Wavelet Resources

Welcome to the MathSoft Wavelet Resources page: your site for One-Stop Shopping for wavelet papers. This page is a list of many preprints on the subject of wavelets and their various applications in the worlds of mathematics, engineering and physics. Many of these sources were tracked down through the Wavelet Digest which is a clearinghouse for wavelet information of all sorts. As a convenience, we now provide links to some of the tools (URL) you need to view papers in this list.

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 a preprint that you are aware of that is available via anonymous ftp and does not appear here please mail dblair@mathsoft.com and it will be added as soon as possible.

Last updated November 27, 1994.

Introductions to Wavelets

C. S. Burrus and R. A. Gopinath, "A Tutorial Overview of Wavelets, Filter Banks and Interrelationships"
E. Gootman and M. Wickerhauser, "Elementary Wavelets."
B. Jawerth and W. Sweldens, "An Overview of Wavelet Based Multiresolution Analysis."
B. Vidakovic, "Wavelets for Kids," also part 2.

General Theory

P. Auscher, G. Weiss and M. V. Wickerhauser, "Local Sine and Cosine Bases of Coifman and Meyer and the Construction of Smooth Wavelets"
G. Beylkin and N. Saito, "Multiresolution Representations using the Autocorrelation Functions of Compactly Supported Wavelets."
G. Beylkin and N. Saito, "Wavelets, their Autocorrelation Functions and Multiresolution Analysis of Signals."
G. Beylkin and B. Torrésani, "Implementation of Operators via Filter Banks, Autocorrelation Shell and Hardy Wavelets."
D. Chen, "Extended Families of Cardinal Spline Wavelets."
D. Chen, "Spline Wavelets of Small Support."
D. Chen, "Characterization of Biorthogonal Cardinal Spline Wavelet Bases."
D. Chen, "Cardinal Spline Wavelets", dissertation. Also part 2, part 3, part 4, part 5 and part 6.
R. Coifman and M. V. Wickerhauser, "Entropy-Based Algorithms for Best Basis Selection"
R. Coifman and M. Wickerhauser, "Best-adapted Wave Packet Bases."
R. Coifman(?), "Numerical Harmonic Analysis."
R. Coifman, Y. Meyer and M. Wickerhauser, "Size Properties of Wavelets Packets."
R. Coifman and Y. Meyer, "Orthonormal Wave Packet Bases."
R. Coifman and M. V. Wickerhauser, "Wavelets and Adapted Waveform Analysis"
R. Coifman, Y. Meyer and M. Wickerhauser, "Adapted Wave Form Analysis, Wavelet Packets and Applications."
S. Dahlke, W. Dahmen, E. Schmitt and I. Weinreich, Multiresolution Analysis and Wavelets on S^2 and S^3."
G. Davis, S. Mallat and Z. Zhang, "Adaptive Nonlinear Approximations."
G. Davis, "Adaptive Nonlinear Approximations."
G. Davis, S. Mallat and Z. Zhang, "Adaptive Time-Frequency Approximations with Matching Pursuits."
B. Jawerth and W. Sweldens, "Weighted Multiwavelets on General Domains."
B. Jawerth and W. Sweldens, "Biorthogonal Smooth Local Trigonometric Bases."
M. K. Kwong and P. T. Peter Tang, "W-Matrices, Nonorthogonal Multiresolution Analysis and Finite Signals of Arbitrary Length."
G. Leaf, J. M. Restrepo and G. Schlossnagle, "Periodized Daubechies Wavelets."
S. Mallat and Z. Zhang, "Matching Pursuit with Time-Frequency Dictionaries."
R. Piessens and W. Sweldens, "Wavelet Sampling Techniques."
M. J. Shensa, "An Inverse DWT for Nonorthogonal Wavelets"
W. Sweldens, "Compactly Supported Wavelets which are Biorthogonal to a Weighted Inner Product."
C. Taswell, "Wavelet Transform Algorithms for Finite Duration Discrete-Time Signals."
C. Taswell, "Near-Best Basis Selection Algorithms with Non-Additive Information Cost Functions."
R. O. Wells Jr., "Recent Advances in Wavelet Technology"
M. Wickerhauser(?), "Entropy of a Vector Relative to a Decomposition."
M. V. Wickerhauser, "Lectures on Wavelet Packet Algorithms"
M. V. Wickerhauser, "Smooth Localized Orthonormal Bases"
V. Zavadsky, "Multiresolution Approximations of Banach Spaces."
V. Zavadsky, "Wavelet Approximation of Sampled Functions."

Frame Decompositions

D. M. Healy, Jr. and S. Li, "On Pseudo Frame Decompositions and Discrete Gabor Expansions."
S. Li, "General Frame Decompsotions, Pseudo-Duals and Applications for Weyl-Heisenberg Frames."
S. Li, "On Dimension Invariance of Discrete Gabor Expansions."

M-Band Wavelets and Filter Banks

C. S. Burrus and R. A. Gopinath, "Wavelets and Filter Banks"
C. S. Burrus and R. A. Gopinath, "Unitary FIR Filter Banks and Symmetry"
C. S. Burrus and R. A. Gopinath, "Theory of Modulated Filter Banks and Modulated Wavelet Tight Frames"
C. S. Burrus and R. A. Gopinath, "Factorization Approach to Time-Varying Unitary Filter Bank Trees and Wavelets"
C. Herley, "Boundary Filters for Finite-Length Signals and Time-Varying Filter Banks."
P. Steffen, P. Heller, R. A. Gopinath and C. S. Burrus, "The Theory of Regular M-Band Wavelets"

Wavelets and General Signal Processing

C. S. Burrus, R. A. Gopinath and J. E. Odegard, "Design of Linear Phase Cosine Modulated Filter Banks for Subband Image Compression"
R. Coifman, "Adapted Multiresolution Analysis, Computation, Signal Processing and Operator Theory"
R. Coifman, Y. Meyer, S. Quake and M. Wickerhauser, "Signal Processing and Compression with Wave Packets."
R. Coifman, Y. Meyer and M. V. Wickerhauser, "Wavelet Analysis and Signal Processing"
M. Goldburg, "Applications of Wavelets to Quantization and Random Process Representations." About 1.1 MB.
D. M. Healy, Jr., J. Lu and J. B. Weaver, "Signal Recovery and Wavelet Reproducing Kernels."
D. M. Healy, Jr. and J. Lu, "Contrast Enhancement via Multiscale Gradient Transformations."
W. Hwang and S. Mallat, "Singularity Detection and Processing with Wavelets."
B Jawerth, Y. Liu and W. Sweldens, "Signal Compression with Smooth Local Trigonometric Bases."
G. Uytterhoeven, "Design and Implementation of Compression Algorithms using Multiwavelets."

Wavelets and Image Processing

E. Adelson and E. Simoncelli, "Subband Image Coding with Three-tap Pyramids."
H. J. Barnard, "Image and Video Coding Using a Wavelet Decomposition." Be forewarned: this is almost 6MB compressed!
M. Bhatia, W. C. Karl, and A. S. Willsky, "A Wavelet-Based Method for Multiscale Tomographic Reconstruction."
M. Bhatia, W. C. Karl, and A. S. Willsky, "Using Natural Wavelet Bases and Multiscale Stochastic Models for Tomographic Reconstruction."
A. Bijaoui, B. Lopez, C. Perrier and J. L. Stark, "Image Reconstruction by the Wavelet Transform Applied to Aperture Synthesis."
A. Bijaoui, F. Murtagh and J. L. Stark, "Image Restoration with Noise Suppression Using a Wavelet Transform and a Multiresolution Support Constraint," with figures.
A. Bijaoui, F. Murtagh and J. L. Stark, "Restauration des Images Multi-Echelles par l'Algorithm a Trous." Be forwarned: this is 4 MB.
A. Bijaoui, F. Murtagh and J. L. Stark, "Multiresolution Support Applied to Image Filtering and Restoration."
A. Bijaoui, F. Murtagh and J. L. Stark, "Multiresolution and Astronomical Image Processing."
A. Bijaoui, F. Murtagh and J. L. Stark, "Image Restoration with Noise Suppression Using a Multiresolution Analysis Support."
A. Bijaoui, F. Murtagh ,J. L. Stark and W. Zeilinger, "Object Detection Using Multiresolution Analysis."
D. M. Healy, Jr., J. Lu and J. B. Weaver, "Contrast Enhancement of Medical Images Using Multiscale Edge Representation."
M. L. Hilton, B. D. Jawerth and A. Sengupta, "Compressing Still and Moving Images with Wavelets" with figure.
M. Louys, F. Murtagh and J. L. Stark, "Astronomical Image Compression Using the Pyramidal Median Transform." Also "summary version."
P. Moulin, "A Multiscale Relaxation Algorithm for SNR Maximization in 2-D Nonorthogonal Subband Coding."
F. Murtagh and J. L. Stark, "Multiresolution Image Analysis Using Wavelets."
F. Murtagh and J. L. Stark, "Image Restoration with Noise Suppression Using the Wavelet Transform," with "figure 1," "figure 2," "figure 3," "figure 4," "figure 5a," "figure 5b," "figure 6," and "figure 7."
G. Weiss, "Time-Frequency and Time-Scaling Methods in Signal and Image Processing"
M. Wickerhauser, "Picture Compression by Best-Basis Subband Coding."
M. V. Wickerhauser, "High-Resolution Still Picture Compression"

The FBI Wavelet Fingerprint Compression Standard

J. N. Bradley and C. M. Brislawn, "Proposed First-Generation WSQ Bit Allocation Procedure"
J. N. Bradley and C. M. Brislawn, "The Wavelet/Scalar Quantization Compression Standard for Digital Fingerprint Images."
J. Bradley, C. Brislawn and T. Hopper, "WSQ Gray-Scale Fingerprint Image Compression Specification."
J. Bradley, C. Brislawn and T. Hopper, "The FBI Wavelet/Scalar Quantization Standard for Gray-Scale Fingerprint Image Compression" with figures.
C. M. Brislawn, Classification of Symmetric Wavelet Transforms"
"The FBI Wavelet/Scalar Quantization Fingerprint Image Compression Standard."

Wavelets and Speech Processing

E. Wesfreid and M. V. Wickerhauser, "Adapted Local Trigonometric Transforms and Speech Processing"
M. Wickerhauser, "Acoustic Signal Compression with Wavelets Packets."

Wavelets and Ordinary Differential Equations

G. Beylkin, "On Wavelet-based Algorithms for Solving Differential Equations."
B Jawerth and W. Sweldens, "Wavelet Multiresolution Analyses Adapted for the Fast Solution of Boundary Value Ordinary Differential Equations."
A. Rieder, "Semi-Algebraic Multi-level Methods Based on Wavelet Decompositions I: Application to Two-Point Boundary Problems"
W. C. Shann and J. C. Xu, "Galerkin-wavelet Methods for Two Point Boundary Value Problems."

Wavelets and Partial Differential Equations

E. Bacry, S. Mallat and G. Papanicolaou, "A Wavelet Based Space-Time Adaptive Numerical Method for Partial Differential Equations"
D. M. Bond and S. A. Vavasis, "Fast Wavelet Transforms for Matrices Arising From Boundary Element Methods."
R. Glowinski, T. Pan , R. O. Wells, Jr. and X. Zhou, "Wavelet and Finite Element Solutions for the Neumann Problem Using Fictitious Domains"
R. Glowinski, A. Rieder, R. O. Wells, Jr. and X. Zhou, "A Wavelet Multigrid Preconditioner for Dirichlet Boundary Value Problems in General Domains."
R. Glowinski, A. Rieder, R. O. Wells, Jr. and X. Zhou, "A Preconditioned CG-Method for Wavelet-Galerkin Discretizations of Elliptic Problems"
F. Heurtaux, F. Planchon and M. V. Wickerhauser, "Scale Decomposition in Burgers' Equation"
G. Leaf and J. M. Restrepo, "Wavelet-Galerkin Discretization of Hyperbolic Equations."
A. Rieder and X. Zhou, "On the Robustness of the Damped V-Cycle of the Wavelet Frequency Decompositions Multigrid Method"
A. Rieder, R. O. Wells, Jr. and X. Zhou, "A Wavelet Approach to Robust Multilevel Solvers for Anisotropic Elliptic Problems."
A. Rieder, R. O. Wells, Jr. and X. Zhou, "On the Wavelet Frequency Decomposition Method"
R. O. Wells, Jr. and X. Zhou, "Wavelet Solutions for the Dirichlet Problem"
R. O. Wells, Jr. and X. Zhou, "Wavelet Interpolation and Approximate Solution of Elliptic Partial Differential Equations"
R. O. Wells, Jr. and X. Zhou, "Representing the Geometry of Domains by Wavelets with Applications to Partial Differential Equations"
R. O. Wells, Jr., "Multiscale Applications of Wavelets to Solutions of Partial Differential Equations"

Wavelets and Numerical Analysis

G. Beylkin, R. Coifman and V. Rokhlin, "Fast Wavelet Transforms and Numerical Algorithms I."
G. Beylkin, "On the Representation of Operators in Bases of Compactly Supported Wavelets."
G. Beylkin, "On the Fast Algorithm for Multiplication of Functions in the Wavelet Bases."
G. Beylkin, "Wavelets and Fast Numerical Algorithms." Lecture notes for an AMS short course, 1993.
G. Beylkin, "Wavelets, Multiresolution Analysis and Fast Numerical Algorithms." Draft of INRIA lectures, May 1991.
G. Beylkin and M. E. Brewster, "A Multiresolution Strategy for Numerical Homogenization."
E. Kolaczyk, "Wavelet Methods for the Inversion of Certain Homogeneous Linear Operators in the Presence of Noisy Data," with fig 5.1, figs 5.2, fig 5.4, fig 5.5, figs 5.6, figs 5.8, fig 5.10, figs 5.11, fig 5.13, and figs 5.14.
R. Piessens and W. Sweldens, "Quadrature Formulae and Asymptotic Error Expansion of Wavelet Approximations of Smooth Functions."
R. Piessens and W. Sweldens, "Asymptotic Error Expansion of Wavelet Approximations of Smooth Functions II."
W. C. Shann, "Quadratures Involving Polynomials and Daubechies' Wavelets."
W. Sweldens, "Construction and Application of Wavelets in Numerical Analysis."
M. Wickerhauser, "Nonstandard Matrix Multiplication."
M. V. Wickerhauser, "Computation with Adapted Time-Frequency Atoms"
M. V. Wickerhauser, "Wavelet Approximations to Jacobians and the Inversion of Complicated Maps"

Wavelets and Statistics

R. Coifman and N. Saito, "Local Discriminant Bases."
R. Coifman and F. Majid, "Adapted Waveform Analysis and Denoising."
A. Davis, A. Marshak and W. Wiscombe, "Wavelet-Based Multifractal Analysis of Non-Stationary and/or Intermittent Geophysical Signals." with figures.
D. Donoho, "Nonlinear Solution of Linear Inverse Problems by Wavelet-Vaguelette Decomposition"
D. Donoho, "Smooth Wavelet Decompositions with Blocky Coefficient Kernels"
D. Donoho, "De-noising by Soft Thresholding"
D. Donoho, "Interpolating Wavelet Transforms"
D. Donoho, "Unconditional Bases are Optimal Bases for Data Compression and for Statistical Estimation"
D. Donoho and I. Johnstone, "Adapting to Unknown Smoothness by Wavelet Shrinkage"
D. Donoho and I. Johnstone, "Ideal Spatial Adaptation via Wavelet Shrinkage"
D. Donoho and I. Johnstone, "Minimax Estimation via Wavelet Shrinkage"
D. Donoho and I. Johnstone, "Minimax Risk over l_p Balls"
D. Donoho, I. Johnstone, G. Kerkyacharian and D. Picard, "Density Estimation via Wavelet Shrinkage"
D. Donoho, I. Johnstone, G. Kerkyacharian and D. Picard, "Wavelet Shrinkage: Asymptopia?"
H. Y. Gao, "Choice of Thresholds for Wavelet Shrinkage Estimate of the Spectrum."
I. Johnstone, "Minimax Bayes, Asymptotic Minimax and Sparse Wavelet Priors"
P. Moulin, "Wavelet Thresholding Techniques for Power Spectrum Estimation."
G.P. Nason, "Wavelet Regression by Cross-Validation"
N. Saito, "Simultaneous Noise Supression and Signal Compression using a Library of Orthonormal Bases and the Minimum Description Length Criterion."
B. Vidakovic, "A Note on Random Densities via Wavelets"
B. Vidakovic, "Nonlinear Wavelet Shrinkage with Bayes Rules and Bayes Factors."
M. V. Wickerhauser, "Fast Approximate Factor Analysis"

Wavelets and Econometrics

S. A. Greenblatt, "Wavelets in Economics: An Application to Outlier Testing."
M. J. Jensen, "Wavelet Analysis of Fractionally Integrated Processes."

Wavelets and Fractals

A. Davis, A. Marshak and W. Wiscombe, "Wavelet-Based Multifractal Analysis of Non-Stationary and/or Intermittent Geophysical Signals." with figures.
W. Hwang and S. Mallat, "Characterization of Self-Similar Multifractals with Wavelet Maxima."

Wavelets and Communication Theory

R. Learned, H. Krim, B. Claus, A. S. Willsky, and W. C. Karl, "Wavelet-Packet-Based Multiple Access Communication."

Wavelets and Computer Graphics

A. Fournier, "Wavelets and their Applications in Computer Graphics." This is 2.5 MB compressed.
C. Herley, "Exact Interpolation and Iterative Subdivision Schemes."

Wavelets and Physics

C. Best and A. Schäfer, "Variational Description of Statistical Field Theories using Daubechies' Wavelets."
G. Beylkin, J. Dunn and D. Gines, "Order N Static and Quasi-Static Computations in Electrodynamics using Wavelets."
J. C. Cohen and T. Chen, "Fundamentals of the Discrete Wavelet Transform for Seismic Data Processing."
W. C. Shann, "Finite Element Methods for Maxwell's Equations with Stationary Magnetic Fields and Galerkin-wavelet Methods for Two Point Boundary Value Problems."
L. R. Watkins and Y. R. Zhou, "Modelling Propagation in Optical Fibres using Wavelets."

Hardware Implementation of Wavelet Transforms

J. Fridman and E. S. Manolakos, "On Linear Space-Time Mapping for the 1-D Discrete Wavelet Transform."
J. Fridman and E. S. Manolakos, "Distributed Memory and Control VLSI Architectures for the 1-D Discrete Wavelet Transform."

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