Wavelet Resources
Welcome to Wavelet Resources page: your comprehensive site for wavelet papers, books, articles, etc. By its very nature this page is perpetually under construction. Any help you can lend in keeping this page up to date will be appreciated greatly. If there is any thing new you want to add, please mail madani@ieee.org and it will be added as soon as possible.
@book{akansu-haddad:1992,
Author = "Akansu, Ali N. and Richard A. Haddad",
Title = "Multiresolution Signal Decomposition: Transforms, Subbands,
and Wavelets",
Publisher = "Academic Press",
Pages = "376",
Keyword = "wavelets, signal processing, multiresolution",
LOC = "TK 5102.5 A414 1992",
ISBN = "0-12-047140-X",
TOC = "
1. Introduction 1,
1.1 Introduction 1,
1.2 Why signal decomposition? 2,
1.3 Decompositions: Transforms, subbands, and wavelets 2,
1.4 Performance evaluation 7,
2. Orthogonal transforms 9,
2.1 Signal expansions in orthogonal functions 10,
2.2 Transform efficiency and coding performance 24,
2.3 Fixed transforms 35,
2.4 Parametric modeling of signal sources 61,
2.5 Lapped orthogonal transforms 76,
2.6 2-D transform implementation 86,
2.7 Summary 90,
3. Theory of subband decomposition 101,
3.1 Multirate signal processing 103,
3.2 Bandpass and modulated signals 115,
3.3 Mth band, mirror, and power complementary filters 119,
3.4 Two-channel filter banks 123,
3.5 M-band filter banks 141,
3.6 Cascaded lattice structures 171,
3.7 IIR subband filter banks 183,
3.8 Two-dimensional subband decomposition 197,
3.9 Quantization effects in filter banks 221,
3.10 Summary 229,
4. Filterbank families: Design and performance 241,
4.1 Binomial QMF-wavelet filters 241,
4.2 Maximally flat filters 248,
4.3 Bernstein QMF-wavelet filters 250,
4.4 Johnston QMF family 254,
4.5 Smith-Barnwell PR-CQF family 256,
4.6 LeGall-Tabatabai PR filter bank 259,
4.7 Princen-Bradley QMF 260,
4.8 Optimal PR-QMF design for subband image coding 260,
4.9 Performance of PR-QMF families 272,
4.10 Aliasing energy in multiresolution decomposition 276,
4.11 Time and frequency localizations 281,
4.12 G_TC and NER performance 284,
4.13 Summary 285,
5. Wavelet transform 291,
5.1 Time-frequency decompositions 292,
5.2 The short-time Fourier transform 300,
5.3 The wavelet transform 304,
5.3.1 The continuous wavelet transform 304,
5.3.2 The discrete wavelet transform 310,
5.4 Multiresolution signal decomposition 313,
5.4.1 Multiresolution signal analysis spaces 313,
5.4.2 The Haar wavelet 315,
5.4.3 Two-band unitary PR-QMF and wavelet bases 321,
5.4.4 Multiresolution pyramid decomposition 326,
5.4.5 Finite resolution wavelet decomposition 331,
5.4.6 The Shannon wavelets 332,
5.5 Wavelet regularity and wavelet families 334,
5.5.1 Regularity or smoothness 336,
5.5.2 The Daubechies wavelets 338,
5.5.3 The Coiflet bases 339,
5.6 Biorthogonal wavelets and filter banks 341,
5.7 Dicussions and conclusion 343,
5.8 Epilogue 345,
A. Resolution of the identity and inversion 353,
B. Orthonormality in frequency 357,
C. Problems 359,
Index 373" }
@incollection{alpert:1992,
Author = "Alpert, B. K.",
Title = "Wavelets and other bases for fast numerical linear algebra",
Booktitle = "Wavelets: A Tutorial in Theory and Applications",
Editor = "C. K. Chui",
Publisher = "Academic Press",
Year = "1992",
Pages = "181--216" }
@article{alpert-beylkin-etal:1993,
Author = "Alpert, B. and G. Beylkin and R. Coifman and V. Rokhlin",
Title = "Wavelet-like bases for the fast solution of second kind
integral equations",
Journal = "SIAM J. Sci. Comput.",
Volume = "14",
Year = "1993",
Pages = "158--184" }
@article{amaratunga-williams-etal:1994,
Author = "Amaratunga, K. and J. R. Williams and S. Qian and J. Weiss",
Title = "Wavelet-Galerkin solutions for one-dimensional partial
differential equations",
Journal = "Int. J. Num. Meth. Eng.",
Volume = "27",
Year = "1994",
Pages = "2703--2716" }
@techreport{andersson-hall-etal:1993,
Author = "Andersson, L. and N. Hall and B. Jawerth and G. Peters",
Title = "Wavelets on closed subsets of the real line",
Year = "1993",
URL = "ftp://maxwell.math.scarolina.edu:pub/imi_93/imi_93_2.ps",
Size = "667,500 bytes",
Pages = "60",
Abstract = "Orthogonal and biorthogonal wavelets are constructed on
a given closed subset of the real line. Wavelets satisfying
certain types of boundary conditions are studied and the concept
of 'wavelet probing' is introduced which allows a number of different
numerical tasks associated with wavelets to be performed quickly.
This paper is at the wavelet archive site." }
@article{argoul-arneodo-etal:1988a,
Author = "Argoul, F. and A. Arneodo and J. ELezgaray and G. Grasseau and
R. Murenzi",
Title = "Wavelet transform of two--dimensional fractal aggregates",
Journal = "Phys. Rev. Lett. A",
Volume = "135",
Pages = "327--336" }
@article{argoul-arneodo-etal:1988b,
Author = "Argoul, F. and A. Arneodo and J. ELezgaray and G. Grasseau and
R. Murenzi",
Title = "Wavelet analysis of the self-similarity of diffusion--limited
aggregates and electrodeposition clusters",
Journal = "Phys. Rev. A",
Volume = "41",
Pages = "5537--5560" }
@article{argoul-arneodo-etal:1989,
Author = "Argoul, F. and A. Arneodo and G. Grasseau and Y. Gagne and
E. J. Hopfinger and U. Frisch",
Title = "Wavelet analysis of turbulence reveals the multifractal nature
of the Richardson cascade",
Journal = "Nature",
Volume = "338",
Year = "1989",
Pages = "51--53" }
@article{arneodo-grasseau-etal:1988,
Author = "Arneodo, A. and G. Grasseau and M. Holschneider",
Title = "Wavelet transform of multifractals",
Journal = "Phys. Rev. Lett.",
Volume = "61",
Year = "1988",
Pages = "2281--2284" }
@article{bacry-arneodo-etal:1990,
Author = "Bacry, E. and A. Arneodo and U. Frisch and Y. Gagne
and E. Hopfinger",
Title = "Wavelet analysis of fully developed turbulence data and
measurement of scaling exponent",
Booktitle = "Turbulence and Coherent Structures",
Editor = "M. Lesieur and O. Metais",
Publisher = "Kluwer Academic Pub.",
Year = "1990",
Pages = "????" }
@article{bacry-mallat-etal:1992,
Author = "Bacry, Emmanual and St/'ephane Mallat and George Papanicolaou",
Title = "A wavelet based space--time adaptive numerical method for
partial differential equations",
Journal = "Mathematical Modelling and Numerical Analysis",
Volume = "26",
Date = "1992",
Pages = "793--834",
Abstract = "This describes a space and time adaptive numerical method based
on wavelet orthonormal bases for solving partial differential equations.
The multiresolution structure of wavelet orthonormal bases provides a
simple way to adapt computational refinements to the local regularity
of the solution." }
@techreport{bacry-mallat-etal:1993,
Author = "Bacry, Emmanual and St/'ephane Mallat and George Papanicolaou",
Title = "A wavelet based space--time adaptive numerical method for
partial differential equations",
Date = "1993",
Institution = "Courant Inst. of Math. Sci., New York Univ., 251 Mercer St.,
New York, N.Y., 10012",
URL = "ftp://cs.nyu.edu:/pub/wave/report/pde.ps.Z",
Size = "218,233 bytes",
Pages = "33",
Abstract = "This describes a space and time adaptive numerical method based
on wavelet orthonormal bases for solving partial differential equations.
The multiresolution structure of wavelet orthonormal bases provides a
simple way to adapt computational refinements to the local regularity
of the solution." }
@article{bacry-muzy-etal:1993,
Author = "Bacry, E. and J. Muzy and A. Arneodo",
Title = "Singularity spectrum of fractal signals from wavelet
analysis: exact results",
Journal = "Journ. of Statistical Physics",
Volume = "70",
Year = "1993",
Pages = "????" }
@article{bendjoya-slezak:1993,
Author = "Bendjoya, Ph. and E. Slezak"
Title = "Wavelet analysis and applications to some dynamical systems"
Journal = "Celestial Mech. and Dyn. Astron."
Volume = "56"
Year = "1993"
Pages = "231--262"
Note = "The wavelet transform appears as a new time-frequency
method which is particulary well-suited to detect and to localize
discontinuities and scaling behaviours in signals. The main properties
of the wavelet transform and its improvements over classical analyzing
methods are summarized. Some results among the first applications
to the dynamical systems are presented: solution of PDEs, fractal and
turbulence characterization, and asteroid family determination from
cluster analysis." }
@article{bendjoya-slezak-etal:1991,
Author = "Bendjoya, Ph. and E. Slezak and Cl. Froeschl/'e",
Title = "The wavelet transform: a new tool for asteroid family
determination",
Journal = "Astron. Astroph.",
Volume = "251",
Year = "1991",
Pages = "312--330" }
@techreport{best-schafer:1994,
Author = "Best, Christoph and Andreas Sch{\"a}fer",
Title = "Variational description of statistical field theories using
Daubechies wavelets",
Year = "1994",
Number = "HEP-LAT/9402012",
Institution = "Insitut f{\"u}r Theoretische Physik, Johann Wolfgang
Goethe-Universit{\"a}t, 60054 Frankfurt am Main, Germany",
URL = "ftp://xxx.lanl.gov/hep-lat/papers/9402/9402012.tar.Z",
Size = "43,560",
Pages = "20",
Keyword = "wavelets, statistical field theories",
Abstract = "Investigates the description of statistical field theories
using Daubechies' orthonormal compact wavelets on a lattice." }
@techreport{beylkin:1992,
Author = "Beylkin, G.",
Title = "On the fast algorithm for multiplication of functions in the
wavelet bases",
Year = "1992",
Month = "jun",
Institution = "Prog. in Appl. Math., Univ. of Colorado at Boulder, Boulder,
CO 80309-0526",
URL = "ftp://amath-ftp.colorado.edu:/pub/wavelets/papers/malgToulouse.ps.Z",
Size = "62,005 bytes",
Pages = "9",
Abstract = "This paper develops a novel approach to the pointwise
multiplication of functions in the wavelet bases based on uncoupling
the interactions between scales. The complexity of the algorithm
is automatically adaptable to the complexity of the wavelet representation
of a function u and proportional to the number of significant cofficients
in the representation of u." }
@techreport{beylkin:1993a,
Author = "Beylkin, G.",
Title = "On factored FIR approximation of IIR filters",
Year = "1993",
Institution = "Prog. in Appl. Math., Univ. of Colorado at Boulder, Boulder,
CO 80309-0526",
URL = "ftp://amath-ftp.colorado.edu:/pub/wavelets/papers/iir2fir.ps.Z",
Size = "135,648 bytes",
Pages = "11",
Abstract = "This paper describes a simple and accurate method of
approximating infinite impulse response (IIR) filters by finite
impulse filters (FIR)." }
@inproceedings{beylkin:1993b,
Author = "Beylkin, Gregory",
Title = "Wavelets and fast numerical algorithms",
Booktitle = "Different Perspectives on Wavelets",
Editor = "Ingrid Daubechies",
Publisher = "American Math. Soc., Providence, RI",
Series = "Proceedings of Symposia in Applied Mathematics",
Volume = "47",
Year = "1993",
Pages = "89--117",
Note = "From an American Math. Soc. short course, Jan. 11--12, 1993, San
Antonio, TX",
Abstract = "Reviews the standard and non--standard representations of
operators in wavelet bases and associated fast numerical algorithms.
The non--standard representation uncouples the interaction among the
scales. Examples of the non--standard forms of several basic operators
are computed explicitly." }
@techreport{beylkin-saito:1993,
Author = "Beylkin, Gregory and Naoki Saito",
Year = "1993",
Title = "Wavelets, their autocorrelation functions, and multiresolution
representation of signals",
Institution = "Prog. in Appl. Math., Univ. of Colorado at Boulder, Boulder,
CO 80309-0526",
URL = "ftp://amath-ftp.colorado.edu:/pub/wavelets/papers/spie.ps.Z",
Size = "160,004 bytes",
Pages = "12",
Abstract = "The properties of the auto-correlation functions of compactly
supported wavelets are summarized as well as their connection to iterative
interpolation schemes and the use of these functions for multiresolution
analysis of signals." }
@article{beylkin-coifman-etal:1991,
Author = "Beylkin, G. and R. Coifman and V. Rokhlin",
Title = "Fast wavelet transforms and numerical algorithms",
Journal = "Comm. in Pure and Applied Math.",
Volume = "44",
Year = "1991",
Pages = "141--183",
Abstract = "A class of algorithms is introduced for the rapid numerical
application of a class of linear operators to arbitrary vectors.
Previously published schemes of this type utilize detailed analytical
information about the operators being applied and are specific to
extremely narrow classes of matrices. In contrast, the methods
presented here are based on the recently developed theory of wavelets
and are applicable to all Calderon-Zygmund and pseudo-differential
operators. The algorithms of this paper require order O(N) or
O(N log N) operations to apply an NxN matrix to a vector and numerical
experiments indicate that many previously intractable problems become
manageable with the techniques presented here." }
@techreport{bhatia-karl-etal:1993,
Author = "Bhatia, M. and W. C. Karl and A. S. Willsky",
Email = "mbhatia@mit.edu",
Title = "A wavelet-based method for multiscale tomographic reconstruction",
Number = "MIT Tech. Rep. LIDS-P-2182",
Year = "1993",
Institution = "Stochastic Systems Group, Lab. for Information and Dec. Systems,
MIT, Cambridge, MA 02139",
URL = "ftp://lids.mit.edu:/pub/ssg/papers/LIDS-P-2182.PS.gz",
Size = "595,196 bytes",
Pages = "31",
Abstract = "A wavelet-based representation of the standard ramp filter
operator of the filtered back-projection (FBP) reconstruction enables
the formulation of a multiscale tomographic reconstruction technique
wherein the object is reconstructed at multiple scales or resolutions.
A complete reconstruction is obtained by combining the reconstructions
at different scales. The framework for multiscale reconstruction
presented here can find application in object feature recognition
directly from projection data, and regularization of imaging problems
where the projection data are noisy." }
@inproceedings{bijaoui:1993,
Author = "Bijaoui, A.",
Title = "Wavelets and astronomical image analysis",
Booktitle = "Wavelets, Fractals, and Fourier Transforms",
Editor = "Farge, M. and J. C. R. Hunt and J. C. Vassilicos",
Publisher = "Clarendon Press",
Year = "1993",
Pages = "195--212",
Keyword = "wavelets, image analysis",
Abstract = "This shows that wavelet analysis is appropriate to study the
distribution of matter in the universe, because of its inhomogeneity
and `spottiness'." }
@inproceedings{bijaoui-slezak-etal:1993,
Author = "Bijaoui, A. and E. Slezak and G. Mars",
Title = "Universe heterogeneities from a wavelet analysis",
Booktitle = "Wavelets, Fractals, and Fourier Transforms",
Editor = "Farge, M. and J. C. R. Hunt and J. C. Vassilicos",
Publisher = "Clarendon Press",
Year = "1993",
Pages = "213--220",
Keyword = "wavelets, image analysis",
Abstract = "This describes a method for the automated detection and
characterization of all the structural components in a catalogue
of galaxies. The local analysis of the distribution is performed
using the wavelet transform." }
@techreport{bond-vavasis:1994,
Author = "Bond, Dave M. and Stephen A. Vavasis",
Title = "Fast wavelet transforms for matrices arising from boundary
element methods",
Year = "1994",
Month = "mar",
Number = "174",
Institution = "Center for Applied Mathematics, Eng. and Theory Center,
Cornell Univ., Ithaca, N.Y. 14853",
URL = "ftp://ftp.tc.cornell.edu/pub/tech.reports/tr174.ps",
Size = "465,044",
Pages = "45",
Abstract = "Wavelet transforms are applied to express matrices
obtained from discretizing the integral equations obtained from
applying the boundary element method to Laplace's equation.
This transforms dense matrices to sparse ones and thus allows
faster inversion." }
@article{bradshaw-mcintosh:1994,
Author = "Bradshaw, G. A. and B. A. McIntosh",
Title = "Determining climate--induced patterns using wavelet analysis",
Journal = "Environmental Pollution",
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." }
@techreport{bray-mccormick-etal:1991,
Author = "Bray, Hubert and Kent McCormick and Raymond O. Wells and
Xiaodong Zhou",
Title = "Wavelet variations on the Shannon sampling theorem",
Year = "1991",
Number = "TR91-09",
Institution = "Computational Math. Lab., Rice University, Houston,
TX 77251-1892",
URL = "ftp://cml.rice.edu/pub/reports/9109.ps.Z",
Size = "76,567",
Pages = "?",
Abstract = "?" }
@manual{buckheit-chen-etal:1995,
Author = "Buckheit, Jonathan and Shaobing Chen and David Donoho and
Iain Johnstone and Jeffrey Scargle",
Title = "About WaveLab",
Year = "1995",
Month = "jan",
Institution = "Stanford University",
URL = "ftp://playfair.stanford.edu/pub/wavelab/AboutWaveLab.ps",
Size = "1,180,309",
Pages = "34",
Abstract = "WaveLab is a library of Matlab routines for wavelet
analysis, wavelet-packet analysis, cosine-packet analysis and
matching pursuit. The library is available free of charge over
the Internet, and versions are provided for Macintosh, UNIX
and Windows machines. It has over 500 .m files which are
documented and cross-referenced in various ways. The software
is available in the same directory as this manual." }
%CCCC
@techreport{cabrera-kreinovich-etal:1992,
Author = "Cabrera, Sergio and Vladik Kreinovich and Ongard Sirisaengtaksin",
Email = "vladik@cs.ep.utexas.edu",
Title = "Wavelets compress better than all other methods: A 1-D
theorem",
Year = "1992",
Institution = "Dept. of Comp. Sci., Univ. of Texas at El Paso, El Paso, TX 79968",
URL = "ftp://cs.ep.utexas.edu:/pub/reports/tr92-25.tex",
Size = "82,806",
Pages = "31",
Abstract = "Wavelet compression is compared with all possible compressions
and is found, for smooth 1-dimensional signals, to be better in the
sense that it requires the smallest number of bytes to store the wavelet
representation." }
@article{chakrabarti-vishwanath:1995,
Author = "Charkrabarti, Chaitali and Mohan Vishwanath",
Title = "Efficient realizations of the discrete and continuous
wavelet transforms: From single chip implementations to mappings
on SIMD array computers",
Journal = "IEEE Trans. Sig. Proc.",
Volume = "43",
Year = "1995",
Pages = "759--771",
Abstract = "This presents a wide range of algorithms and architectures
for computing the 1-D and 2-D discrete wavelet transform (DWT) and the
1-D and 2-D continuous wavelet transform (CWT). The algorithms and
architectures presented here are independent of the size and nature
of the wavelet function. New on-line algorithms are proposed for
the DWT and the CWT that require significantly small storage. The
proposed systolic array and the parallel filter architectures
implement these on-line algorithms and are optimal both with respect
to area and time (under the word-serial model). Moreover, these
architectures are very regular and support single chip implementations
in VLSI. The proposed SIMD architectures implement the existing
pyramid and a'trous algorithms and are optimal with respect to
time." }
@phdthesis{chen:1994,
Author = "Chen, Debao",
Title = "Cardinal spline wavelets",
Year = "1994",
Institution = "Univ. of Texas at Austin",
URL = "ftp://fireant.ma.utexas.edu/pub/papers/CNA/d.chen/diss[1-6].ps",
Size = "(various)",
Pages = "103",
Keyword = "wavelets, splines",
Abstract = "This studies the general structure of cardinal spline
wavelets." }
@book{chui:1992a,
Author = "Chui, C. K.",
Title = "An Introduction to Wavelets",
Publisher = "Academic Press, Inc.",
Year = "1992" }
@book{chui:1992b,
Editor = "Chui, C. K.",
Title = "Wavelets: A Tutorial in Theory and Applications",
Publisher = "Academic Press",
Year = "1992" }
@incollection{cohen.a:1992,
Author = "Cohen, A.",
Title = "Biorthogonal wavelets",
Booktitle = "Wavelets: A Tutorial in Theory and Applications",
Editor = "C. K. Chui",
Publisher = "Academic Press",
Year = "1992",
Pages = "123--152" }
@article{cohen.a-daubechies:1993,
Author = "Cohen, A. and Ingrid Daubechies",
Title = "Orthonormal bases of compactly supported wavelets: III. Better
frequency resolution",
Journal = "SIAM J. Math. Anal.",
Volume = "24",
Year = "1993",
Pages = "520--527",
Abstract = "Standard orthonormal bases of wavelets with dilation factor 2 use
wavelets with one octave bandwidth. Orthonormal bases with 1/2 octave
or even smaller bandwidth wavelets are constructed." }
@unpublished{cohen.j:1992,
Author = "Cohen, Jack K.",
Email = "jkc@keller.mines.colorado.edu",
Title = "Wavelets--a new orthonormal basis",
Institution = "Colorado School of Mines",
Year = "1992",
URL = "ftp://hilbert.mines.colorado.edu/pub/wavelets/Tutor.ps.Z",
Size = "112,093",
Pages = "12",
Abstract = "This describes the wavelet transform, a new orthonormal
basis which, unlike the non-local Fourier and Fourier-like methods,
is a localized basis." }
@unpublished{cohen.j:1993a,
Author = "Cohen, Jack K.",,
Email = "jkc@keller.mines.colorado.edu",
Title = "The Stein wavelet",
Year = "Nov. 2, 1993",
Institution = "Colorado School of Mines",
URL = "ftp://hilbert.mines.colorado.edu:pub/wavelets/Stein.400dpi.ps.z",
Size = "83,275 bytes",
Pages = "6",
Abstract = "This is a Mathematica notebook converted to TeX using
nb2tex from mathsource and then converted to postscript. The
notebook gives details for the construction of the Littlewood-Paley-Stein
wavelet." }
@unpublished{cohen.j:1993b,
Author = "Cohen, Jack K.",,
Email = "jkc@keller.mines.colorado.edu",
Title = "The foot problem in wavelet packet splitting",
Year = "Nov. 1, 1993",
Institution = "Colorado School of Mines",
URL = "ftp://hilbert.mines.colorado.edu:pub/wavelets/PacketFeet.400dpi.ps.z",
Size = "441,923 bytes",
Pages = "35",
Abstract = "This is a Mathematica notebook converted to TeX using
nb2tex from mathsource and then converted to postscript. The
notebook discusses the problem of pieces of non-adjacent bands
creeping in when constructing wavelet packets." }
@unpublished{cohen.j:1993c,
Author = "Cohen, Jack K.",,
Email = "jkc@keller.mines.colorado.edu",
Title = "Schauder basis for C[0,1]",
Year = "Nov. 11, 1993",
Institution = "Colorado School of Mines",
URL = "ftp://hilbert.mines.colorado.edu:pub/wavelets/Schauder.400dpi.ps.z",
Size = "231,729 bytes",
Pages = "19",
Abstract = "This is a Mathematica notebook converted to TeX using
nb2tex from mathsource and then converted to postscript. The
notebook discusses the Schauder basis for C[0,1] in the context
of wavelets." }
@unpublished{cohen.j:1993d,
Author = "Cohen, Jack K.",,
Email = "jkc@keller.mines.colorado.edu",
Title = "Battle-Lemarie wavelets",
Year = "Nov. 1, 1993",
Institution = "Colorado School of Mines",
URL = "ftp://hilbert.mines.colorado.edu:pub/wavelets/Spline.400dpi.ps.z",
Size = "120,847 bytes",
Pages = "11",
Abstract = "This is a Mathematica notebook converted to TeX using
nb2tex from mathsource and then converted to postscript. The
notebook discusses the details about and construction of
Battle-Lamarie wavelets." }
@unpublished{cohen.j:1993e,
Author = "Cohen, Jack K.",,
Email = "jkc@keller.mines.colorado.edu",
Title = "Dauchechies minimum phase wavelets",
Year = "Nov. 22, 1993",
Institution = "Colorado School of Mines",
URL = "ftp://hilbert.mines.colorado.edu:pub/wavelets/Daubechies.400dpi.ps.z",
Size = "211,543 bytes",
Pages = "15",
Abstract = "This is a Mathematica notebook converted to TeX using
nb2tex from mathsource and then converted to postscript. The
notebook discusses Daubechies minimum phase wavelets." }
@unpublished{cohen.j:1993f,
Author = "Cohen, Jack K.",,
Email = "jkc@keller.mines.colorado.edu",
Title = "Meyer wavelets",
Year = "Nov. 1, 1993",
Institution = "Colorado School of Mines",
URL = "ftp://hilbert.mines.colorado.edu:pub/wavelets/Meyer.400dpi.ps.z",
Size = "138,220 bytes",
Pages = "25",
Abstract = "This is a Mathematica notebook converted to TeX using
nb2tex from mathsource and then converted to postscript. The
notebook discusses Meyer wavelets." }
@techreport{cohen.j-chen:1994,
Author = "Cohen, Jack C. and Tong Chen",
Title = "Fundamentals of the discrete wavelet transform for seismic
data processing",
YEar = "1994",
Number = "CWP-130P",
Institution = "Center for Wave Phenomena, Colorado School of Mines,
Golden, Colorado 80401",
URL = "ftp://ftp.mines.colorado.edu/pub/papers/math_cs_dept/cwp-130P.ps.Z",
Size = "1,553,553",
Pages = "48",
Abstract = "This explains and illustrates the effect of the discrete
wavelet transform on seismic data, providing the information necessary
for researchers to assess its possible use in their areas of data
procesisng. Examples are shown." }
@article{cohen.l:1989,
Author = "Cohen, L.",
Title = "Time--frequency distributions -- A review",
Journal = "Proc. IEEE",
Volume = "77",
Year = "1989",
Pages = "941--981",
Abstract = "A review and tutorial of the fundamental ideas and methods of
joint time--frequency distributions is presented. The objective of
the field is to describe how the spectral content of a signal is changing
in time, and to develop the mathematical and physical ideas needed to
understand what a time--varying spectrum is. The basic goal is to devise
a distribution that represents the energy or intensity of a signal
simultaneously in time and frequency. This review especially reflects
recent advances in the field such as the use of wavelets." }
@techreport{coifman-meyer-etal:1990,
Author = "Coifman, Ronald R. and Yves Meyer and Steven Quake and M. Victor
Wickerhauser",
Title = "Signal processing and compression with wave packets",
Year = "Apr. 5, 1990",
Institution = "Numerical Algorithms Res. Group, Dept. of Math., Yale Univ.,
New Haven, CT 06520",
URL = "ftp://math.yale.edu:/pub/wavelets/cmqw.tex",
Size = "33,511 bytes",
Pages = "15",
Abstract = "Algorithms for signal processing and data compression based on
a collection of orthogonal functions called fast wave packets are
described. Fast wave packets generalize the compactly supported
wavelets of Daubechies and Meyer. The algorithms described combine the
projection of a sequence onto fast wave packet components, the selection
of an optimal orthonormal basis subset, some linear or quasilinear
processing of the coefficients, and then reconstruction of the transformed
sequence." }
@incollection{coifman-meyer-etal:1991,
Author = "Coifman, Ronald R. and Yves Meyer and M. Victor Wickerhauser",
Title = "Wavelet analysis and signal processing",
Booktitle = "Wavelets and Their Applications",
Editor = "M. B. Ruskai et al.",
Publisher = "Jones and Barlett, Boston",
Year = "1992",
Pages = "153--178",
Note = "This is also available in the form of a technical report at
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." }
@techreport{coifman-wickerhauser:1991,
Author = "Coifman, Ronald R. and M. Victor Wickerhauser",
Title = "Wavelets and adapted waveform analysis",
Year = "1991",
Institution = "Numerical Algorithms Res. Group, Dept. of Math., Yale Univ.,
New Haven, CT 06520",
URL = "ftp://wuarchive.wustl.edu:/doc/techreports/wustl.edu/math/wawa.ps.Z",
Size = "878,503 bytes",
Pages = "33",
Abstract = "This describes tools for adapting methods of analysis to various
tasks occuring in harmonic and numerical analysis and signal processing.
The main point is that by choosing an orthonormal basis in which space
and frequency are suitably localized one can achieve understanding of
both structure and efficiency in computation." }
@article{coifman-wickerhauser:1992,
Author = "Coifman, R. R. and M. V. Wickerhauser",
Title = "Entropy-based algorithms for best-basis selection",
Journal = "IEEE Trans. Info. Theory",
Volume = "38",
Year = "1992",
Pages = "713--718" }
@inproceedings{coifman-wickerhauser:1993,
Author = "Coifman, Ronald R. and M. Victor Wickerhauser",
Title = "Wavelets and adapted waveform analysis: A toolkit for signal
processing and numerical analysis",
Booktitle = "Different Perspectives on Wavelets",
Editor = "Ingrid Daubechies",
Publisher = "American Math. Soc., Providence, RI",
Series = "Proceedings of Symposia in Applied Mathematics",
Volume = "47",
Year = "1993",
Pages = "119--153",
Note = "From an American Math. Soc. short course, Jan. 11--12, 1993, San
Antonio, TX",
Abstract = "Wavelet analysis or, more generally, Adapted Waveform
Analysis (AWA) consists of a versatile collection of tools for the
analysis and manipulation of signals such as sound and images, as
well as more general digital data sets (including linear and non--linear
operators occurring in the simulations of physical processes). AWA
provides us with the ability to represent a function or signal in a mode
similar to a musical score, where each note corresponds to a waveform
having a duration, pitch and amplitude. The goal is to transcribe as
efficiently as possible, and to orchestrate into different structures." }
%% 1/26/96
@article{collineau-brunet:1993,
Author = "Collineau, S. and Y. Brunet",
Title = "Detection of turbulent coherent motions in a forest
canopy. Part I: Wavelet analysis",
Journal = "Boundary-Layer Meteorology",
Volume = "65",
Year = "1993",
Pages = "357--379" }
@book{combes-grossman-etal:1989,
Editor = "Combes, J. M. and A. Grossman and Ph. Tchamitchian",
Title = "Wavelets: Time-Frequency Methods and Phase Space",
Publisher = "Springer-Verlag",
Year = "1989",
Pages = "315",
LOC = "QC 174.85 P48 W38 1989",
ISBN = "0-387-51159-8",
TOC = "
I. Introduction to wavelet transforms,
1. Reading and understanding continuous wavelet transforms -
A. Grossmann, R. Kronland-Martinet, and J. Morlet 2,
2. Orthonormal wavelets - Y. Meyer 21,
3. Orthonormal bases of wavelets with finite support:
Connection with discrete filters - I. Daubechies 38,
II. Some topics in signal analysis,
4. Some aspects of non-stationary signal processing with
emphasis on time-frequency and time-scale methods -
P. Flandrin 68,
5. Detection of abrupt changes in signal processing -
M. Basseville 99,
6. The computer, music, and sound models - J.-C. Risset 102,
III. Wavelets and signal processing,
7. Wavelets and seismic interpretation - J. L. Larsonneur
and J. Morlet 126,
8. Wavelet transformations in signal detection - F.B. Tuteur 132,
9. Use of wavelet transforms in the study of propagation of
transient acoustic signals across a plane interface
between two homogeneous media - S. Ginette, A. Grossmann,
and Ph. Tchamitchian 139,
10. Time-frequency analysis of signals related to scattering
problems in acoustics. Part I: Wigner-Ville analysis of
echoes scattered by a spherical shell - J. P. Sessarego,
J. Sageloli, P. Flandrin, and M. Zakharia 147,
11. Coherence and projectors in acoustics - J. G. Slama 154,
12. Wavelets and granular analysis of speech - J. S. Lienard
and C. d'Alessandro 158,
13. Time-frequency representations of broad-band signals -
J. Bertrand and P. Bertrand 164,
14. Operator groups and ambiguity functions in signal
processing - A. Berthon 172,
IV. Mathematics and mathematical physics,
15. Wavelet transform analysis of invariant measures of some
dynamical systems - A. Arneodo, G. Grasseau, and
M. Holschneider 182,
16. Holomorphic integral representations for the solutions of
the Helmholtz equation - J. Bros 197,
17. Wavelets and path integral - T. Paul 204,
18. Mean value theorems and concentration operators in
Bargmann and Bergman space - K. Seip 209,
19. Besov Sobolev algebras of symbols - G. Bohnke 216,
20. Poincare coherent states and relativistic phase space
analysis - J.-P. Antoine 221,
21. A relativistic Wigner function affiliated with the
Weyl-Poincare gruop - J. Bertrand and P. Bertrand 232,
22. Wavelet transforms associated to the n-dimensional
Euclidean group with dilations: Signals in more than
one dimension - R. Murenzi 239,
23. Construction of wavelets on open sets - S. Jaffard 247,
24. Wavelets on chord-arc curves - P. Auscher 253,
25. Multiresolution analysis in non-homogeneous media -
R. R. Coifman 259,
26. About wavelets and elliptic operators - Ph. Tchamitchian 263,
27. Towards a method for solving PDEs using wavelet bases -
V. Perrier 269,
V. Implementations,
28. A real-time algorithm for signal analysis with the help
of the wavelet transform - M. Holschneider, R.
Kronland-Martinet, J. Morlet and Ph. Tchamitchian 286,
29. An implementation of the ``algorithme a trous'' to
compute the wavelet transform -P. Dutilleux 293,
30. An algorithm for fast imaging of wavelet transforms -
P. Hanusse 305,
Subject index 313,
Index of contributors 315" }
%DDDD
@article{dallard-browand:1993,
Author = "Dallard, T. and F. K. Browand",
Title = "The growth of large scales at defect sites in the plane mixing
layer",
Journal = "J. Fluid Mech.",
Volume = "247",
Year = "1993",
Pages = "339--368" }
@article{dallard-spedding:1993,
Author = "Dallard, T. and G. R. Spedding",
Title = "2-D wavelet transforms: generalisation of the Hardy space and
application to experimental studies",
Journal = "Eur. J. Mech., B/Fluids",
Volume = "12",
Year = "1993",
Pages = "107--134" }
@book{daubechies:1992,
Author = "Daubechies, Ingrid",
Title = "Ten Lectures on Wavelets",
Publisher = "Society for Industrial and Applied Math., Philadelphia",
Year = "1992",
Pages = "357",
LOC = "QA 403.3 D38 1992",
ISBN = "0-89871-274-2",
TOC =
1. The what, why, and how of wavelets 1,
1.1 Time-frequency localization 1,
1.2 The wavelet transform: Analogies and differences with
the windowed Fourier transform 3,
1.3 Different types of wavelet transform 7,
1.3.1 The continuous wavelet transform 7,
1.3.2 The discrete but redundant wavelet transform-frames 8,
1.3.3 Orthogonal wavelet bases: Multiresolution analysis 10,
2. The continuous wavelet transform 17,
2.1 Bandlimited functions and Shannon's theorem 17,
2.2 Bandlimited functions as a special case of a reproducing
kernel Hilbert space 20,
2.3 Band- and timelimiting 21,
2.4 The continuous wavelet transform 24,
2.5 The reproducing kernel Hilbert space underlying the
continuous wavelet transform 31,
2.6 The continuous wavelet transform in higher dimensions 33,
2.7 Parallels with the continuous windowed Fourier transform 34,
2.8 The continuous transform as tools to build useful operators 35,
2.9 The continous wavelet transform as a mathematical zoom:
The characterization of local regularity 45,
3. Discrete wavelet transforms: Frames 53,
3.1 Discretizing the wavelet transform 53,
3.2 Generalities about frames 56,
3.3 Frames of wavelets 63,
3.3.1 A necessary condition: Admissibility of the
mother wavelet 63,
3.3.2 A sufficient condition and estimates for the frame
bounds 67,
3.3.3 The dual frame 69,
3.3.4 Some variations on the basic scheme 71,
3.3.5 Examples 73,
A. Tight frames 73,
B. The Mexican hat function 75,
C. A modulated Gaussian 76,
D. An example that is easy to implement 78,
3.4 Frames for the windowed Fourier transform 80,
3.4.1 A necessary condition: Sufficiently high
time-frequency density 81,
3.4.2 A sufficient condition and estimates for the frame
bounds 82,
3.4.3 The dual frame 83,
3.4.4 Examples 83,
A. Tight frames with compact support in time or frequency 83,
B. The Gaussian 84,
3.5 Time-frequency localization 86,
3.6 Redundancy in frames: What does it buy? 97,
3.7 Some concluding remarks 100,
4. Time-frequency density and orthonormal bases 107,
4.1 The role of time-frequency density in wavelet and windowed
Fourier frames 107,
4.2 Orthonormal bases 115,
4.2.1 Orthonormal wavelet bases 115,
4.2.2 The windowed Fourier transform revisited: ``Good''
orthonormal bases after all! 120,
5. Orthonormal bases of wavelets and multiresolution analysis 129,
5.1 The basic idea 129,
5.2 Examples 137,
5.3 Relaxing some of the conditions 139,
5.3.1 Riesz bases of scaling functions 139,
5.3.2 Using the scaling function as a starting point 140,
5.4 More examples: The Battle-Lemari{\'e} family 146,
5.5 Regularity of orthonormal wavelet bases 153,
5.6 Connection with subband filtering schemes 156,
6. Orthonormal bases of compactly supported wavelets 167,
6.1 Construction of m0 167,
6.2 Correspondence with orthonormal wavelet bases 174,
6.3 Necessary and sufficient conditions for orthonormality 182,
6.4 Examples of compactly supported wavelets generating an
orthonormal basis 194,
6.5 The cascade algorithm: The link with subdivision or
refinement schemes 202,
7. More about the regularity of compactly supported wavelets 215,
7.1 Fourier-based methods 215,
7.1.1 Brute force methods 216,
7.1.2 Decay estimates from invariant cycles 220,
7.1.3 Little-Paley type estimates 226,
7.2 A direct method 232,
7.3 Compactly supported wavelets with more regularity 241,
7.4 Regularity or vanishing moments? 242,
8. Symmetry for cmpactly supported wavelet bases 251,
8.1 Absence of symmetry for compactly supported orthonormal
wavelets 251,
8.1.1 Closer to linear phase 254,
8.2 Coiflets 258,
8.3 Symmetric biorthogonal wavelet bases 259,
8.3.1 Exact reconstruction 262,
8.3.2 Scaling functions and wavelets 263,
8.3.3 Regularity and vanishing moments 269,
8.3.4 Symmetry 269,
8.3.5 Biorthogonal bases close to an orthonormal basis 278,
9. Characterization of functional spaces by means of wavelets 289,
9.1 Wavelets: Unconditional bases 289,
9.2 Characterization of function spaces by means of wavelets 298,
9.3 Wavelets for ${L^1}$(|0,1|) 304,
9.4 An amusing contrast between wavelet expansions and Fourier
series 307,
10. Generalizations and tricks for orthonormal wavelet bases 313,
10.1 Multidimensional wavelet bases with dilation factor 2 313,
10.2 One-dimensional orthonormal wavelet bases with integer
dilation factor larger than 2 319,
10.3 Multidimensional wavelet bases with matrix dilations 321,
10.4 One-dimensional orthonormal wavelet bases with non-integer
dilation factors 323,
10.5 Better frequency resolution: The splitting trick 326,
10.5 Wavelet packet bases 331,
10.6 Wavelet bases on an interval 333" }
@inproceedings{daubechies:1993a,
Author = "Daubechies, Ingrid",
Title = "Wavelet transforms and orthonormal wavelet bases",
Booktitle = "Different Perspectives on Wavelets",
Editor = "Ingrid Daubechies",
Publisher = "American Math. Soc., Providence, RI",
Series = "Proceedings of Symposia in Applied Mathematics",
Volume = "47",
Year = "1993",
Pages = "1--33",
Note = "From an American Math. Soc. short course, Jan. 11--12, 1993, San
Antonio, TX",
Abstract = "Introduces the wavelet transform and discusses its motivation
as a time--frequency localization tool. Reviews the different types of
wavelet transform, with special emphasis on orthonormal wavelet bases
and their properties. Concludes with a short discussion of
shortcomings." }
@article{daubechies:1993b,
Author = "Daubechies, Ingrid",
Title = "Orthonormal bases of compactly supported wavelets: II. Variations
on a theme",
Journal = "SIAM J. Math. Anal.",
Volume = "24",
Year = "1993",
Pages = "499--519",
Abstract = "Several variations are given on the construction of orthonormal
bases of wavelets with compact support. They have, respectively, more
symmetry, more regularity, and more vanishing moments for the scaling
function than the examples in daubechies:1988." }
@article{daubechies-lagarias:1991,
Author = "Daubechies, I[ngrid]. and J. Lagarias",
Title = "Two-scale difference equations, I",
Journal = "SIAM J. Math. Anal.",
Volume = "22",
Year = "1991",
Pages = "1388--1410" }
@article{daubechies-lagarias:1992,
Author = "Daubechies, I. and J. Lagarias",
Title = "Two-scale difference equations, II",
Journal = "SIAM J. Math. Anal.",
Volume = "23",
Year = "1992",
Pages = "1031--1079" }
@incollection{davis-marshak-etal:1994,
Author = "Davis, Anthony and Alexander Marshak and Warren Wiscombe",
Title = "Wavelet-based multifractal analysis of non-stationary
and/or intermittent geophysical signals",
Booktitle = "Wavelets in Geophysics",
Editor = "Efi Foufoula-Georgiou and Praveen Kumar",
Publisher = "Academic Press",
Year = "1994",
Pages = "249--298",
Keyword = "wavelets, fractals, signal processing",
Abstract = "This shows how wavelet transforms can be used to compute
simple yet dynamically meaningful statistical properties of a
one-dimensional data set representative of a geophysical field or
time-series. This paper is available via anonymous ftp at
ftp://climate.gsfc.nasa.gov/pub/marshak/Wavelets.paper/wavelets.text.PS.Z
(99,067) with the figures in wavelets.figs.PS.Z (399,610)." }
@techreport{deboor-devore-etal:1992,
Author = "de Boor, Carl and Ronald A. DeVore and Amos Ron",
Title = "On the construction of multivariate (pre)wavelets",
Year = "1992",
Month = "Feb",
Number = "92-09",
Institution = "Cent. for Math. Sci., Univ. of Wisconsin-Madison,
610 Walnut St., Madison, WI 53705",
URL = "ftp://stolp.cs.wisc.edu/wavelet.ps.Z",
Size = "154,254",
Pages = "42",
Keyword = "wavelets",
Abstract = "A new approach to the construction of wavelets and
prewavelets from multiresolution is presented. The method uses only
properties of shift-invariant spaces and orthogonal projectors onto
these spaces, and requires neither decay nor stability of the scaling
function." }
@article{devore-lucier:1991,
Author = "DeVore, R. and B. J. Lucier",
Title = "Wavelets",
Journal = "Acta Numerica",
Volume = "1",
Year = "1991",
Pages = "1--56",
Keyword = "wavelets",
Abstract = "This is an introduction to some aspects of wavelets, chiefly
from the viewpoint of the experience of the authors in approximation
theory and data compression, although signal processing is touched upon.
The paper starts with a discussion of Haar wavelets, proceeds to
construction of general wavelets, continues with sections on fast
wavelet transforms and smoothness spaces and wavelet coefficients,
and concludes with some applications, e.g. image compression and the
numerical solution of partial differential equations. A copy of
this paper can also be obtained via anonymous ftp at URL address
ftp://ftp.gwdg.de/pub/math/wavelets/papers/waveletGeneral.ps.gz (166,109)." }
@article{devore-jawerth-etal:1992,
Author = "DeVore, R. and B. Jawerth and B. J. Lucier",
Title = "Image compression through wavelet transform coding",
Journal = "IEEE Trans. Inform. Theory",
Volume = "38",
Year = "1992",
Pages = "719--746" }
@article{dijkerman-mazumdar:1994,
Author = "Dijkerman, Robert W. and Ravi R. Mazumdar",
Title = "Wavelet representations of stochastic processes and
multiresolution stochastic models",
Journal = "IEEE Trans. Sig. Proc.",
Volume = "42",
Year = "1994",
Pages = "1640--1652",
Keyword = "waveelts, stochastic processes",
Abstract = "This describes the use of compactly supported wavelets to
obtain multiresolution representation of stochastic processes with
paths in L$^2$ defined in the time domain. The correlation structure
of the discrete wavelet coefficients of a stochastic process is
derived and new results on how and when to obtain strong decay in
correlation along time as well as across scales are given." }
@techreport{donoho:1992,
Author = "Donoho, David L.",
Title = "Wavelet shrinkage and W.V.D - A ten-minute tour",
Year = "1992",
Institution = "Stanford Univ.",
URL = "ftp://playfair.stanford.edu:pub/reports/toulouse.tex",
Size = "27,718 bytes",
Pages = "12",
Abstract = "According to the List file at the same address, there is
supposed to be a toulouseps.shar file containing the figures for
this paper available. As of 7/11/93 it ain't." }
@inproceedings{donoho:1993a,
Author = "Donoho, David L.",
Title = "Nonlinear wavelet methods for recovery of signals, densities,
and spectra from indirect and noisy data",
Booktitle = "Different Perspectives on Wavelets",
Editor = "Ingrid Daubechies",
Publisher = "American Math. Soc., Providence, RI",
Series = "Proceedings of Symposia in Applied Mathematics",
Volume = "47",
Year = "1993",
Pages = "173--205",
Note = "From an American Math. Soc. short course, Jan. 11--12, 1993, San
Antonio, TX",
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. This can also
be obtained via anonymous ftp (donoho:1993b)." }
@techreport{donoho:1993b,
Author = "Donoho, David L.",
Title = "Nonlinear wavelet methods for recovery of signals, densities,
and spectral from indirect and noisy data",
Year = "1993",
Institution = "Stanford Univ.",
URL = "ftp://playfair.stanford.edu:pub/software/wavelets/ShortCourse.ps",
Size = "????? bytes",
Pages = "33",
Keyword = "wavelets",
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. The size indicated
above is for the text only. The 28 figures are contained in the separate
file ShortCourseFigs.epsf.shar.Z (812,771)." }
@article{donoho:1993c,
Author = "Donoho, D. L.",
Title = "Unconditional bases are optimal bases for data compression
and for statistical estimation",
Journal = "Applied and Computational Harmonic Analysis",
Volume = "1",
Year = "1993",
Pages = "100--115" }
@article{donoho-johnstone:1994,
Author = "Donoho, D. L. and I. M. Johnstone",
Title = "Ideal spatial adaptation via wavelet shrinkage",
Journal = "Biometrika",
Volume = "81",
Year = "1994",
Pages = "425--455" }
@EEEE
@techreport{edwards:1992,
Author = "Edwards, Tim",
Email = "tim@sinh.stanford.edu",
Title = "Discrete wavelet transforms: Theory and application (Draft \#2)",
Year = "June 4, 1992",
Institution = "Stanford University",
URL = "ftp://isl.stanford.edu:/pub/godfrey/reports/wavelets/wave_paper/wave_paper.ps",
Size = "438,782 bytes",
Pages = "27",
Keyword = "wavelets",
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." }
%FFFF
@article{farge:1992,
Author = "Farge, Marie",
Title = "Wavelet transforms and their applications to turbulence",
Journal = "Ann. Rev. Fluid. Mech.",
Volume = "24",
Year = "1992",
Pages = "395--457",
Abstract = "Gives a general representation of both the continuous
and discrete wavelet transforms, in a manner as complete and detailed
as possible, to provide the reader with the basic information with
which to start using these transforms. Brief reference is made to
papers dealing with applications, and several new diagnostics, all
based on wavelet coefficients, which may be useful to analyze, model,
or compute turbulent flows are presented." }
@incollection{farge-holschneider-etal:1989,
Author = "Farge, M[arie] and M. Holschneider and J. F. Colonna",
Title = "Wavelet analysis of coherent structures in 2-D turbulent flows",
Booktitle = "Topological Fluid Mechanics",
Editor = "K. Moffatt",
Publisher = "Cambridge Univ. Press",
Year = "1989,
Pages = "765--767" }
@book{farge-hunt-etal:1993,
Editor = "Farge, M. and J. C. R. Hunt and J. C. Vassilicos",
Title = "Wavelets, Fractals, and Fourier Transforms: Based on the
proceedings of a a conference on Wavelets, Fractals and Fourier
Transforms: New Developments and New Applications organized by
the Institute of Mathematics and Applications and Soci{\'e}t{\'e}
de Mathematiques Appliqu{\'e}es et Industrielles and held at
Newnham College, Cambridge in December 1990",
Publisher = "Clarendon Press",
Year = "1993",
Pages = "403",
ISBN = "0-19-853647-X",
LOC = "QA 403.3 W38 1993",
Keyword = "wavelets, fractals, Fourier transforms",
TOC = "
Section 1,
1. Wavelets, fractals and Fourier transforms: Detection and
analysis of structure - J.C.R. Hunt, N.K.-R. Kevlahan,
J.C. Vassilicos and M. Farge 1,
2. Wavelets, fractals and order-two densities - K.J. Falconer 39,
3. Orthonormal and continuous wavelet transform: Algorithms
and applications to the study of pointwise properties of
functions - S. Jaffard 47,
4. Iterated function systems and their applications - J. Stark
and P. Bressloff 65,
5. Biorthogonal bases of symmetric compactly supported
wavelets - C. Herley and M. Vetterli 91,
6. Fractional Brownian motion and wavelets - P. Flandrin 109,
7. The wavelet Gibbs phenomenon - H. O. Rasmussen 123,
8. Multiscale segmentation of well logs - P.L. Verner and
J.A.H. Alkemade 143,
Section 2,
9. Scale-invariance and self-similar `wavelet' transforms:
An analysis of natural scenes and mammalian visual
systems - D.J. Field 151,
10. Wavelets and astronomical image analysis - A. Bijaoui and
A. Fresnel 195,
11. Universe heterogeneities from a wavelet analysis - A. Bijaoui,
E. Slezak and G. Mars 213,
12. The wavelet transform applied to flow around Antarctica -
B. Sinha and K.J. Richards 221,
13. Quantification of scale cascades in the stratosphere using
wavelet transforms - P.H. Haynes and W.A. Norton 229,
Section 3,
14. Multiple-scale correlation detection, wavelet transforms
and multifractal turbulence - J.G. Jones, P.G. Earwicker,
and G.W. Foster 235,
15. Wavelet analysis of turbulence: The mixed energy
cascade - C. Meneveau 251,
16. Hierarchical models of turbulence - P. Frick and V. Zimin 265,
17. Characterisation of TM traffic in the frequency domain -
M. Luoni 285,
18. The self-similarity of D-dimensional potential turbulence -
S.N. Gurbatov and A.I. Saichev 295,
19. Solution of Burgers' equation by Fourier transform
methods - J. Caldwell 309,
20. Spiral structures in turbulent flow - H.K. Moffatt 317,
21. Fractals in turbulence - J.C. Vassilicos 325,
22. The physical models and mathematical description of
1/f noise - A. Malakhov and A. Yakimov 341,
23. Fractal models of density interfaces - J.M. Redondo 353,
24. The fractal dimension of oil-water interfaces in channel
flows - G. Saether, K. Bendiksen, J. Muller and
E. Froland 371,
25. Fractal aggregates in the atmosphere - J.M. Redondo,
R.M. Gonzalez, and J.L. Cano 379,
26. Morphology of disorder materials studied by multifractal
analysis - J. Muller 397" }
@inproceedings{field:1993,
Author = "Field, D. J.",
Title = "Scale-invariance and self-similar `wavelet' transforms: An
analysis of natural scenes and mammalian visual systems",
Booktitle = "Wavelets, Fractals, and Fourier Transforms",
Editor = "Farge, M. and J. C. R. Hunt and J. C. Vassilicos",
Publisher = "Clarendon Press",
Year = "1993",
Pages = "151-194",
Keyword = "wavelets",
Abstract = "The processing of spatial patterns by the mammalian visual
system shows a number of similarities to the `wavelet transforms'
which have recently attracted considerable interest outside of the
study of sensory systems. This paper looks at the question of why
this strategy of representing the visual environment would evolve.
It is proposed that natural scenes are approximately scale invariant
with regards to both their power and phase spectra, and as such
wavelet-like transforms are capable of producing a sparse, informative
representation of these images. It is suggested that self-similar
codes like the wavelet are effective for so many natural phenomena
because such phenomena show similar structures to those found in these
natural scenes." }
@article{flandrin:1992,
Author = "Flandrin, P.",
Title = "Wavelet analysis and synthesis of fractional Brownian motion",
Journal = "IEEE Trans. Inf. Theory",
Volume = "38",
Year = "1992",
Pages = "????" }
@unpublished{fournier.ai:1995,
Author = "Fournier, Aime",
Title = "Wavelet representation of lower-atmospheric long nonlinear wave
dynamics, governed by the Benjamin-Davis-Ono-Burgers equation",
Year = "1995",
Institution = "Yale Univ. Physics Dept. and Dept. of Geology and Geophysics,
POB 208109, New Haven, CT 06520-8109",
URL = "ftp://flint.geology.yale.edu/pub/wrnlwd0.ps.gz",
Size = "492,302",
Pages = "10",
Abstract = "A modified technique is presented for projecting a large
class of nonlinear PDEs with respect to (x,t) onto a finite number
of ODEs with respect to t. Improved description compared to standard
finite-difference or Fourier spectral methods involves using an
orthonormal basis of wavelet functions. Whereas Fourier projection
represents the interaction between spatial scales throughout the
x-domain, wavelet representation does the same locally. This
technique is applied to solving the BDO-Burgers equation." }
@unpublished{fournier.al:1994,
Editor = "Fournier, Alain",
Email = "fournier@cs.ubc.ca",
Title = "Wavelets and their applications in computer graphics",
Institution = "Univ. of British Columbia",
Year = "1994",
URL = "http://www.cs.ubc.ca/nest/imager/contributions/bobl/wvlt/download/notes.ps.Z.saveme",
Size = "2,519,265",
Pages = "162",
Keyword = "wavelets, computer graphics",
Abstract = "These are notes from a course on wavelets given at SIGGRAPH '94.
The sections include an introduction, multiresolution and wavelets,
wavelets, signal compression and image processing, curves and surfaces,
wavelet radiosity, and applications. Their is a software package
associate with this document (./wvlt_r1_3.shar.saveme)." }
%GGGG
@techreport{gagnon-lina:1994,
Author = "Gagnon, L. and J. M. Lina",
Email = "lgagnon@lps.umontreal.ca; lina@lps.umontreal.ca",
Title = "Wavelets and numerical split-step method: A global
adaptive scheme",
Year = "1994",
Month = "jun",
Number = "UdeM-PHYSNUM-ANS-16",
Institution = "Groupe PHYSNUM, Labo. de Phys. Nucl., Universit{\'e}
de Montr{\'e}al, Qu{\'e}bec, H3C 3J7, Canada",
URL = "ftp://lpssua.lps.umontreal.ca/pub/wavelet/gagnon2.ps.Z",
Size = "440,399",
Pages = "33",
Abstract = "This proposes and studies a way of implementing global
adaptive discretization in the symmetrized split-step method using
complex symmetric Daubechies' wavelets. The scheme is based on
the interpolation properties of the corresponding scaling functions
and is aplied on nonlinear Schr{\'o}dinger type equations." }
@article{gamage-blumen:1993,
Author = "Gamage, Nimal and William Blumen",
Title = "Comparative analysis of low--level cold fronts: Wavelet, Fourier,
and empirical orthogonal function decompositions",
Journal = "Monthly Weather Review",
Volume = "121",
Year = "1993",
Pages = "2867--2878",
Abstract = "The relative merits of using both global and local (with respect
to the span of a basis element) transforms to depict cold--front features
are explored. It is concluded that the wavelet or local transform provides
a superior representation of frontal phenomena when compared with global
transform methods."
%% 1/26/96
@article{gamage-hagelberg:1993,
Author = "Gamage, N. and C. Hagelberg",
Title = "Detection and analysis of microfronts and associated
coherent events using localized transforms",
Journal = "J. Atmos. Sci.",
Volume = "50",
Year = "1993",
Pages = "750--756" }
%% 1/26/96
@article{gambis:1992,
Author = "Gambis, D.",
Title = "Wavelet transform analysis of the length of the day and the
El Nino/Southern Oscillation variations at intraseasonal and
interannual time scales",
Journal = "Ann. Geophys.",
Volume = "10",
Year = "1992",
Pages = "429--437" }
@phdthesis{gao:1993,
Author = "Gao, H.-Y.",
Title = "Wavelet estimation of spectral densities in time series",
Institution = "University of California, Berkeley",
Year = "1993",
Note = "I don't have this nor do I know how to get it."
@Article{gao.w-li:1993,
Author = "Gao, W. and B. L. Li",
Title = "Wavelet analysis of coherent structures at the atmosphere--forest
interface",
Journal = "J. Appl. Meteorol.",
Volume = "32",
Year = "1993",
Pages = "1717--1725",
Keyword = "coherent structures, wavelets" }
@techreport{gilbert:1992,
Author = "Gilbert, John E.",
Title = "Wavelets: Theory and applications",
Year = "1992",
Institution = "University of Texas",
URL = "ftp://math.utexas.edu:/pub/papers/lakey/m391c/gilbertnotes.ps",
Size = "473,166 bytes",
Pages = "66",
Keyword = "wavelets",
Note = "The last time I checked (Jan. 1995) this was no longer at
the above address. You might want to contact the author if you
really want the thing.",
Abstract = "These are lecture notes for a course on wavelet analysis.
The first part covers Fourier analysis on Euclidean space and the
second wavelet analysis including such topics as the continuous
wavelet transform, pre-historic wavelets, image analysis and
multi-resolution, splines as pre-wavelets, and Daubechies
reconstruction." }
@inproceedings{glowinski-lawton-etal:1990,
Author = "Glowinski, Roland and Wayne Lawton and Michel Ravachol and
Eric Tenenbaum",
Title = "Wavelet solutions of linear and nonlinear elliptic, parabolic
and hyperbolic problems in one space dimension",
Booktitle = "Computing Methods in Applied Sciences and Engineering",
Editor = "Roland Glowinski and Alain Lichnewsky",
Publisher = "Society for Industrial and Applied Mathematics",
Note = "Proceedings of the Ninth International Conference on Computing
Methods in Applied Sciences and Engineering",
Year = "1990",
Pages = "55--120",
Abstract = "This discusses the Daubechies wavelet solution of boundary
value problems and initial boundary value problems for ordinary and
partial differential equations in one space dimension. The theoretical
and numerical results suggest that for the above class of problems
wavelets provide a robust and accurate alternative to more traditional
methods such as finite differences and finite elements." }
@techreport{glowinski-pan-etal:1993,
Author = "Glowinski, Roland and T. W. Pan and Raymond O. Wells, Jr. and
Xiaodong Zhou",
Title = "Wavelet and finite element solutions for the Neumann problem
using fictitious domains",
Number = "TR92-01",
Year = "1993",
Month = "aug",
Institution = "Computational Math. Lab., Rice University, Houston, TX 77251-1892",
URL = "ftp://cml.rice.edu/pub/reports/9201.ps.Z",
Size = "385,687",
Pages = "36",
Keyword = "wavelets, finite elements",
Abstract = "The boundary value problem is formulated for an open domain
with a rectifiable boundary of any shape which is embedded in a larger
and simpler domain (usually rectilinear in shape). The elliptic boundary
value problem in the original domain is reformulated in a weak form
as an integral equation in the larger domain, which involves introducing
a regularization (or penalty) parameter. Solutions depending on this
parameter converge to solutions of the original equation as the parameter
converges to zero. Both wavelet and finite element Galerkin methods are
used for numerical approximations in the larger domain for fixed and small
values of the parameter, in which fast periodic solvers can be implemented
due to its rectinlinearity." }
@techreport{glowinski-rieder-etal:1993,
Author = "Glowinski, Roland and Andreas Rieder and Raymond O. Wells, Jr. and
Xiaodong Zhou",
Title = "A wavelet multilevel method for Dirichlet boundary value problems
in general domains",
Year = "1993",
Month = "sep",
Number = "9306",
Institution = "Computational Math. Lab., Rice University, Houston, TX 77251-1892",
URL = "ftp://cml.rice.edu/pub/reports/9306.ps.Z",
Size = "144,071",
Pages = "37",
Keyword = "wavelets",
Abstract = "A multilevel method for the efficient solution of the linear
system arising from a Wavelet-Galerkin discretization of a Dirichlet
boundary value problem via a penalty/fictitious domain formulation
is presented. The presence of the penalty term requires a modified
coarse grid correction process to guarantee a convergence rate which
is independent of the discretization step size. Numerical experiments
confirm the result." }
@phdthesis{goldburg:1993,
Author = "Goldburg, Marc",
Title = "Applications of wavelets to quantization and random process
representations",
Year = "1993",
Institution = "Dept. of Elect. Eng., Stanford Univ.",
URL = "ftp://rascals.stanford.edu:/pub/marcg/mgThesis2side.ps.Z",
Size = "1,099,639 bytes",
Pages = "164",
Abstract = "This thesis examines the utility of the wavelet transform
for three different signal processing applications: the representation
of continuously indexed random processes; transform vector quantization
systems; and partial representations and subband coding of discretely
indexed random processes." }
@manual{gollmer:1992,
Author = "Gollmer, Steven",
Title = "DAUBWAVE.DOC",
Year = "1992",
Month = "oct",
URL = "ftp://freehep.scri.fsu.edu:/freehep/lattice_field_theory/daubwave/daubwave.tar",
Psize = "71,680 bytes",
File = "daubwave.doc",
Size = "34,803",
Pages = "15",
Keyword = "wavelets",
Abstract = "The purpose of this program is to perform wavelet based operations
on a data set. It should be useful in learning orthogonal wavelet
analysis as well as data analysis using orthogonal wavelets. This program
uses orthogonal wavelet analysis based on Daubechies' derived
coefficients. This manual details how to perform wavelet transforms
and inverse transforms using the program as well as how to use band pass,
low pass, high pass, and notch filters." }
@article{gollmer-harshvardhan-etal:1995,
Author = "Gollmer, S. and Harshvardhan and R. F. Cahalan and J. B.
Snider",
Title = "Windowed and wavelet analysis of marine stratocumulus
cloud inhomogeneity",
Journal = "J. Atmos. Sci.",
Volume = "52",
Year = "1995",
Pages = "3013--3030" }
@phdthesis{gopinath:1993,
Author = "Gopinath, Ramesh A.",
Title = "Wavelets and filter banks - New results and applications",
Year = "1993",
Institution = "Dept. of Elec. and Comp. Eng., Rice Univ., Houston, TX 77251",
URL = "ftp://cml.rice.edu:/pub/ramesh/papers/phd.ps.Z",
Size = "1,340,089 bytes",
Pages = "270",
Abstract = "Wavelet transforms provide a new technique for time--scale
analysis of non--stationary signals. Wavelet analysis uses orthonormal
bases in which computations can be done efficiently with multirate
systems known as filter banks. This thesis develops a comprehensive
set of tools for multidimensional multirate signal analysis and uses
them to investigate two multirate systems: filter banks and
transmultiplexers. Also described are the design of optimal wavelets
for signal representation and the wavelet sampling theorem. Application
of wavelets in signal interpolation and in the approximation of linear--
translation invariant operators is investigated." }
@techreport{gopinath-burrus:1991a,
Author = "Gopinath, R. A. and C. S. Burrus",
Title = "Wavelet-based lowpass/bandpass interpolation",
Year = "1991",
Number = "TR91-06",
Institution = "Computational Math. Lab., Rice University, Houston,
TX 77251-1892",
URL = "ftp://cml.rice.edu/pub/reports/9106.ps.Z",
Size = "92,999",
Pages = "?",
Abstract = "?" }
@techreport{gopinath-burrus:1991b,
Author = "Gopinath, R. A. and C. S. Burrus",
Title = "On the correlation structure of multiplicity M scaling functions
and wavelets",
Year = "1991",
Number = "TR91-19",
Institution = "Computational Math. Lab., Rice University, Houston,
TX 77251-1892",
URL = "ftp://cml.rice.edu/pub/reports/9119.ps.Z",
Size = "57,763",
Pages = "?",
Abstract = "?" }
@techreport{gopinath-burrus:1991c,
Author = "Gopinath, Ramesh A. and C. S. Burrus",
Title = "Wavelets and filter banks",
Year = "1991",
Number = "TR91-20",
Institution = "Dept. of Elec. and Comp. Eng., Rice Univ., Houston, TX 77251",
URL = "ftp://cml.rice.edu:/pub/reports/9120.ps.Z",
Size = "210,708 bytes",
Pages = "48",
Abstract = "Wavelet and short-time Fourier analysis is introduced in the
context of frequency decompositions. Wavelet type frequency
decompositions are associated with filter banks, and using this
fact, filter bank theory is used to construct multiplicity M wavelet
frames and tight frames. Efficient computational structures for both
filter banks and wavelets are discussed." }
@techreport{gopinath-burrus:1993,
Author = "Gopinath, R. A. and C. S. Burris",
Title = "A tutorial overview of filter banks, wavelets and
interrelations",
Year = "1993",
Number = "TR93-01",
Institution = "Dept. of Elec. and Comp. Eng., Rice Univ., Houston, TX 77251",
URL = "ftp://cml.rice.edu/pub/reports/9301.ps.Z",
Size = "65,365",
Pages = "4",
Keyword = "wavelets, filter banks",
Abstract = "This reviews the theoretical and practical correspondences
between wavelets and filter banks." }
@article{goubet:1992,
Author = "Goubet, Olivier",
Title = "Construction of approximate inertial manifolds using wavelets",
Journal = "SIAM J. Math. Anal.",
Volume = "23",
Year = "1992",
Pages = "1455--1481",
Abstract = "Approximate inertial manifolds are constructed for a class of
dissipative evolution equations. The innovation is that these manifolds
are defined as graphs on orthonormal wavelet bases." }
@inproceedings{grossman-kronland-martinet:1989,
Author = "Grossmann, A. and R. Kronland-Martinet and J. Morlet",
Title = "Reading and understanding continuous wavelet transforms",
Editor = "Combes, J. M. and A. Grossman and Ph. Tchamitchian",
Title = "Wavelets: Time-Frequency Methods and Phase Space",
Publisher = "Springer-Verlag",
Year = "1989",
Pages = "2--20",
Keyword = "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." }
%HHHH
@unpublished{harrod-nagy-etal:1994,
Author = "Harrod, William J. and James G. Nagy and Robert J. Plemmons",
Title = "Image restoration using fast Fourier and wavelet transforms",
Year = "1994",
Institution = "Cray Res., Inc., Eagan, MN 55121",
URL = "ftp://deacon.mathscs.wfu.edu/pub/plemmons/fftrest.ps.Z",
Size = "359,959",
Pages = "16",
Keyword = "wavelets, image processing, FFT",
Abstract = "Image restoration can be modeled as a discrte, ill-posed,
2D inverse problem which can be solved by a preconditioned conjugate
gradient least squares algorithm. The preconditioning is usually
accomplished via FFT techniques, but for some situations this is
not viable. The possible use of wavelet transform based conjugate
gradient iterative methods of solution are thus explored." }
@inproceedings{haynes-norton:1993,
Author = "Haynes, P. H. and W. A. Norton",
Title = "Quantification of scale cascades in the stratosphere using
wavelet transforms",
Booktitle = "Wavelets, Fractals, and Fourier Transforms",
Editor = "Farge, M. and J. C. R. Hunt and J. C. Vassilicos",
Publisher = "Clarendon Press",
Year = "1993",
Pages = "229--234",
Keyword = "wavelets, image analysis",
Abstract = "The wavelet transform is applied to analyse stirring in the
atmosphere. This reveals that small scale filamentary structure found
in mid-latitudes does not occur inside the polar vortex." }
@article{healy-weaver:1992,
Author = "Healy, D. M. and J. B. Weaver",
Title = "Two applications of wavelet transforms in magnetic resonance
imaging",
Journal = "IEEE Trans. Inform. Theory",
Volume = "38",
Year = "1992",
Pages = "840--862" }
@inproceedings{heil:1992,
Author = "Heil, Christopher",
Email = "heil@math.mit.edu",
Title = "Methods of solving dilation equations",
Booktitle = "Probabilistic and Stochastic Methods in Analysis with
Applications",
Editor = "J. S. Byrnes et al.",
Publisher = "Kluwer Academic Pub.",
Series = "NATO Adv. Sci. Inst. Ser. C: Math. Phys. Sci.",
Number = "372",
Year = "1992",
Pages = "161--200",
URL = "ftp://131.130.22.36/tex/HEIL/italy91.ps.Z",
Size = "166,232",
Keyword = "wavelets, dilation equations",
Abstract = "This paper discusses solving a general dilation equation to
find a scaling function and determining when such a scaling function
will generate a multiresolution analysis. Two methods for solving
dilation equations are presented, one involving the use of the Fourier
transform and one operating in the time domain using linear algebra.
This paper is also available via anonymous ftp." }
@incollection{heil-colella:1993,
Author = "Heil, Christopher and David Colella",
Email = "heil@math.mit.edu",
Title = "Dilation equations and the smoothness of compactly supported
wavelets",
Booktitle = "Wavelets: Mathematics and Applications",
Editor = "J. Benedetto and M. Frazier",
Publisher = "CRC Press, Boca Raton, FL",
Year = "1993",
Pages = "161--200",
URL = "ftp://131.130.22.36/tex/HEIL/crc.ps.Z",
Size = "212,761",
Keyword = "wavelets, dilation equations",
Abstract = "This discusses the construction of compactly supported wavelets
with specified amounts of smoothness, which reduces to the construction
of scaling functions, i.e. solutions of dilation equations. This article
characterizes all smooth, compactly supported scaling functions in terms
of a joint spectral radius of two matrices constructed from the
coefficients of the dilation equation. Numerous examples are provided.
This paper is also available via anonymous ftp." }
@article{heil-walnut:1989,
Author = "Heil, C. E. and D. F. Walnut",
Email = "heil@math.mit.edu",
Title = "Continuous and discrete wavelet transforms",
Journal = "SIAM Review",
Volume = "31",
Year = "1989",
Pages = "628--666",
URL = "ftp://131.130.22.36/tex/HEIL/siam.ps.Z",
Size = "182,588",
Keyword = "wavelets",
Abstract = "This is an expository survey of results on integral
representations and discrete sum expansions of functions in terms
of coherent states. Two types of coherent states are considered:
Weyl-Heisenberg coherent states, which arise from translations and
modulations of a single function, and affine coherent states, called
``wavelets'', which arise as translations and dilations of a single
function. This paper is also available via anonymous ftp." }
@article{herley-vetterli:1994,
Author = "Herley, Cormac and Martin Vetterli",
Title = "Orthogonal time-varying filter banks and wavelet packets",
Journal = "IEEE Trans. Sig. Proc.",
Volume = "42",
Year = "1994",
Pages = "2650--2663",
Abstract = "The construction of orthogonal time-varying filter
banks is considered. A set of orthogonal boundary filters is
constructed that allows the filter bank to be applied to one-sided
or finite-length signals without redundancy or distortion." }
@incollection{hertaux-planchon-etal:1994,
Author = "Hertaux, F. and F. Planchon and M. V. Wickerhauser",
Title = "Scale decomposition in Burgers' equation",
Booktitle = "Wavelets: Mathematics and Applications",
Editor = "?",
Publisher = "CRC Press",
Year = "1994",
Pages = "505--523" }
@article{hlawatsch-boudreax-bartels:1992,
Author = "Hlawatsch, F. and G. F. Boudreaux-Bartels",
Title = "Linear and quadratic time-frequency signals representations",
Journal = "IEEE Signal Processing Magazine",
Volume = "?",
Year = "1992",
Month = "apr",
Pages = "21--67",
Keyword = "time-frequency signal representations, wavelets, short-time
Fourier transform, Wigner distribution, ambiguity function",
Abstract = "This is a tutorial reviewing both linear and quadratic
representations of time-frequency signals. The linear representations
discussed are the short-time Fourier transform and the wavelet transform.
The section on quadratic representations concentrates on the Wigner
distribution, the ambiguity function, smoothed version of the Wigner
distribution, and various classes of quadratic time-frequency
representations." }
@article{hlawatsch-kozek:1994,
Author = "Hlawatsch, Franz and Werner Kozek",
Title = "Time-frequency projection filters and time-frequency signal
expansions",
Journal = "IEEE Trans. Sig. Proc.",
Volume = "42",
Year = "1994",
Pages = "3321--3334" }
@inproceedings{hunt-kevlahan-etal:1993,
Author = "Hunt, J.C.R. and N.K.-R. Kevlahan and J. C. Vassilicos
and M. Farge",
Title = "Wavelets, fractals and Fourier transforms: Detection and
analysis of structure",
Booktitle = "Wavelets, Fractals, and Fourier Transforms",
Editor = "Farge, M. and J. C. R. Hunt and J. C. Vassilicos",
Publisher = "Clarendon Press",
Year = "1993",
Pages = "1--38",
Keyword = "wavelets, fractals, Fourier transforms",
Abstract = "An introduction to some of the underlying ideas behind the
different techniques of describing complete signals in terms of
wavelets and Fourier transforms or only certain of their properties
using fractals." }
@techreport{hwang:1993,
Author = "Hwang, Wen-Liang",
Title = "Singularity detection, noise reduction and multifractal
characterization using wavelets",
Year = "1993",
Institution = "Dept. of Comp. Sci., New York Univ.",
URL = "ftp://cs.nyu.edu:/pub/wave/software/wave1.tar.Z",
Psize = "3,462,116 bytes",
File = "(see comments)",
Size = "(see comments)",
Pages = "109",
Keyword = "wavelets, fractals, noise reduction",
Abstract = "The document is contained in parts in 4 directories within
the package and must be processed using LaTeX and dvips. The final
PostScript source code file is huge." }
%IIII %JJJJ
@techreport{jameson:93a,
Author = "Jameson, Leland",
Title = "On the spline-based wavelet differentiation matrix",
Year = "1993",
Number = "93-80",
Institution = "Inst. for Comp. Appl. in Sci. and Eng., NASA Langley
Res. Cent., Hampton, VA 23681",
URL = "ftp://ftp.icase.edu/pub/techreports/93/93-80.ps.Z",
Size = "83,531",
Pages = "35",
Abstract = "The differentiation matrix for a spline-based wavelet basis
will be constructed. An nth order spline basis will be proven to
be accurate of order 2n+2 when periodic boundary conditions are
assumed. This accuracy is lost with other boundary conditions.
It is shown that spline-based bases generate a class of compact
finite-difference schemes." }
@techreport{jameson:93b,
Author = "Jameson, Leland",
Title = "On the differentiation matrix for Daubechies-based wavelets
on an interval",
Year = "1993",
Number = "93-94",
Institution = "Inst. for Comp. Appl. in Sci. and Eng., NASA Langley
Res. Cent., Hampton, VA 23681",
URL = "ftp://ftp.icase.edu/pub/techreports/93/93-94.ps.Z",
Size = "106,039",
Pages = "34",
Abstract = "The differentiation matrix for a Daubechies-based wavelet
basis defined on an interval will be constructed. The differentiation
matrix based on the currently available boundary constructions does
not maintain the superconvergence encountered under periodic
boundary conditions." }
@techreport{jameson:93c,
Author = "Jameson, Leland",
Title = "On the Daubechies-based wavelet differentiation matrix",
Year = "1993",
Number = "93-95",
Institution = "Inst. for Comp. Appl. in Sci. and Eng., NASA Langley
Res. Cent., Hampton, VA 23681",
URL = "ftp://ftp.icase.edu/pub/techreports/93/93-95.ps.Z",
Size = "116,409",
Pages = "51",
Abstract = "The differentiation matrix for a Daubechies-based wavelet
basis will be constructed and superconvergence will be proven for
periodic boundary conditions. It is illustrated that Daubechies-
based wavelet methods are equivalent to finite difference methods
with grid refinement in regions of the domain where small-scale
structure is present." }
@techreport{jameson:94,
Author = "Jameson, Leland",
Title = "On the wavelet optimized finite difference method",
Year = "1994",
Number = "94-09",
Institution = "Inst. for Comp. Appl. in Sci. and Eng., NASA Langley
Res. Cent., Hampton, VA 23681",
URL = "ftp://ftp.icase.edu/pub/techreports/94/94-09.ps.Z",
Size = "674,125",
Pages = "45",
Abstract = "This introduces a wavelet-optimized finite difference method
which is equivalent to a wavelet method in its multiresolution approach
but which does not suffer from difficulties with nonlinear terms and
boundary conditions, since all calculations are done in physical space.
With this method an arbitrarily good approximation to a conservative
difference method for solving nonlinear conservation laws can be
obtained." }
@techreport{jawerth-sweldens:1993a,
Author = "Jawerth, Bjorn and Wim Sweldens",
Title = "Wavelet multiresolution analyses adapted for the fast solution
of boundary value ordinary differential equations",
Year = "1993",
Institution = "University of South Carolina",
URL = "ftp://casper.cs.yale.edu:mgnet/copper93/jawerth-sweldens.ps",
Size = "154,619 bytes",
Pages = "15",
Abstract = "Ideas on how to use wavelets in the solution of boundary value
ODEs. Rather than using classical wavelets, they are adapted so that
they become (bi)orthogonal with respect to the inner product defined by
the operator. The stiffness matrix in a Galerkin method then becomes
diagonal and can thus be trivially inverted. One can construct an
O(N) algorithm for various constant and variable coefficient operators." }
@techreport{jawerth-sweldens:1993b,
Author = "Jawerth, Bjorn and Wim Sweldens",
Title = "An overview of wavelet based multiresolution analyses",
Year = "Feb. 8, 1993",
Institution = "University of South Carolina",
URL = "ftp://maxwell.math.scarolina.edu:/pub/wavelet/papers/varia/sirev-36-3.tex",
Size = "142,288 bytes",
Pages = "39",
Abstract = "An overview of some wavelet based multiresolution analyses
is given. First, the continuous wavelet transform in its simplest
form is discussed, then the definition of multiresolution analysis is
given and it is shown how wavelets fit into it. Also discussed are
the fast wavelet transform, wavelets on closed sets, multidimensional
wavelets, and wavelet packets, and several examples of wavelet families
are given and compared." }
@article{joly-maday-etal:1994,
Author = "Joly, P. and Y. Maday and V. Perrier",
Title = "Towards a method for solving partial differential equations
by using wavelet packet bases",
Journal = "Computer Methods in Applied Mechanics and Engineering",
Volume = "116",
Year = "1994",
Pages = "301--307" }
@inproceedings{jones-earwicker-etal:1993,
Author = "Jones, J.G. and P.G. Earwicker and G.W. Foster",
Title = "Multiple-scale correlation detection, wavelet transforms and
multifractal turbulence",
Booktitle = "Wavelets, Fractals, and Fourier Transforms",
Editor = "Farge, M. and J. C. R. Hunt and J. C. Vassilicos",
Publisher = "Clarendon Press",
Year = "1993",
Pages = "235--250",
Keyword = "wavelets, turbulence",
Abstract = "This first describes a re-interpretation of the equation for
the wavelet transform in terms of a process of discrete feature
extraction via correlation detection. Then features are extracted
using this method from measured samples of atmospheric turbulence
and are subjected to statistical analysis. Basis indices which
characterize the fractal structure of the turbulence are derived and
the multifractal nature of the turbulence confirmed." }
%KKKK
@unpublished{kautsky:1994,
Author = "Kautsky, Jaroslav",
Title = "An algebraic construction of discrete wavelet transforms",
Year = "1994",
Institution = "School of Information Sci. and Tech., Flinders Univ.,
GPO Box 2100, Adelaide, SA 5001, Australia",
URL = "ftp://ftp.cs.flinders.edu.au/pub/wavelets/jk1.ps",
Size = "204,768",
Pages = "18",
Keyword = "wavelets",
Abstract = "Discrete wavelets are viewed as linear algebraic transforms
given by banded orthogonal matrices which can be built up from small matrix
blocks satisfying certain conditions. A generalization of the finite
support Daubechies wavelets is discussed and some special cases promising
more rpaid signal reduction are derived." }
@unpublished{kautsky-turcajova:1994a,
Author = "Kautsky, Jaroslav and Radka Turcajov{\'a}",
Title = "Discrete biorthogonal wavelet transforms as block circulant
matrices",
Year = "1994",
Institution = "School of Information Sci. and Tech., Flinders Univ.,
GPO Box 2100, Adelaide, SA 5001, Australia",
URL = "ftp://ftp.cs.flinders.edu.au/pub/wavelets/bio1.ps",
Size = "158,125",
Pages = "12",
Keyword = "wavelets",
Abstract = "A complete characterization of banded block circulant matrices
with banded inverse is derived by factorizations similar to those used
for orthogonal matrices of this kind. Matrices of this type appear in
the description of the action of perfect reconstruction filter banks as
well as biorthogonal higher multiplicity wavelet transforms." }
@unpublished{kautsky-turcajova:1994b,
Author = "Kautsky, Jaroslav and Radka Turcajov{\'a}",
Title = "Pollen product factorization and construction of higher
multiplicity wavelets",
Year = "1994",
Institution = "School of Information Sci. and Tech., Flinders Univ.,
GPO Box 2100, Adelaide, SA 5001, Australia",
URL = "ftp://ftp.cs.flinders.edu.au/pub/wavelets/jkrt2.ps",
Size = "164,210",
Pages = "12",
Keyword = "wavelets",
Abstract = "This describes a simple, explicit and numerically reliable
algorithm for construction of regular higher multiplicity wavelets.
The existence and uniqueness of the factorization of wavelet matrices
with respect to the Pollen product is also resolved." }
@phdthesis{kolaczyk:1994,
Author = "Kolaczyk, Eric D.",
Title = "Wavelet methods for the inversion of certain homogeneous
linear operators in the presence of noisy data",
Year = "1994",
Month = "oct",
Institution = "Stanford Univ.",
URL = "ftp://galton.uchicago.edu/pub/kolaczyk/Thesis/KolaczykThesis_Text.ps.Z",
Size = "433,249",
Pages = "152",
Keyword = "wavelets, inverse methods",
Abstract = "This explores the use of wavelets in certain linear inverse
problems with discrete, noisy data, i.e. ill-posed problems where small
changes in the data may lead to large changes in the recovered field.
The theoretical framework is that of wavelet-vaguelette decomposition
(WVD), where wavelets and vaguelettes (almost wavelets) are used to
decompose the operator. The primary motivation for this work is that
of attacking the problem of reconstructing images from tomographic
data using wavelets. Note: In addition to the text, the site also
contains 10 PostScript figures that were separated from the text." }
@book{koornwinder:1993,
Editor = "Koornwinder, Tom H.",
Title = "Wavelets: An Elementary Treatment of Theory and Applications",
Publisher = "World Scientific",
Year = "1993",
Pages = "225",
LOC = "QA 403.3 W385 1993",
ISBN = "981-02-1388-3",
Note = "
\begin{enumerate}
\item Wavelets: first steps - N. M. Temme
\item Wavelets: Mathematical preliminaries - P. W. Hemker,
T. H. Koornwinder, N. M. Temme
\item The continuous wavelet transform - T. H. Koornwinder
\item Discrete wavelets and multiresolution analysis - H. J. A. M. Heijmans
\item Image compression using wavelets - P. Nacken
\item Computing with Daubechies wavelets - A. B. O. Daalhuis
\item Wavelet bases adapted to inhomogeneous cases - P. H. Hemker and
F. Plantevin
\item Conjugate gradient filters for multiresolution analysis and
synthesis - E. H. Dooijes
\item Calculation of the wavelet decomposition using quadrature
formulae - W. Sweldens and R. Piessens
\item Fast wavelet transforms and Calderon-Zygmund operators -
T. H. Koornwinder
\item The finite wavelet transform with an application to seismic
processing - J. A. H. Alkemade
\item Wavelets understand fractals - M. Hazewinkel
\end{enumerate}" }
@techreport{kreinovich-sirisaengtaksin-etal:1992,
Author = "Kreinovich, Vladik and Ongard Sirisaengtaksin and Sergio Cabrera",
Email = "vladik@cs.ep.utexas.edu",
Title = "Wavelet neural networks are optimal approximators for functions
of one variable",
Year = "1992",
Institution = "Dept. of Comp. Sci., Univ. of Texas at El Paso, El Paso, TX 79968",
URL = "ftp://cs.ep.utexas.edu:/pub/reports/tr92-29.tex",
Size = "90,812 bytes",
Pages = "33",
Keyword = "neural networks, wavelets",
Abstract = "It is shown that for some special neurons, neural networks
are optimal approximators for functions of one variable in the sense
that they require the smallest possible number of bits that must be
stored to reconstruct a function with a given precision." }
@article{kronland-martinet-morlet-etal:1987,
Author = "Kronland-Martinet, R. and J. Morlet and A. Grossmann",
Title = "Analysis of sound patterns through wavelet transform",
Journal = "Int. J. Pattern Recognition and Artif. Intell.",
Volume = "?",
Year = "1987",
Pages = "273--302" }
@article{kumar-foufoula-georgiou:1993a,
Author = "Kumar, Praveau and Efi Foufoula--Georgiou",
Title = "A new look at rainfall fluctuations and scaling properties of
spatial rainfall using orthogonal wavelets",
Journal = "J. Appl. Meteorol.",
Volume = "32",
Year = "1993",
Pages = "209--222" }
%% 1/26/96
@article{kumar-foufoula-georgiou:1993b,
Author = "Kumar, P. and E. Foufoula-Georgiou",
Title = "A multicomponent decomposition of spatial rainfall fields.
I. Segregation of large and small-scale features using wavelet
transforms",
Journal = "Water Resources Res.",
Volume = "29",
Year = "1993",
Pages = "2515--2532" }
@unpublished{kwong-tang:1994a,
Author = "Kwong, Man Kam and P. T. Peter Tang",
Email = "[kwong,tang]@mcs.anl.gov",
Title = "W-matrices, nonorthogonal multiresolution analysis, and
finite signals of arbitrary length",
Year = "1994",
Institution = "Math. and Comp. Sci. Div., Argonne National Lab.,
Argonne, IL 60439-4844",
URL = "ftp://info.mcs.anl.gov/pub/W-transform/wtransf1.ps.Z",
Size = "590,729",
Pages = "24",
Keyword = "wavelets",
Abstract = "This proposes a new class of discrete transforms that
includes the classical Haar and Daubechies wavelet transforms.
The new class treats the endpoints of a signal differently than
conventional techniques and allows efficient handling of signals
of any length." }
@unpublished{kwong-tang:1994b,
Author = "Kwong, Man Kam and P. T. Peter Tang",
Email = "[kwong,tang]@mcs.anl.gov",
Title = "MATLAB implementation of W-matrix multiresolution analysis",
Year = "1994",
Institution = "Math. and Comp. Sci. Div., Argonne National Lab.,
Argonne, IL 60439-4844",
URL = "ftp://info.mcs.anl.gov/pub/W-transform/wtransf2.ps.Z",
Size = "107,235",
Pages = "39",
Keyword = "wavelets",
Abstract = "Presents a MATLAB toolbox for multiresolution analysis
based on the W-transform. The toolbox contains basic commands to
perform forward and inverse transforms on finite 1D and 2D signals
of arbitrary length, to perform multiresolution analysis of
given signals to a specified number of levels, to visualize the
wavelet decomposition, and to do compression. Examples are
discussed." }
%LLLL
@techreport{laine-schuler:1993,
Author = "Laine, Andrew and Jian Fan",
Title = "An adaptive approach for texture segmentation by multi-channel
wavelet frames",
Year = "1993",
Number = "25",
Institution = "Univ. of Florida",
URL = "ftp://ftp.cis.ufl.edu/cis/tech-reports/tr93/tr93-025.ps.Z",
Size = "1,310,748",
Pages = "?",
Keyword = "wavelets",
Abstract = "This introduces an adaptive approach for texture feature
extraction based on multi-channel wavelet frames and two-dimensional
envelope detection. Representations obtained from both standard wavelets
and wavelet packets are evaluated for reliable texture segmentation.
Algorithms for envelope detection based on edge detection and the
Hilbert transform are presented. Analytic filters are selected
for each technique based on performance evaluation. A K-means clustering
algorithm was used to test the performance of each representation feature
set. Experimental results for both natural textures and synthetic
textures are shown." }
@unpublished{lakey:1993,
Author = "LaKey, Joseph D.",,
Title = "Lecture notes, Math 391 C, Fall 1993",
Year = "1993",
Institution = "University of Texas",
URL = "ftp://math.utexas.edu:pub/papers/laKey/m391c/m391c.dvi",
Size = "656,740 bytes",
Pages = "178",
Note = "The last time I checked (Jan. 1995) this was longer longer
available at the given address. You might want to check with the
author if you really want this.",
Abstract = "These are notes for a course on wavelets given by Dr. Joseph
LaKey at the University of Texas during Fall 1993. In addition to the
dvi file, there are 19 additional postscript figure files at the same
site. The dvi file is processed using the dvips utility to create a
postscript file containing both text and figures." }
%% 1/26/96
@article{lau-weng:1995,
Author = "Lau, K.-M. and Hengyi Weng",
Title = "Climate signal detection using wavelet transform: How to
make a time series sing",
Journal = "BAMS",
Volume = "76",
Year = "1995",
Pages = "2391--2402",
Abstract = "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 (whence the title). Using an analogy between WT representation
of a time sereis 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 O18 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 (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." }
@techreport{learned-willsky:1993,
Author = "Learned, Rachel E. and Alan S. Willsky",
Email = "learned@mit.edu",
Title = "Wavelet packet approach to transient signal classification",
Year = "1993",
Institution = "Dept. of Elect. Eng. and Comp. Sci. and the Lab. for Information
and Decision Systems, Room 35-439, 77 Massachusetts Ave., Cambridge,
MA 02139",
URL = "ftp://lids.mit.edu:/pub/ssg/papers/LIDS-P-2199.PS.gz",
Size = "329,878 bytes",
Pages = "55",
Keyword = "wavelets",
Abstract = "This describes an investigation to explore the feasibility
of applying the wavelet packet transform to automatic detection and
classification of a specific set of transient signals in background
noise. In particular, a noncoherent wavelet-packet-based algorithm
specific to the detection and classification of underwater acoustic
signals generated by snapping shrimp and sperm whale clicks is
proposed." }
@inproceedings{lemarie-rieusset:1993,
Author = "Lemarie-Rieusset, Pierre Gilles",
Title = "Projection operators in multiresolution analysis",
Booktitle = "Different Perspectives on Wavelets",
Editor = "Ingrid Daubechies",
Publisher = "American Math. Soc., Providence, RI",
Series = "Proceedings of Symposia in Applied Mathematics",
Volume = "47",
Year = "1993",
Pages = "59--76",
Note = "From an American Math. Soc. short course, Jan. 11--12, 1993, San
Antonio, TX",
Abstract = "Describes various ways to deal with a bi--orthogonal multiresolution
analysis." }
@article{lewis-knowles:1990,
Author = "Lewis, A. S. and G. Knowles",
Title = "Video compression using 3d wavelet transforms",
Journal = "Electron. Lett.",
Volume = "26",
Year = "1990",
Pages = "396--398" }
@article{liandrat-moret-bailly:1990,
Author = "Liandrat, J. and F. Moret-Bailly",
Title = "The wavelet transform: Some applications to fluid dynamics
and turbulence",
Journal = "Eur. J. Mech., B/Fluids",
Vol = "9",
Year = "1990",
Pages = "1--19",
Keyword = "wavelets, turbulence",
Abstract = "In this paper the basic definitions and the most attractive
properties of the wavelet transform are reviewed and explained using
the classical language of turbulence. It is shown that the wavelet
transform appears to be a natural alternative to the decompositions
commonly used in fluid dynamics and turbulence (i.e. Fourier decomposition).
Some especially interesting properties of the wavelet transform for
interpretation or numerical approximation of turbulence are demonstrated
on experimentally or numerically generated signal examples." }
%% 1/26/96
@incollection{liu:1994,
Author = "Liu, P. C.",
Title = "Wavelet spectrum analysis and ocean waves",
Booktitle = "Wavelets in Geophysics",
Editor = "E. Foufoula and P. Kumar",
Publisher = "Academic Press",
Year = "1994",
Pages = "151--166" }
@phdthesis{luettgen:1993,
Author = "Luettgen, Mark R.",
Title = "Image processing with multiscale stochastic models",
Year = "May 1993",
Institution = "Dept. of Elect. Eng. and Comp. Sci. M.I.T.",
URL = "ftp://lids.mit.edu:pub/ssg/papers/LIDS-TH-2178.PS.z",
Size = "2,085,899 bytes",
Pages = "217",
Abstract = "Image processing algorithms and applications for a particular
class of multiscale models are developed. These algorithms are shown
to be related to wavelets and to be usable in the context of regularizing
ill-posed inverse problems at a significant computational savings. It is
concluded that the multiscale paradigm is a powerful paradigm for image
processing because of the efficient algorithms it admits and the rich
class of phenomena it can be used to describe." }
%MMMM
%% 1/25/96
@article{mak:1995,
Author = "Mak, Mankin",
Title= "Orthogonal wavelet analysis: Interannual variability in the
sea surface temperature",
Journal = "Bull. Amer. Meteorol. Soc.",
Volume = "76",
Year = "1995",
Pages = "2179--2186",
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 Nino (abnormally warm) and La Nina
(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{mallat:1989,
Author = "Mallat, S. G.",
Title = "A theory for multiresolution signal decomposition: The wavelet
representation",
Journal = "IEEE Trans. Pattern Anal. Machine Intell.",
Volume = "11",
Year = "1989",
Pages = "674--693" }
@article{mallat-hwang:1992,
Author = "Mallat, S. and W. L. Hwang",
Title = "Singularity detection and processing with wavelets",
Journal = "IEEE Trans. Info. Theory",
Volume = "38",
Year = "1992",
Pages = "617--643" }
@article{mallat-zhang:1993,
Author = "Mallat, S. and S. Zhang",
Title = "Matching pursuits with time-frequency dictionaries",
Journal = "IEEE Trans. Sig. Proc.",
Volume = "41",
Year = "1993",
Pages = "3397--3415" }
@techreport{mann-haykin:1991,
Author = "Mann, Steve and Simon Haykin",
Title = "The chirplet transform: A new signal analysis technique based
on affine relationships in the time-frequency plane",
Year = "1991",
Institution = "M.I.T., 20 Ames St., Cambridge, MA 02139",
URL = "ftp://media-lab.media.mit.edu:/pub/chirplet/chirplet_papers/assp.ps.Z",
Size = "3,401,739 bytes",
Pages = "46",
Keyword = "chirplets, signal analysis",
Abstract = "A multidimensional space is considered that includes both
the time-frequency and time-scale planes, which encompasses both the
short-time Fourier and wavelet transforms as slices along the
time-frequency and time-scale axes, respectively. Chirplets are
generalized wavelets, related to eachother by two-dimensional affine
coordinate transformations (translations, dilations, rotations, and
shears) in the time-frequency plane, as opposed to wavelets, related
to each other by one-dimensional affine coordinate transformations
in the time-domain only (translations and dilations). Practical
applications of chirplets in such areas as machine vision, image
processing, and radar are discussed." }
@article{mann-haykin:1992,
Author = "Mann, S. and S. Haykin",
Title = "Adaptive ``chirplet'' transform: an adaptive generalization
of the wavelet transform",
Journal = "Optical Eng.",
Volume = "31",
Year = "1992",
Pages = "1243--1256" }
@techreport{mccormick-wells:1991,
Author = "McCormick, Kent and Raymond O. Wells, Jr.",
Title = "Wavelet calculus and finite difference operators",
Year = "1991",
Number = "TR91-02",
Institution = "Computational Math. Lab., Rice University, Houston,
TX 77251-1892",
URL = "ftp://cml.rice.edu/pub/reports/9102.ps.Z",
Size = "85,285",
Pages = "?",
Abstract = "?" }
@article{meneveau:1991,
Author = "Meneveau, Charles",
Title = "Analysis of turbulence in the orthonormal wavelet representation",
Journal = "J. Fluid Mech.",
Volume = "232",
Year = "1991",
Pages = "469--520",
Abstract = "A decomposition of turbulent velocity fields into modes that
exhibit both localization in wavenumber and physical space is performed.
This reviews some basic properties of such a decomposition, the wavelet
transform. The wavelet-transformed Navier-Stokes equations are derived
and the kinetic energy and flux of kinetic energy are studied as
functions of scale and position." }
@inproceedings{meneveau:1993,
Author = "Meneveau, C.",
Title = "Wavelet analysis of turbulence: The mixed energy cascade",
Booktitle = "Wavelets, Fractals, and Fourier Transforms",
Editor = "Farge, M. and J. C. R. Hunt and J. C. Vassilicos",
Publisher = "Clarendon Press",
Year = "1993",
Pages = "251--264",
Keyword = "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." }
@inproceedings{meyer:1989,
Author = "Meyer, Y.
Title = "Orthonormal wavelets",
Editor = "Combes, J. M. and A. Grossman and Ph. Tchamitchian",
Title = "Wavelets: Time-Frequency Methods and Phase Space",
Publisher = "Springer-Verlag",
Year = "1989",
Pages = "21--37",
Keyword = "wavelets",
Abstract = "A survey to help the scientific community to use wavelets as
an alternative to the standard Fourier analysis." }
@inproceedings{meyer:1993,
Author = "Meyer, Yves",
Title = "Wavelets and operators",
Booktitle = "Different Perspectives on Wavelets",
Editor = "Ingrid Daubechies",
Publisher = "American Math. Soc., Providence, RI",
Series = "Proceedings of Symposia in Applied Mathematics",
Volume = "47",
Year = "1993",
Pages = "35--58",
Note = "From an American Math. Soc. short course, Jan. 11--12, 1993, San
Antonio, TX",
Abstract = "Addresses the possibility of using wavelet analysis for
studying operators." }
@article{meyers-obrien:1994,
Author = "Meyers, Steven D. and James J. O'Brien",
Title = "Spatial and temporal 26-day SST variations in the equatorial
Indian Ocean using wavelet analysis",
Journal = GRL,
Volume = "21",
Year = "1994",
Pages = "777--780",
Keyword = "wavelets, Indian Ocean, SST",
Abstract = "Two-year sea-surface temperature time series of satellite
data at two sites in the equatorial Indian Ocean are examined for
oscillations with periods 2-70 days using wavelet transforms." }
@article{meyers-kelly-etal:1993,
Author = "Meyers, S. D. and B. G. Kelly and J. J. O'Brien",
Title = "An introduction to wavelet analysis in oceanography and
meteorology: With application to the dispersoion of Yanai waves",
Journal = "Monthly Weather Review",
Volume = "121",
Year = "1993",
Pages = "2858--2866",
Abstract = "Wavelet analysis, an important addition to standard signal
analysis methods, is unlike Fourier analysis in that while the latter
yields an average amplitude and phase for each harmonic, the former
produces an ``instantaneous'' estimate or local value for the amplitude
and phase of each harmonic. This allows detailed study of nonstationary
spatial or time--dependent signal characteristics. The wavelet transform
is discussed, examples are given, and some methods for preprocessing
data for wavelet analysis are compared. Yanai waves are studied using
wavelet analysis."
@techreport{misra-nichols:1993,
Author = "Misra, Manavendra and Terry Nichols",
Email = "mmisra@mines.colorado.edu; tnichols@mines.colorado.edu",
Title = "Computation of 2-D wavelet transforms on the Connection Machine-2",
Year = "1993",
Number = "MCS9317",
Institution = "Dept. of Math. and Comp. Sci., Colorado School of Mines,
Golden, Colorado 80401",
URL = "ftp://ftp.mines.colorado.edu/pub/papers/math_cs_dept/mcs9317.ps.Z",
Size = "135,136",
Pages = "10",
Abstract = "This discusses the parallel implementation of the 2-D
Gabor based wavelet transform on the CM-2 machine." }
@article{morlet-arens-etal:1982,
Author = "Morlet, J. and G. Arens and I. Fourgeau and D. Giard",
Title = "Wave propagation and sampling theory",
Journal = "Geophysics",
Volume = "47",
Year = "1982",
Pages = "203--236" }
@article{moulin:1994,
Author = "Moulin, Pierre",
Title = "Wavelet thresholding techniques for power spectrum estimation",
Journal = "IEEE Trans. Sig. Proc.",
Volume = "42",
Year = "1994",
Pages = "3126--3136",
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.}
@article{muzy-barcy-etal:1991,
Author = "Muzy, J. F. and E. Barcy and A. Arneodo",
Title = "Wavelets and multifractal formalism for singular signals:
applications to turbulence data",
Journal = "Phys. Rev. Lett.",
Volume = "67",
Year = "1991",
Pages = "3515--3518" }
%NNNN
@techreport{nason:1994,
Author = "Nason, G. P.",
Title = "Wavelet regression by cross-validation",
Year = "Mar. 24, 1994",
Institution = "Dept. of Math., Univ. of Bristol, University Walk,
Bristol, BS8 1TW, U.K.",
URL = "ftp://playfair.stanford.edu:/pub/reports/wvcx.ps.gz",
Size = "312,417 bytes",
Pages = "45",
Keyword = "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{nason-silverman:1994,
Author = "Nason, G. P. and B. W. Silverman",
Title = "The discrete wavelet transform in S",
Journal = "J. of Computational and Graphical Statistics",
Volume = "3",
Year = "1994",
Pages = "163--191" }
@unpublished{nason-silverman:1995,
Author = "Nason, G. P. and B. W. Silverman",
Title = "The stationary wavelet transform and some statistical
applications",
Institution = "Dept. of Math., Univ. of Bristol, Bristol BS8 1TW, UK",
Year = "1995",
URL = "ftp://poisson.stats.bris.ac.uk/pub/reports/Silverman/swtsa.ps.gz",
Size = "191,317",
Pages = "19",
Abstract = "The basics of the discrete wavelet transform are reviewed.
A stationary wavelet transform, where the coefficient sequences are
not decimated at each stage, is described. Two different approaches
to the construction of an inverse of the stationary wavelet transform
are set out. The application of the stationary wavelet transform
as an exploratory statistical method is discussed, together with
its potential use in nonparametric regression. The technique is
illustrate by application to data sets from astronomy and
veterinary anatomy." }
@book{newland:1993a,
Author = "Newland, D. E.",
Title = "An Introduction to Random Vibrations, Spectral \&
Wavelet Analysis (Third Edition)",
Publisher = "Longman Scientific \& Technical",
Year = "1993",
Pages = "477",
ISBN = "0-470-22153-4",
Note = "
\begin{enumerate}
\item Introduction to probability distributions and averages
\begin{enumerate}
\item Probability density function
\item Gaussian distribution
\item Calculation of averages
\item Probability distribution function
\end{enumerate}
\item Joint probability distributions, ensemble averages
\begin{enumerate}
\item Second-order probability functions
\item Second-order averages
\item Conditional probability
\item Second-order Gaussian distribution
\item Ensemble averaging
\end{enumerate}
\item Correlation
\begin{enumerate}
\item Autocorrelation
\item Cross-correlation
\end{enumerate}
\item Fourier analysis
\begin{enumerate}
\item ourier integral
\item Complex form of the Fourier transform
\end{enumerate}
\item Spectral density
\begin{enumerate}
\item Narrow band and broad band processes
\item Spectral density of a derived process
\item Cross-spectral density
\item Note on the units of spectral density
\end{enumerate}
\item Excitation -- response relations for linear systems
\begin{enumerate}
\item Classical approach
\item Frequency response method
\item Impulse response method
\item Relationship between the frequency response and impulse
response functions
\item Calculation of response to an arbitrary input
\end{enumerate}
\item Transission of random vibration
\begin{enumerate}
\item Mean level
\item Autocorrelation
\item Spectral density
\item Mean square response
\item Cross-correlation
\item Cross-spectral density
\item Probability distributions
\end{enumerate}
\item Statistics of narrow band processes
\begin{enumerate}
\item Crossing analysis
\item Distribution of peaks
\item Frequency of maxima
\end{enumerate}
\item Accuracy of measurements
\begin{enumerate}
\item Analogue spectrum analysis
\item Variance of the measurement
\item Analaysis of finite length records
\item Confidence limits
\end{enumerate}
\item Digital spectral analysis I: Discrete Fourier transforms
\begin{enumerate}
\item Discrete Fourier transforms
\item Fourier transforms of periodic functions
\item Aliasing
\item Calculation of spectral estimates
\end{enumerate}
\item Digital spectral analysis II: Windows and smoothing
\begin{enumerate}
\item Relationship between linear and circular correlation
\item Fourier transform of a train of aperiodic functions
\item Basic lag and spectral windows
\item Smoothing spectral estimates
\item Extending record length by adding zeros
\item Summary
\item Practical considerations
\end{enumerate}
\item The fast Fourier transform
\begin{enumerate}
\item Basic theory
\item Sample calculation
\item Programming flow charts
\item Practical value of FFT
\item Alternative algorithms
\end{enumerate}
\item Pseudo random processes
\begin{enumerate}
\item Random binary process
\item Pseudo random binary signals
\item Random multi-level process
\item Spectrum of a multi-level process
\item Generation of random numbers
\item Synthesis of correlated noise sources
\end{enumerate}
\item Application notes
\begin{enumerate}
\item Response of a resonant mode to broad band excitation
\item Fatigue and failure due to random vibration
\item Excitation by random surface irregularities
\item Simulation of random environments
\item Frequency response function and coherency measurements
\item Local spectral density calculations
\item Weibull distribution of peaks
\end{enumerate}
\item Multi-dimensional spectral analysis
\begin{enumerate}
\item Two-dimensional Fourier series
\item Properties of the two-dimensional DFT
\item Spectral density of a multi-dimensional random process
\item Discrete spectral density and circular correlation
functions for a 2-D random process
\item Two-dimensional windows
\item Two-dimensional smoothing
\item Artificial generation of a 2-D random process
\item Generation of an isotropic surface
\item Cross-spectral density between parallel tracks across
a random surface
\end{enumerate}
\item Response of continuous linear systems to stationary random
excitation
\begin{enumerate}
\item Response to excitation applied at a point
\item Reponse to distributed excitation
\item Normal mode analysis
\item Kinetic energy of a flat plate subjected to
uncorrelated random excitation
\item Single degree-of-freedom analogy
\end{enumerate}
\item Discrete wavelet analysis
\begin{enumerate}
\item Basic ideas
\item Dilation equations
\item Dilation wavelets
\item Properties of the wavelet coefficients
\item Circular wavelet transforms
\item Discrete wavelet transforms
\item Properties of the DWT
\item Mean-square maps
\item Convolution by wavelets
\item Two-dimensional wavelet transforms
\item Harmonic wavelets
\item Discrete harmonic wavelet transform
\item Concluding comments
\end{enumerate}
\end{enumerate}" }
@article{newland:1993b,
Author = "Newland, David E.",
Title = "Harmonic wavelet analysis",
Journal = "Proc. R. Soc. Lond. A",
Volume = "443",
Year = "1993",
Pages = "203--225",
Abstract = "A new harmonic wavelet is suggested whose shape can be expressed
in functional form. Its frequency spectrum is confined exactly to
an octave band so that it is compact in the frequency (rather than in
the x) domain. An efficient implementation of a discrete transform
using this wavelet is based on the 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{newland:1994a,
Author = "Newland, David E.",
Title = "Harmonic and musical wavelets",
Journal = "Proc. R. Soc. Lond. A",
Volume = "444",
Year = "1994",
Pages = "605--620" }
@article{newland:1994b,
Author = "Newland, David E.",
Title = "Some properties of discrete wavelet maps",
Journal = "Probabilisitic Eng. Mech.",
Volume = "9",
Year = "1994",
Pages = "59--69" }
%OOOO
@techreport{odegard-gopinath-etal:1991,
Author = "Odegard, J. E. and R. A. Gopinath and C. S. Burrus",
Title = "Optimal wavelets for signal decomposition and the existence of
scale limited signals",
Year = "1991",
Number = "TR91-07",
Institution = "Computational Math. Lab., Rice University, Houston,
TX 77251-1892",
URL = "ftp://cml.rice.edu/pub/reports/9107.ps.Z",
Size = "55,674",
Pages = "?",
Abstract = "?" }
@phdthesis{ogden:1994,
Author = "Ogden, R. T.",
Title = "Wavelet thresholding in nonparametric regression with change
point application",
Institution = "Texas A\&M University",
Year = "1994" }
@article{onsay-haddow:1994,
Author = "{\"O}nsay, Taner and Alan G. Haddow",
Title = "Wavelet transform analysis of transient wave propagation in
a dispersive medium",
Journal = JASA,
Volume = "95",
Pages = "1441--1449",
Keyword = "wavelets",
Abstract = "The wavelet transform is applied to the analysis of transient
waves propagating in a dispersive medium. The wavelet transform of the
acceleration process of the transient flexural vibrations of an impact
excited uniform beam resulted in a time-scale representation which
provided a clear exposition of the time evolution of the spectral
components during the dispersion process. Based on the examples,
the advantanges and shortcomings of the wavelet transform are
discussed." }
@article{ozaktas-barshan-etal:1994,
Author = "Ozaktas, Haldun M. and Billur Barshan and David Mendlovic and
Levent Onural",
Title = "Convolution, filtering, and multiplexing in fractional Fourier
domains and their relation to chirp and wavelet transforms",
Journal = "J. Opt. Soc. Am. A",
Volume = "11",
Year = "1994",
Pages = "547--559",
Keyword = "Fourier transforms, fractinal Fourier transforms, wavelets,
chirplets",
Abstract = "A concise introduction to the concept of fractional Fourier
transforms is followed by a discussion of their relation to chirp and
wavelet transforms. The notion of fractional Fourier domains is
developed in conjunction with the Wigner distribution of a signal.
Convolution, filtering, and multiplexing of signals in fractional
domains are discussed, revealing that under certain conditions one can
improve on the special cases of these operations in the conventional
space and frequency domains." }
%PPPP %QQQQ
@article{qian-weiss:1993,
Author = "Qian, Sam and John Weiss"
Title = "Wavelets and the numerical solution of partial differential equations"
Journal = "J. Comp. Phys."
Volume = "106"
Year = "1993"
Pages = "155--175"
Note = "A numerical method for the solution of PDEs in nonseparable
domains usings a wavelet-Galerkin solver with a nontrivial adaptation
of the standard capacitance method is presented. The numerical solutions
exhibit spectral convergence at a rate that is independent of the
geometry." }
%RRRR
@inproceedings{rasmussen:1993,
Author = "Rasmussen, H. O.",
Title = "The wavelet Gibbs phenomenon",
Booktitle = "Wavelets, Fractals, and Fourier Transforms",
Editor = "Farge, M. and J. C. R. Hunt and J. C. Vassilicos",
Publisher = "Clarendon Press",
Year = "1993",
Pages = "123--142",
Keyword = "wavelets, Gibbs phenomenon",
Abstract = "This demonstrates the existence of a Gibbs phenomenon for
the continuous wavelet transform. An expression for the value of
the overshoot is derived, and it is shown tha the reconstructed
function may have a number of local extrema that do not disappear as
more small-scale wavelets are included. The wavelet overshoot is
always less than the Fourier overshoot, and it is possible to choose
the analysing wavelet such that there is no overshoot." }
@techreport{restrepo-leaf:1994,
Author = "Restrepo, Juan Mario and Gary K. Leaf",
Title = "Wavelet-Galerkin discretization of hyperbolic equations",
Year = "1994",
Number = "P448",
Institution = "Math. and Comp. Sci. Div., Argonne National Lab.,
Argonne, IL 60439",
URL = "ftp://info.mcs.anl.gov/pub/tech_reports/reports/P448.ps.Z",
Size = "356,406",
Pages = "18",
Keyword = "wavelets, Galerkin method",
Abstract = "The relative merits of the wavelet-Galerkin solution of
hyperbolic partial differential equations, typical of geophysical
problems, are quantitatively and qualitatively compared to
traditional finite difference and Fourier-pseudo-spectral methods.
The wavelet-Galerkin solution presented here is found to be a viable
alternative to the two conventional techniques." }
@techreport{restrepo-leaf-etal:1994,
Author = "Restrepo, Juan Mario and Gary K. Leaf and George
Schlossnagle",
Title = "Periodized Daubechies wavelets",
Year = "1994",
Number = "P423",
Institution = "Math. and Comp. Sci. Div., Argonne National Lab.,
Argonne, IL 60439",
URL = "ftp://info.mcs.anl.gov/pub/tech_reports/reports/P423.ps.Z",
Size = "176,365",
Pages = "33",
Keyword = "wavelets, Dauchechies",
Abstract = "The properties of periodized Daubechies wavelets on
[0,1] are detailed. Numerical examples illustrate the analytical
estimates for convergence and demonstrate by comparison with
Fourier spectral methods the superiority of wavelet projection
methods for approximations." }
@techreport{rieder:1993,
Author = "Rieder, Andreas",
Title = "Semi-algebraic multi-level methods based on wavelet
decompositions I: Application to two-point boundary value problems",
Year = "1993",
Month = "apr",
Number = "9304",
Institution = "Computational Math. Lab., Rice University, Houston, TX 77251-1892",
URL = "ftp://cml.rice.edu:pub/reports/9304.ps.z",
Size = "107,701 bytes",
Pages = "31",
Keyword = "wavelets, boundary value problems",
Abstract = "The goal of this article is to clarify more precisely the
vague but often indicated connection between wavelet and multi-grid
theory. As such, a multi-level method based on a wavelet approximation
of the successive error of a classical iterative solver is presented.
The resulting iteration is a hybrid between a purely algebraic
multi-level technique and the usual multi-grid technique related to a
discretization of an elliptic differential operator. This new approach
has the capacity to solve linear equations arising from the discretization
of integral operators of the first kind by multi-level techniques." }
@techreport{rieder-wells-etal:1993,
Author = "Rieder, Andreas and Raymond O. Wells, Jr. and Xiaodong Zhou",
Title = "A wavelet approach to robust multilevel solvers for anisotropic
elliptic problems",
Year = "1993",
Month = "oct",
Institution = "Computational Math. Lab., Rice University, Houston, TX 77251-1892",
URL = "ftp://cml.rice.edu:pub/reports/9307.ps.Z",
Size = "168,206 bytes",
Pages = "42",
Keyword = "wavelets, elliptic solvers",
Abstract = "A wavelet variation of the frequency decomposition multigrid
(FDMGM) method is presented that allows a deeper analysis of this method.
The orthogonality and multiresolution structure of wavelets yield the
robustness of the additive as well as of the multiplicative version of
the FDMGM relative to any intermediate level. Aspects of the robustness
of the multilevel scheme are discussed and numerical experiments used
to confirm the theoretical results." }
@article{rioul:1992,
Author = "Rioul, Olivier",
Title = "Simply regularity criteria for subdivision schemes",
Journal = "SIAM J. Math. Anal.",
Volume = "23",
Year = "1992",
Pages = "1544--1576",
Abstract = "Convergent subdivision schemes arise in several fields of
applied mathematics (computer-aided geometric design, fractals,
compactly supported wavelets) and signal processing (multiresolution
decomposition, filter banks). In this paper, a polynomial description
is used to study the existence of H\"older regularity of limit functions
of binary subdivision schemes." }
@article{rioul-duhamel:1992,
Author = "Rioul, O[livier] and P. Duhamel",
Title = "Fast algorithms for the discrete and continuous wavelet
transforms",
Journal = "IEEE Trans. Info. Theory",
Volume = "38",
Year = "1992",
Pages = "569--586" }
@article{rioul-vetterli:1991,
Author = "Rioul, O[livier]. and M. Vetterli",
Title = "Wavelets and signal processing",
Journal = "IEEE Signal Processing Magazine",
Year = "1991",
Month = "oct",
Pages = "14--37" }
@book{ruskai-beylkin-etal:1992,
Editor = "Ruskai, Mary Beth and Gregory Beylkin and Ronald Coifman and
Ingrid Daubechies and Stephane Mallat and Yves Meyer and Louise Raphael",
Title = "Wavelets and Their Applications",
Publisher = "Jones and Bartlett Publ.",
Year = "1992",
Pages = "474",
LOC = "QA 403.5 W38 1992",
ISBN = "0-86720-225-4",
Note = "
\begin{enumerate}
\item Introduction
\begin{enumerate}
\item Introduction - M. B. Ruskai
\end{enumerate}
\item Signal analysis
\begin{enumerate}
\item Wavelets and filter banks for discrete-time signal processing -
M. Vetterli
\item Wavelets for quincunx pyramid - J.-C. Feauveau
\item Wavelet transform maxima and multiscale edges - S. Mallat
and S. Zhong
\item Wavelets and digital signal processing - A. Cohen
\item Ridge and skeleton extraction from the wavelet transform -
Ph. Tchamitchian and B. Torresani
\item Wavelet analysis and signal processing - R. R. Coifman,
Y. Meyer, and V. Wickerhauser
\end{enumerate}
\item Numerical analysis
\begin{enumerate}
\item Wavelets in numerical analysis - G. Beylkin, R. R. Coifman and
V. Rokhlin
\item Construction of simple multiscale bases for fast matrix
operations - B. K. Alpert
\item Numerical resolution of nonlinear PDEs using the
wavelet approach - J. Liandrat, V. Perrier and Ph. Tchamitchian
\end{enumerate}
\item Other applications
\begin{enumerate}
\item The optical wavelet transform - A. Arneodo, F. Argoul, E. Freysz,
J. F. Muzy and B. Pouligny
\item The continuous wavelet transform of two-dimensional turbulent
flows - M. Farge
\item Wavelets and quantum mechanics - T. Paul and K. Seip
\item Wavelets: A renormalization group point of view - G. Battle
\end{enumerate}
\item Theoretical developments
\begin{enumerate}
\item Non-orthogonal wavelet and Gabor expansions, and group
representations - H.G. Feichtinger and K. Grochenig
\item Applications of the $\phi$ and wavelet transforms to the
theory of function spaces - M. Frazier and B. Jawerth
\item On cardinal spline-wavelets - C. K. Chui
\item Wavelet bases for L$^2$(R) with rational dilation
factor - P. Auscher
\item Size properties of wavelet packets - R. R. Coifman,
Y. Meyer and V. Wickerhauser
\end{enumerate}
\end{enumerate}" }
%SSSS
@techreport{saito-beylkin:1992,
Author = "Saito, Naoki and Gregory Beylkin",
Title = "Multiresolution representations using the auto-correlation functions
of compactly supported wavelets",
Year = "Jan. 9, 1992",
Institution = "Dept. of Math., Yale Univ., New Haven, CT 06520",
URL = "ftp://amath-ftp.colorado.edu:/pub/wavelets/papers/minframe.ps.Z",
Size = "493,997 bytes",
Pages = "46",
Keyword = "wavelets",
Abstract = "This proposes a hybrid shift-invariant multiresolution
representation which uses dilations and translations of the auto-correlation
functions of compactly supported wavelets." }
@techreport{schlossnagle-restrepo-etal:1993,
Author = "Schlossnagle, George and Juan Mario Restrepo and Gary K. Leaf",
Title = "Periodized wavelets",
Year = "1993",
Number = "ANL9334",
Institution = "Math. and Comp. Sci. Div., Argonne National Lab.,
Argonne, IL 60439",
URL = "ftp://info.mcs.anl.gov/pub/tech_reports/reports/ANL9334.ps.Z",
Size = "112,481",
Pages = "20",
Keyword = "wavelets",
Abstract = "The properties of periodized Daubechies wavelets on
[0,1] are detailed. Numerical examples illustrate the analytical
estimates for convergence and demonstrate by comparison with
Fourier spectral methods the superiority of wavelet projection
methods for approximations." }
@book{schumaker-webb:1994,
Editor = "Schumaker, L. L. and G. Webb",
Title = "Recent Advances in Wavelet Analysis",
Publisher = "Academic Press",
Series = "Wavelet Analysis and Its Applications",
Number = "3",
Year = "1994" }
%% 1/26/96
@article{shen-wang-etal:1994,
Author = "Shen, Z. and W. Wang and L. Mei",
Title = "Finestructure of wind waves analyzed with wavelet transform",
Journal = "JPO",
Volume = "24",
Year = "1994",
Pages = "1085--1094" }
@techreport{shensa:1993,
Author = "Shensa, M. J.",
Email = "shensa@nosc.mil",
Title = "An inverse DWT for nonorthogonal wavelets",
Number = "1621",
Year = "1993",
Month = "jul",
Institution = "NCCOSC RDTE DIV, code 782, San Diego, CA 92152-5702",
URL = "ftp://ftp.nosc.mil/pub/Shensa/WTinverse_TR1621.ps.Z",
Size = "200,705",
Pages = "52",
Keyword = "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. This paper offers new
algorithms for the DWT." }
@inproceedings{sinha-richards:1993,
Author = "Sinha, B. and K. J. Richards",
Title = "The wavelet transform applied to flow around Antarctica",
Booktitle = "Wavelets, Fractals, and Fourier Transforms",
Editor = "Farge, M. and J. C. R. Hunt and J. C. Vassilicos",
Publisher = "Clarendon Press",
Year = "1993",
Pages = "221--228",
Keyword = "wavelets, image analysis",
Abstract = "This uses a 2-D Morlet wavelet transform of the streamfunction
derived from the Fine Resolution Arctic Model to analyse oceanic eddies
on a wide range of scales." }
@article{slezak-bijaoui-etal:1990,
Author = "Sl\'ezak, E. and A. Bijaoui and G. Mars",
Title = "Identification of structures from galaxy count: use of the
wavelet transform",
Journal = "Astron. Astroph.",
Volume = "227",
Year = "1990",
Pages = "301--316" }
@article{sodagar-nayebi-etal:1994,
Author = "Sodagar, Iraj and Kambiz Nayebi and Thomas P. Barnell III",
Title = "Time-varying filter banks and wavelets",
Journal = "IEEE Trans., Sig. Proc.",
Volume = "42",
Year = "1994",
Pages = "2983--2996" }
@article{spedding-browand-etal:1993,
Author = "Spedding, G. R. and F. K. Browand and N. E. Huang and
S. R. Long",
Title = "A 2-D complex wavelet analysis of an unsteady wind-generated
surface wave field",
Journal = DAO,
Volume = "20",
Year = "1993",
Pages = "55--77",
Keyword = "wavelets, wind waves",
Abstract = "2-D, complex wavelet functions are used to decompose a
wave field to measure the energy of the wave field as a function
of wavenumber as well as the spatial distribution of the wavenumbers." }
@article{starck-bijaoui:1994,
Author = "Starck, Jean-Luc and Albert Bijaoui",
Title = "Filtering and deconvolution by the wavelet transform",
Journal = "Signal Processing",
Volume = "35",
Year = "1994",
Pages = "195--211",
Keyword = "wavelets, filtering, deconvolution",
Abstract = "A new approach to filtering based on the wavelet transform is
presented and several algorithms are proposed. A criterion of quality,
which takes into account the resolution, is used to compare these
algorithms. It is shown that deconvolution can be done using filtered
wavelet coefficients. By computing the wavelet from the point spread
function, a new transform algorithm and a reconstruction method related
to it are found." }
@article{strang:1989,
Author = "Strang, Gilbert",
Title = "Wavelets and dilation equations: A brief introduction",
Journal = "SIAM Review",
Volume = "31",
Year = "1989",
Pages = "614--627",
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." }
@article{strang:1993,
Author = "Strang, Gilbert",
Title = "Wavelet transforms versus Fourier transforms",
Journal = "Bull. (New Series) AMS",
Volume = "28",
Year = "1993",
Pages = "288--305",
Abstract = "This is a very basic introduction to wavelets. Wavelets
are constructed and studied in relation to the Fourier transform.
The contest between these transforms is informally commented on
in reference to signal processing, especially for video and image
compression. It is stated that wavelets are already competitive
with the Fourier transform for these applications, and head for the
identification of fingerprints. Samples of the developing theory
concerning these results are presented." }
@article{strang:1995,
Author = "Strang, Gilbert",
Title = "Short wavelets and matrix dilation equations",
Journal = "IEEE Trans. Sig. Proc.",
Volume = "43",
Year = "1995",
Pages = "108--115" }
@article{strichartz:1993,
Author = "Strichartz, Robert S.",
Title = "How to make wavelets",
Journal = "American Mathematical Monthly",
Volume = "100",
Year = "1993",
Pages = "539--556",
Abstract = "This is an elementary mathematical introduction to wavelets
with sections on Haar wavelets, multiresolution analysis, their
relationship to the Fourier transform, and the construction of
wavelets." }
@mastersthesis{strohmer:1992,
Author = "Strohmer, Thomas",
Title = "Irregular sampling, frames and pseudoinverse",
Year = "1992",
Institution = "Universit{\"a}t Wien",
URL = "ftp://131.130.22.36/tex/NUHAG/masterstrohmer.ps.Z",
Size = "342,343",
Pages = "84",
Keyword = "wavelets, digital signal processing, irregular sampling",
Abstract = "The purpose of this thesis is to point out the connections
between the theory of frames in Hilbert spaces, the theory of
pseudoinverse operators and the irregular sampling problem for
band-limited functions. The three parts of the thesis are (1)
a section on frames (significant to wavelet theory), (2) a section
on linear algebra where the pseudoinverse of a matrix is defined,
and (3) a section on the 1D discrete reconstruction problem for
band-limited functions from irregularly spaced sampling points." }
@phdthesis{sweldens:1994,
Author = "Sweldens, Wim",
Title = "The construction and application of wavelets in numerical
analysis",
Year = "1994",
Month = "mar",
Institution = "Departement Computerwetenschappen, K.U. Leuven and
Dept. of Math., Univ. of S. Carolina, Columbia, S.C. 29208",
URL = "ftp://maxwell.math.scarolina.edu/pub/wavelet/papers/varia/thesis/thesis[1-6].ps",
Size = "682,479; 811,088; 1,204,962; 1,588,071; 942,484; 609,104",
Pages = "198",
Keyword = "wavelets, numerical methods",
Abstract = "This thesis investigates the use of wavelets in numerical
analysis problems. In the first part two basic tools, quadrature
formulae and asymptotic error expansions, are constructed. The former
provides an easy way to calculate the wavelet coefficients, while the
latter allows a simple comparison of different wavelet families.
In the second part wavelets adapted to a weighted inner product are
constructed and studied, and it is shown how these can be used for the
rapid solution of ordinary differential equations. The final part
studies smooth local trigonometric functions, which can be seen as the
Fourier transform of wavelets. Their construction is generalized to the
biorthogonal case and they are used in data compression algorithms, with
examples concerning image compression shown." }
@article{sweldens-piessens:1994,
Author = "Sweldens, Wim and Robert Piessens",
Title = "Quadrature formulae and asymptotic error expansions for wavelet
approximations of smooth functions",
Journal = "SIAM J. Numer. Anal.",
Volume = "31",
Year = "1994",
Pages = "1240--1264",
Keyword = "wavelets",
Abstract = "This deals with problems encountered when using wavelets
in numerical analysis. Quadrature formulae are constructed for the
calculation of inner products of smooth functions and scaling
functions. Several types are discussed and compared for different
classes of wavelets. A modified, well-conditioned construction using
Chebyshev polynomials is also presented." }
%TTTT
@techreport{taswell:1994,
Author = "Taswell, Carl",
Email = "taswell@sccm.stanford.edu",
Title = "Near-best basis selection algorithms with non-additive
information cost functions",
Year = "1994",
Institution = "Scientific Computing and Computational Mathematics,
Bldg. 469, Room 314, Stanford Univ., Stanford, CA 94305-2140",
URL = "ftp://simplicity.stanford.edu/pub/taswell/nbbsa.ps.Z",
Size = "260,715",
Pages = "4",
Keyword = "wavelets",
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." }
@techreport{taswell-mcgill:1993,
Author = "Taswell, Carl and Kevin C. McGill",
Email = "taswell@sccm.stanford.edu; mcgill@roses.stanford.edu",
Title = "Wavelet transform algorithms for finite-duration discrete-time
signals",
Year = "1993",
Month = "oct",
Number = "NA-91-07",
Institution = "Scientific Computing and Computational Mathematics,
Bldg. 469, Room 314, Stanford Univ., Stanford, CA 94305-2140",
URL = "ftp://simplicity.stanford.edu/pub/taswell/wta.ps.Z",
Size = "513,919",
Pages = "21",
Keyword = "wavelets",
Abstract = "Algorithms are presented for the wavelet and inverse wavelet
transforms for finite-duration discrete-time signals of arbitrary
length not restricted to a power of two." }
@inproceedings{tchamitchian:1993,
Author = "Tchamitchian, Philippe",
Title = "Wavelets and differential operators",
Booktitle = "Different Perspectives on Wavelets",
Editor = "Ingrid Daubechies",
Publisher = "American Math. Soc., Providence, RI",
Series = "Proceedings of Symposia in Applied Mathematics",
Volume = "47",
Year = "1993",
Pages = "77--88",
Note = "From an American Math. Soc. short course, Jan. 11--12, 1993, San
Antonio, TX" }
@article{tewfik-sinha-etal:1992,
Author = "Tewfik, A. H. and D. Sinha and P. Jorgensen",
Title = "On the optimal choice of a wavelet for signal representation",
Journal = "IEEE Trans. Inf. Theory",
Volume = "38",
Year = "1992",
Pages = "747--765" }
@unpublished{turcajova:1994,
Author = "Turcajov{\'a}, Radka",
Title = "Factorizations and construction of linear phase paraunitary
filter banks and higher multiplicity wavelets",
Year = "1994",
Institution = "School of Information Sci. and Tech., Flinders Univ.,
GPO Box 2100, Adelaide, SA 5001, Australia",
URL = "ftp://ftp.cs.flinders.edu.au/pub/wavelets/symm.ps",
Size = "211,390",
Pages = "20",
Keyword = "wavelets",
Abstract = "Paraunitary matrices can be factored into shift products of
orthogonal matrices or linear factors. These factorizations also allow
the derivation of lattice structures for linear phase paraunitary
filter banks and also for the construction of symmetric higher
multiplicity wavelets." }
@unpublished{turcajova-kautsky:1994,
Author = "Turcajov{\'a}, Radka and Jaroslav Kautsky",
Title = "Shift products and factorizations of wavelet matrices",
Year = "1994",
Institution = "School of Information Sci. and Tech., Flinders Univ.,
GPO Box 2100, Adelaide, SA 5001, Australia",
URL = "ftp://ftp.cs.flinders.edu.au/pub/wavelets/shift.ps",
Size = "169,779",
Pages = "14",
Keyword = "wavelets",
Abstract = "A class of so-called shift products of wavelet matrices is
introduced. These products are based on circulations of columns of
orthogonal banded block circulant matrices arising in applications
of discrete orthogonal wavelet transforms." }
@Article{turner-leclerc:1994,
Author = "Turner, B. J. and M. Y. LeClerc",
Title = "Conditional sampling of coherent structures in atmospheric
turbulence using the wavelet transform",
Journal = "J. Atmospheric and Oceanic Techn.",
Volume = "11",
Year = "1994",
Pages = "205--209".
Keyword = "coherent structures, atmospheric turbulence, wavelets" }
%UUUU
@article{unser-aldroubi-etal:1993,
Author = "Unser, Michael and Akram Aldroubi and M. Eden",
Title = "A family of polynomial spline wavelet transforms",
Journal = "Signal Processing",
Volume = "30",
Year = "1993",
Pages = "141--162" }
@article{unser-aldroubi-etal:1994,
Author = "Unser, Michael and Akram Aldroubi and Steven J. Schiff",
Title = "Fast implementation of the continuous wavelet transform
with integer scales",
Journal = "IEEE Trans. Sig. Proc.",
Volume = "42",
Year = "1994",
Pages = "3519--3523",
Abstract = "This describes a fast noniterative algorithm for the
evaluation of continuous spline wavelet transforms at any integer
scale m. In this approach, the input signal and the analyzing
wavelet are both represented by polynomial splines. The algorithm
uses a combination of moving sum and zero-padded filters, and its complexity
per scale is O(N), where N is the signal length. The computation is
exact, and the implementation is noniterative across scales. Examples
of splines wavelets that exhibit properties desirable for either
singularity detection or Gabor-like time-frequency signal analysis
are presented." }
%VVVV
@article{vergassola-frisch:1991,
Author = "Vergassola, M. and U. Frisch",
Title = "Wavelet transforms of self--similar processes",
Journal = "Physica D",
Volume = "54",
Year = "1991",
Pages = "58--64" }
@unpublished{vidakovic:1993,
Author = "Vidakovi{\'c}, Brani",
Title = "A note on random densities via wavelets",
Year = "1993",
Institution = "Duke University, Durham, NC 27708-0251",
URL = "ftp://ftp.isds.duke.edu/pub/brani/papers/WavRanDens.ps.Z",
Size = "93,611",
Keyword = "wavelets",
Abstract = "This defines a random density via orthogonal bases of
wavelets and explores some of its basic properties." }
@unpublished{vidakovic-muller:1994,
Author = "Vidakovi{\'c}, Brani and Peter M{\"u}ller",
Title = "Wavelets for kids: A tutorial introduction",
Year = "1994",
Institution = "Duke University, Durham, NC 27708-0251",
URL = "ftp://ftp.isds.duke.edu/pub/brani/papers/wav4kids[A-B].ps.Z",
Size = "318,373; 70,903",
Keyword = "wavelets",
Abstract = "This paper is intended to serve as a very first introduction
to wavelets for the statistical community. References for further
reading are given as well as some Mathematica procedures." }
@article{villemoes:1992,
Author = "Villemoes, L. F.",
Title = "Energy moments in time and frequency for two--scale difference
equation solutions and wavelets",
Journal = "SIAM J. Math. Anal.",
Volume = "23",
Year = "1992",
Pages = "1519--1543" }
@article{vishwanath:1994,
Author = "Vishwanath, Mohan",
Title = "The recursive pyramid algorithm for the discrete wavelet transform",
Journal = "IEEE Trans. Signal Proc.",
Volume = "42",
Year = "1994",
Pages = "673--676",
Keyword = "wavelets, recursive pyramid algorithm",
Abstract = "The recursive pyramid algorithm (RPA) is a reformulation of
the classical pyramid algorithm (PA) for computing the discrete wavelet
transform (DWT). The RPA computes the N-point DWT in real time (running
DWT) using just L(log N-1) words of storage, as compared with O(N) words
required by the PA where L is the length of the wavelet filter. The RPA
is combined with the short-length FIR filter algorithms to reduce the
number of multiplications and additions." }
%WWWW
@article{weiss:1994,
Author = "Weiss, Lora G.",
Title = "Wavelets and wideband correlation processing",
Journal = "IEEE Signal Processing Magazine",
Volume = "?",
Year = "1994",
Month = "jan",
Pages = "13--32",
Keyword = "wavelets, wideband correlation processing",
Abstract = "Wavelets are introduced and discussed along with wideband
correlation processing. The connections between the two tools are
investigated." }
@techreport{wells:1994a,
Author = "Wells, Raymond O., Jr.",
Title = "Adaptive wave propagation modeling",
Year = "1994",
Number = "TR94-10",
Institution = "Dept. of Math., Rice Univ., Houston, TX 77251-1892",
URL = "ftp://cml.rice.edu/pub/reports/9410.ps.Z",
Size = "71,435",
Pages = "12",
Abstract = "This discusses current attempts to use acoustic and
electromagnetic wave propagation to model physical phenomena and the
role that wavelet analysis is playing in these efforts. The areas
of application are (1) computational fluid dynamics, (2) the geophysical
modeling of the ocean floor using acoustic waves, (3) the modeling
of SAR radar images in the context of automatic target recognition
efforts, and (4) global illumination in computer graphics, i.e. simulation
of reflected and absorbed light in everyday environments." }
@techreport{wells:1994b,
Author = "Wells, Raymond O., Jr.",
Title = "Recent advances in wavelet technology",
Year = "1994",
Month = "mar",
Number = "TR94-12",
Institution = "Dept. of Math., Rice Univ., Houston, TX 77251-1892",
URL = "ftp://cml.rice.edu/pub/reports/9412.ps.Z",
Size = "38,567",
Pages = "8",
Abstract = "This reviews some recent developments in wavelet technology
at the Computational Mathematics Laboratory at Rice, which has as its
primary focus research in the theory and applications of wavelets and
more generally multiscale phenomena in mathematics, science and
engineering. Brief synopses are given of the advances in the areas
of wavelet mathematics, wavelet multiscale representation of data,
image compression and telecommunications technology, and wavelet-based
numerical solutions of differential equations." }
@techreport{wells-zhou:1992a,
Author = "Wells, Raymond O., Jr. and Xiaodong Zhou",
Title = "Adaptive wave propagation modeling",
Year = "1992",
Number = "TR92-02",
Institution = "Dept. of Math., Rice Univ., Houston, TX 77251-1892",
URL = "ftp://cml.rice.edu/pub/reports/9202.ps.Z",
Size = "629,946",
Pages = "?",
Abstract = "?" }
@techreport{wells-zhou:1992b,
Author = "Wells, Raymond O., Jr. and Ziaodong Zhou",
Title = "Wavelet interpolation and approximate solutions of elliptic
partial differential equations",
Year = "1992",
Number = "TR92-03",
Institution = "Dept. of Math., Rice Univ., Houston, TX 77251-1892",
URL = "ftp://cml.rice.edu/pub/reports/9203.ps.Z",
Size = "76,105",
Pages = "?",
Abstract = "?" }
%% 1/26/96
@article{weng-lau:1994,
Author = "Weng, H.-Y. and K.-M. Lau",
Title = "Wavelet, period-doubling and time-frequency localization
with application to satellite data analysis",
Journal = "J. Atmos. Sci.",
Volume = "51",
Year = "1994",
Pages = "2523--2541" }
@unpublished{wickerhauser:1991,
Author = "Wickerhauser, Mladen V.",
Email = "victor@jezebel.wustl.edu",
Title = "Lectures on wavelet packet algorithms",
Year = "Nov. 18, 1991",
Institution = "Dept. of Math., Washington Univ., St. Louis, MO 63130",
URL = "ftp://wuarchive.wustl.edu:/doc/techreports/wustl.edu/math/inria300.ps.Z",
Size = "2,026,711 bytes",
Pages = "75",
Keyword = "wavelets",
Abstract = "A series of lecture notes which begin by defining continuous
wavelet packets and then defines several discrete algorithms and explores
their advantages and disadvantages. Linear and nonlinear compression
methods are also explored." }
@techreport{wickerhauser:1992,
Author = "Wickerhauser, Mladen V.",
Email = "victor@jezebel.wustl.edu",
Title = "Fast approximate factor analysis",
Year = "1992",
Institution = "Dept. of Math., Washington Univ., St. Louis, MO 63130",
URL = "ftp://wuarchive.wustl.edu:/doc/techreports/wustl.edu/math/fakle.ps.Z",
Size = "353,603 bytes",
Pages = "10",
Keyword = "wavelets",
Abstract = "The principal orthogonal factor analysis or Karhunen-Loeve
algorithm may be sped up by a low-complexity preprocessing step. A
fast transform is selected from a large library of wavelet-like
orthonormal bases, so as to maximize transform coding gain for an
ensemble of vectors. On the top few coefficients in the new basis,
in order of variance across the ensemble, are then decorrelated by
diagonalizing the autocovariance matrix." }
@inproceedings{wickerhauser:1993,
Author = "Wickerhauser, Mladen Victor",
Title = "Best--adapted wavelet packet bases",
Booktitle = "Different Perspectives on Wavelets",
Editor = "Ingrid Daubechies",
Publisher = "American Math. Soc., Providence, RI",
Series = "Proceedings of Symposia in Applied Mathematics",
Volume = "47",
Year = "1993",
Pages = "155--171",
Note = "From an American Math. Soc. short course, Jan. 11--12, 1993, San
Antonio, TX",
Abstract = "A review of the construction of orthogonal wavelet packets, using
the quadarature mirror filters algorithm slightly generalized to the
case of p $\ge$ 2 wavelets and scaling functions." }
@book{wickerhauser:1994,
Author = "Wickerhauser, M. V.",
Title = "Adapted Wavelet Analysis, from Theory to Software",
Publisher = "A. K. Peters, Boston",
Year = "1994" }
%% 1/26/96
@article{willemsen:1995,
Author = "Willemsen, Jorge E.",
Title = "Analysis of SWADE Discus N wind speed adn wave height
time series. Part I: Discrete wavelet packet representations",
Journal = "J. of Atmos. and Oceanic Techn.",
Volume = "12",
Year = "1995",
Pages = "1248--1270",
Abstract = "Discus N denotes a single buoy employed during the
SWADE experiment, equipped to record wave amplitude and wind speed
time series at a rate of 1 Hz. Over the course of approximately
4.5 days, two clear-cut examples of sea response to wind activity
took place. It is easy to verify tha the spectral content of the
time series is changing. Wavelet analysis (WA) is a powerful
tool for analyzing such nonstationary series. The paper
illustrates the use of this technique to characterize the observed
wave response in a quantitative manner and to compare this
response to simultaneously measured wind state data. For reasons that
will be reviewed, unlike Fourier analysis, a WA requires
"fine-tuning" of the basis functions to fit the problem under
consideration. Within geophysical applications it has become
common to utilize the "Morlet" wavelet because of its strong
resemblance to well-known spectrogram analysis techniques. However,
it will be seen that a relatively new technique known as the
discrete wavelet packet transform is in principle especially
well suited to optimal time-frequency localizations that are
useful in analyzing nonstationary processes." }
@article{wornell:1990,
Author = "Wornell, G. W.",
Title = "A Karhunen--Loeve--like expansion for 1/f processes via wavelet",
Journal = "IEEE Trans. Inform. Theory",
Volume = "36",
Year = "1990",
Pages = "859--861" }
%XXXX
@techreport{xia-suter:1994,
Author = "Xia, Xiang-Gen and Bruce W. Suter",
Title = "Vector-valued wavelets and vector filter banks",
Year = "1994",
Month = "aug",
Institution = "Dept. of Elect. and Comp. Eng., Air Force Inst. of Tech.,
2950 P Street, Wright-Patterson AFB, OH 45433-7765",
URL = "ftp://archive.afit.af.mil/pub/wavelets/vwfb.ps.Z",
Size = "130,957",
Pages = "24",
Abstract = "This introduces vector-valued multiresolution analysis and
vector-valued wavelets, constructed using paraunitary vector filter
bank theory, for vector-valued signal spaces. In particular,
vector-valued Meyer wavelets that are band-limited are constructed." }
@article{xia-xhang:1993,
Author = "Xia, X.-G. and Z. Zhang",
Title = "On sampling theorem, wavelets and wavelet transforms",
Journal = "IEEE Trans. Sig. Proc.",
Volume = "41",
Year = "1993",
Pages = "3524--3535" }
@techreport{xu-shann:1993,
Author = "Xu, Jin-Chao and Wei-Chang Shann",
Email = "xu@math.psu.edu; t210001@sparc20.ncu.edu.tw",
Title = "Galerkin-wavelet methods for two-point boundary value problems",
Year = "1993",
Institution = "Dept. of Math., Pennsylvania State Univ., University Park, PA 16802",
URL = "ftp://maxwell.math.scarolina.edu:/pub/wavelet/papers/galerkin.ps.Z",
Size = "179,186 bytes",
Pages = "22",
Keyword = "wavelets, Galerkin methods",
Abstract = "Anti-derivatives of wavelets are used for the numerical solution
of differential equations. Optimal error estimates are obtained in the
applications to two-point boundary value problems of second order. The
orthogonal property of the wavelets is used to construct efficient iterative
methods for the solution of the resultant linear algebraic systems and
numerical examples are given." }
%YYYY
%% 1/26/96
@article{yamada-ohkitani:1991,
Author = "Yamada, M. and K. Ohkitani",
Title = "An identification of energy cascade in turbulence by
orthonormal wavelet analysis",
Journal = "Prog. Theor. Phys.",
Volume = "86",
Year = "1991",
Pages = "799--815" }
@article{yen:1994,
Author = "Yen, Nai-chyuan",
Title = "Wave packet decomposition",
Journal = JASA,
Volume = "95",
Year = "1994",
Pages = "889--896",
Keyword = "wave packets, wavelets",
Abstract = "This discusses a signal processing approach conceived from
the observations of wave packets in scattering phenomena where the
natural representation of a signal is examined through the dynamic
time and frequency properties of its energy distribution. For a
time-varying signal from a physical system with finite energy content,
the selected natural frame component functions, which may not be
necessarily orthogonal, can form a complete set for the particular
signal under analysis. The decomposition with these nonorthogonal
frames then becomes optimal and unique. Algorithms for evaluting
the composition of this type of frame are given and examples are
presented." }
@book{young:1993,
Author = "Young, R. K.",
Title = "Wavelet Theory and Its Applications",
Publisher = "Kluwer Academic Pub.",
Year = "1994" }
%ZZZZ
@article{zhang.j-walter:1994,
Author = "Zhang, Jun and Gilbert Walter",
Title = "A wavelet-based KL-like expansion for wide-sense stationary
random processes",
Journal = "IEEE Trans. Sig. Proc.",
Volume = "42",
Year = "1994",
Pages = "1737--1745",
Keyword = "wavelets, Karhunen-Loeve transform",
Abstract = "The describes a wavelet-based series expansion for wide-sense
stationary processes. The expansion coefficients are uncorrelated
random variables, a property similar to that of a KL expansion although,
unlike the KL expansion, the wavelet-based expansion does not require
the solution of the eigen equation and does not require that the process
be time-limited. The basis functions of this expansion can be obtained
easily from wavelets of the Lemaire-Meyer type and the power spectral
density of the process." }
@phdthesis{zubair:1993,
Author = "Zubair, Lareef M.",
Email = "zubair@chaos.yale.edu",
Title = "Studies in turbulence using wavelet transforms for data
compression and scale separation,"
Year = "May 1993",
Institution = "Yale University",
URL = "ftp://(see comments)"
Size = "(see comments)"
Pages = "221",
Abstract = "The ftp address where this can be obtained along with the
necessary username and password can be obtained via an e-mail message
to the author. The wavelet transform is used to study the structure
of turbulent flows. The structure of scalar and vorticity fields are
studied using the continuous wavelet transform, the wavelet-packet
transform is assessed as a tool for data compression, and a power-spectra
and filtering technique based on the transform is introduced." }
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