functions or power spectra, the topic would be of
                 interest in signal processing. In this paper, we
                 summarize the fractal dimensions and the relationship
                 of the fractal in probability measure, variance, time
                 series, time-averaging autocorrelation,
                 ensemble-averaging autocorrelation, time-averaging
                 power spectrum, average power spectrum and distribution
                 functions for stationary and nonstationary processes.
                 We also propose that the preservation of the
                 one-dimensional self-similarity of a fractal signal is
                 obtained by using the continuous wavelet transform
                 (CWT) and the discrete wavelet transform (DWT) with the
                 perfect reconstruction quadrature mirror filter
                 structure. Moreover, we extend the results to the
                 two-dimensional case and point out the relationship of
                 the self-similarities between the CWT and DWT of the
                 fractal signals. A fractional Brownian motion process
                 is provided as an example to show the results of this
                 paper.",
}

@Article{xia-ger-har-sut:design,
  title =        "Design of prefilters for discrete multiwavelet
                 transforms",
  author =       "Xiang-Gen Xia and Jeffrey S. Geronimo and Douglas P.
                 Hardin and Bruce W. Suter",
  journal =      IEEETSP,
  volume =       "44",
  number =       "1",
  year =         "1996",
  pages =        "25--35",
  keywords =     "discrete multiwavelet transforms pyramid algorithm
                 single wavelet transform coefficients tree-structured
                 multirate filter banks premultirate filter banks vector
                 filter banks discrete vector-valued wavelet transform
                 discrete-time vector-valued signals discrete
                 multiwavelet transform energy compaction.",
  abstract =     "The pyramid algorithm for computing single wavelet
                 transform coefficients is well known. The pyramid
                 algorithm can be implemented by using tree-structured
                 multirate filter banks. The authors propose a general
                 algorithm to compute multiwavelet transform
                 coefficients by adding proper premultirate filter banks
                 before the vector filter banks that generate
                 multiwavelets. The proposed algorithm can be thought of
                 as a discrete vector-valued wavelet transform for
                 certain discrete-time vector-valued signals. The
                 proposed algorithm can be also thought of as a discrete
                 multiwavelet transform for discrete-time signals. The
                 authors then present some numerical experiments to
                 illustrate the performance of the algorithm, which
                 indicates that the energy compaction for discrete
                 multiwavelet transforms may be better than the one for
                 conventional discrete wavelet transforms.",
}

@Article{xia-kuo-zha:optimal,
  title =        "{W}avelet coefficient computation with optimal
                 prefiltering",
  journal =      IEEETSP,
  volume =       "42",
  number =       "8",
  year =         "1994",
  pages =        "2191--7",
  author =       "Gen Xia Xiang and C. C. J. Kuo and Zhang Zhen",
  abstract =     "Discrete wavelet transform (DWT) is often used to
                 approximate wavelet series transform (WST) and
                 continuous wavelet transform (CWT), since it can be
                 computed numerically. In this research, we first study
                 the accuracy of the computed DWT coefficients obtained
                 from the Shensa (see ibid., vol.40, no.10, p.2464-2482,
                 1992) algorithm as an approximate of the WST
                 coefficients. Based on the accuracy analysis, we then
                 propose a procedure to design optimal FIR prefilters
                 used in the Shensa algorithm to reduce the
                 approximation error. Finally, numerical examples are
                 presented to demonstrate the performance of the optimal
                 FIR prefilters.",
  keywords =     "wavelet coefficient. optimal prefiltering. discrete
                 wavelet transform. DWT. wavelet series transform.
                 continuous wavelet transform. WST. CWT. accuracy
                 analysis. optimal FIR prefilters. approximation error
                 reduction. Shensa algorithm.",
}

@Article{yan-sag-tsu:system,
  title =        "System impulse response identification using a
                 multiresolution neural network",
  author =       "Zi-Jiang Yang and Setsuo Sagara and Teruo Tsuji",
  journal =      "Automatica",
  volume =       "33",
  number =       "7",
  year =         "1997",
  pages =        "1345--1350",
  keywords =     "system impulse response identification multiresolution
                 neural network discrete-time impulse response model
                 linear system sampled input-output data I/O data
                 high-frequency components continuous-time impulse
                 response scaling functions wavelet functions genetic
                 algorithm AIC redundant subsystems",
  abstract =     "This paper proposes a new identification method for
                 the discrete-time impulse response model of a linear
                 system from sampled input-output data. Our attention is
                 especially focused on identification of the impulse
                 response, which includes high-frequency components
                 locally. The continuous-time impulse response of the
                 system is approximated by a multiresolution neural
                 network composed of the scaling and wavelet functions.
                 Hence the system under study can be viewed as the
                 weighted sum of a group of subsystems in which the
                 scaling functions and wavelet functions are interpreted
                 as their impulse responses respectively. Then the
                 genetic algorithm and the AIC are introduced to select
                 significant subsystems at each resolution level such
                 that some redundant subsystems that are sensitive to
                 the noise effects are discarded. It is shown through a
                 simulation that the proposed method yields accurate
                 estimate of the impulse response, even in the
                 ill-conditioned cases.",
}

@Article{yu-mykland:looking,
  title =        "Looking at {M}arkov samplers through cusum path plots:
                 {A} simple diagnostic idea",
  author =       "Bin Yu and Per Mykland",
  journal =      SC,
  volume =       "8",
  number =       "3",
  year =         "1998",
  pages =        "275--286",
}

@Unpublished{zha:temporal-spatial,
  title =        "Multiresolution analysis for temporal-spatial
                 processes: {A} preliminary report",
  author =       "Jun Zhai",
  year =         "1997",
  note =         "Department of Statistics, North Carolina State
                 University",
}

@Article{zie-stu:relation,
  title =        "The relation of the {A}llan- and $\Delta$-variance to
                 the continuous wavelet transform",
  author =       "M. Zielinsky and J. Stutzki",
  journal =      AandA,
  volume =       "347",
  number =       "2",
  year =         "1999",
  pages =        "630--633",
  url =          "http://xxx.lanl.gov/abs/astro-ph/9904190",
  abstract =     "This paper is understood as a supplement to the paper
                 by Stutzki et al. 1998, where we have shown the
                 usefulness of the Allan-variance and its higher
                 dimensional generalization, the Delta-variance, for the
                 characterization of molecular cloud structures. In this
                 study we present the connection between the Allan- and
                 Delta-variance and a more popular structure analysis
                 tool: the wavelet transform. We show that the Allan-
                 and Delta-variances are the variances of wavelet
                 transform coefficients.",
}

@Book{fou-kum:geophysics,
  title =        "Wavelets in Geophysics",
  booktitle =    "Wavelets in Geophysics",
  editor =       "Efi Foufoula-Georgiou and Praveen Kumar",
  series =       "Wavelet Analysis and its Applications",
  volume =       "4",
  publisher =    "Academic Press, Inc",
  year =         "1994",
  address =      SD,
  url =          "http://www.apcatalog.com/cgi-bin/AP?ISBN=0122628500&LOCATION=US&FORM=FORM2",
  abstract =     "Applications of wavelet analysis to the geophysical
                 sciences grew from Jean Morlet's work on seismic
                 signals in the 1980s. Used to detect signals against
                 noise, wavelet analysis excels for transients or for
                 spatially localized phenomena. In this fourth volume in
                 the renown WAVELET ANALYSIS AND ITS APPLICATIONS
                 Series, Efi Foufoula-Georgiou and Praveen Kumar begin
                 with a self-contained overview of the nature, power,
                 and scope of wavelet transforms. The eleven original
                 papers that follow in this edited treatise show how
                 geophysical researchers are using wavelets to analyze
                 such diverse phenomena as intermittent atmospheric
                 turbulence, seafloor bathymetry, marine and other
                 seismic data, and flow in aquifiers. Wavelets in
                 Geophysics will make informative reading for
                 geophysicists seeking an up-to-date account of how
                 these tools are being used as well as for wavelet
                 researchers searching for ideas for applications, or
                 even new points of departure.",
}

@Book{ant-opp:wavelets,
  title =        "Wavelets and Statistics",
  booktitle =    "Wavelets and Statistics",
  editor =       "Anestis Antoniadis and Georges Oppenheim",
  series =       "Lecture Notes in Statistics",
  volume =       "103",
  year =         "1995",
  publisher =    "Springer-Verlag",
  address =      NY,
  ISBN =         "0-387-94564-4",
  url =          "http://www.springer-ny.com/catalog/np/aug95np/DATA/0-387-94564-4.html",
  abstract =     "Wavelets theory has found applications in a remarkable
                 diversity of disciplines. The volume presents the
                 proceedings of a conference held at Villard de Lans,
                 France in 1994. Both statistical results and practical
                 contributions were presented. The material is wide in
                 scope and ranges from the development of new tools for
                 nonparametric curve estimation to applied problems such
                 as detection of transients in signal processing and
                 image segmentation.",
}

@Proceedings{com-gro-tch:wavelets,
  editor =       "Jean-Michel Combes and Alexander Grossman and Philippe
                 Tchamitchian",
  title =        "Wavelets: Time-Frequency Methods and Phase Space",
  booktitle =    "Wavelets: Time-Frequency Methods and Phase Space",
  series =       "Inverse Problems and Theoretical Imaging",
  publisher =    "Springer-Verlag",
  year =         "1989",
  address =      "Berlin",
  note =         "Proceedings of the International Conference,
                 Marseille, France, December 14-18, 1987",
}

@Book{dag-ste:goodness,
  title =        "Goodness-of-Fit Techniques",
  booktitle =    "Goodness-of-Fit Techniques",
  editor =       "Ralph B. D'Agostino and Michael A. Stephens",
  volume =       "68",
  series =       "STATISTICS: Textbooks and Monographs",
  publisher =    "Marcel Dekker",
  address =      NY,
  year =         "1986",
  pages =        "560",
}

@Proceedings{lai-uns-ald:wavelet6,
  title =        "Wavelet applications in signal and image processing
                 {VI}",
  booktitle =    "Wavelet applications in signal and image processing
                 {VI}",
  editor =       "Andrew F. Laine and Michael A. Unser and Akram
                 Aldroubi",
  volume =       "3458",
  year =         "1998",
  pages =        "284",
  series =       "Proceedings of SPIE",
  note =         "19-24 July, 1998, San Diego, California",
  keywords =     "Image-processing, Signal-processing, Wavelets",
  url =          "http://www.spie.org/web/abstracts/3400/3458.html",
}

@Proceedings{lai-uns:wavelet2,
  title =        "Wavelet applications in signal and image processing
                 {II}",
  booktitle =    "Wavelet applications in signal and image processing
                 {II}",
  editor =       "Andrew F. Laine and Michael A. Unser",
  volume =       "2303",
  year =         "1994",
  pages =        "602",
  series =       "Proceedings of SPIE",
  note =         "24-29 July, 1994, San Diego, California",
  keywords =     "Image-processing, Signal-processing, Wavelets",
  url =          "http://www.spie.org/web/abstracts/2300/2303.html",
}

@Proceedings{lai-uns:wavelet3,
  title =        "Wavelet applications in signal and image processing
                 {III}",
  booktitle =    "Wavelet applications in signal and image processing
                 {III}",
  editor =       "Andrew F. Laine and Michael A. Unser and Mladen V.
                 Wickerhauser",
  volume =       "2569",
  year =         "1995",
  pages =        "900",
  series =       "Proceedings of SPIE",
  note =         "12-14 July, 1995, San Diego, California",
  keywords =     "Image-processing, Signal-processing, Wavelets",
  url =          "http://www.spie.org/web/abstracts/2500/2569.html",
}

@Proceedings{lai:wavelet1,
  title =        "Mathematical Imaging: Wavelet Applications in Signal
                 and Image Processing",
  booktitle =    "Mathematical Imaging: Wavelet Applications in Signal
                 and Image Processing",
  editor =       "Andrew F. Laine",
  volume =       "2034",
  series =       "Proceedings of the SPIE",
  year =         "1993",
  note =         "11-16 July, 1993, San Diego, California",
  url =          "http://www.spie.org/web/abstracts/2000/2034.html",
}

@Book{mul-vid:biwbm,
  title =        "Bayesian Inference in Wavelet-based Models",
  booktitle =    "Bayesian Inference in Wavelet-based Models",
  editor =       "Peter M{\"u}ller and Brani Vidakovic",
  publisher =    "Springer Verlag",
  address =      NY,
  volume =       "141",
  series =       "Lecture Notes in Statistics",
  year =         "1999",
}

@Book{rao-pri-les:applications,
  title =        "Applications of Time Series Analysis in Astronomy and
                 Meteorology",
  booktitle =    "Applications of Time Series Analysis in Astronomy and
                 Meteorology",
  editor =       "T. Subba Rao and M. B. Priestly and O. Lessi",
  year =         "1997",
  publisher =    "Chapman \& Hall",
  address =      "London",
  ISBN =         "0-412-63800-2",
  abstract =     "Statistical techniques, in particular time series
                 techniques, are widely used in astronomy and
                 meteorology. Despite this, until recently there have
                 been few attempts to bring researchers from the fields
                 of statistics, astronomy and meteorology together to
                 discuss and formalize important problems. Applications
                 of Time Series Analysis in Astronomy and Meteorology
                 brings together a series of papers by experts in these
                 fields evenly devoted to the theory and methodology of
                 time series and to its applications to astronomy,
                 meteorology and climatology. The topics covered include
                 detection of periodicities, spectral analysis of
                 unequally spaced data, detection of change points and
                 higher order spectral methods of non-linear and
                 non-Gaussian signals. Estimation of fractal dimension
                 and applications of wavelet methods to astronomy are
                 also considered. In addition, this book includes a
                 floppy disc containing data sets to serve as a
                 benchmark series. Applications of Time Series Analysis
                 in Astronomy and Meteorology is of interest to
                 statisticians, astronomers, meteorologists and
                 climatologists alike.",
}

@Book{sta-var:methods,
  title =        "Statistical Methods for Physical Science",
  booktitle =    "Statistical Methods for Physical Science",
  editor =       "John L. Stanford and Stephen B. Vardeman",
  series =       "Methods of Experimental Physics",
  volume =       "28",
  year =         "1994",
  publisher =    "Academic Press, Inc.",
  address =      "Boston",
  keywords =     "physical sciences, experiments, statistical methods",
}

@Proceedings{szu:wavelet1,
  title =        "Wavelet Applications",
  booktitle =    "Wavelet Applications",
  editor =       "Harold H. Szu",
  volume =       "2242",
  year =         "1994",
  series =       "Proceedings of SPIE",
  pages =        "994",
  note =         "4-8, April 1994, Orlando, Florida",
  keywords =     "Image-processing, Signal-processing, Wavelets",
  url =          "http://www.spie.org/web/abstracts/2200/2242.html",
}

@Proceedings{szu:wavelet2,
  title =        "Wavelet Applications {II}",
  booktitle =    "Wavelet Applications {II}",
  editor =       "Harold H. Szu",
  volume =       "2491",
  year =         "1995",
  series =       "Proceedings of SPIE",
  pages =        "1183",
  note =         "17-21, April 1995, Orlando, Florida",
  keywords =     "Image-processing, Signal-processing, Wavelets",
  url =          "http://www.spie.org/web/abstracts/2400/2491.html",
}

@Proceedings{szu:wavelet3,
  title =        "Wavelet Applications {III}",
  booktitle =    "Wavelet Applications {III}",
  editor =       "Harold H. Szu",
  volume =       "2762",
  year =         "1996",
  series =       "Proceedings of SPIE",
  pages =        "668",
  note =         "8-12 April 1996, Orlando, Florida",
  keywords =     "Image-processing, Signal-processing, Wavelets",
  url =          "http://www.spie.org/web/abstracts/2700/2762.html",
}

@Proceedings{szu:wavelet5,
  title =        "Wavelet Applications {V}",
  booktitle =    "Wavelet Applications {V}",
  editor =       "Harold H. Szu",
  volume =       "3391",
  year =         "1998",
  series =       "Proceedings of SPIE",
  note =         "14-16 April 1998, Orlando, Florida",
  keywords =     "Image-processing, Signal-processing, Wavelets",
  url =          "http://www.spie.org/web/abstracts/3300/3391.html",
}

@Proceedings{szu:wavelet6,
  title =        "Wavelet Applications {VI}",
  booktitle =    "Wavelet Applications {VI}",
  editor =       "Harold H. Szu",
  volume =       "3723",
  year =         "1999",
  series =       "Proceedings of SPIE",
  pages =        "478",
  note =         "4-9 April 1999, Orlando, Florida",
  keywords =     "Image-processing, Signal-processing, Wavelets",
  url =          "http://www.spie.org/web/abstracts/3700/3723.html",
}

@Proceedings{uns-ald-lai:wavelet4,
  title =        "Wavelet Applications in Signal and Image Processing
                 {IV}",
  booktitle =    "Wavelet Applications in Signal and Image Processing
                 {IV}",
  editor =       "Michael A. Unser and Akram Aldroubi and Andrew F.
                 Laine",
  volume =       "2825",
  year =         "1996",
  pages =        "1044",
  series =       "Proceedings of SPIE",
  note =         "4-9 August, 1996, Denver, Colorado",
  keywords =     "Image-processing, Signal-processing, Wavelets",
  url =          "http://www.spie.org/web/abstracts/2800/2825.html",
}

@Proceedings{uns-ald-lai:wavelet7,
  title =        "Wavelet Applications in Signal and Image Processing
                 {VII}",
  booktitle =    "Wavelet Applications in Signal and Image Processing
                 {VII}",
  editor =       "Michael A. Unser and Akram Aldroubi and Andrew F.
                 Laine",
  volume =       "3813",
  year =         "1999",
  series =       "Proceedings of SPIE",
  note =         "?-? October, 1996, Denver, Colorado",
  keywords =     "Image-processing, Signal-processing, Wavelets",
  url =          "http://www.spie.org/web/abstracts/3800/3813.html",
}
