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 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 wavelets@mathsoft.com and it will be added as soon as possible.

Many thanks are due to Steve Baum for compiling baum.bib, an exhaustive list in BibTex of wavelet references for both published papers and technical reports. Most of the papers in his list that are available via anonymous ftp have been added here; most of those that didn't make it to the page couldn't be found at the supplied address.

One quick plug: MathSoft develops and markets S+Wavelets, an object-oriented toolkit for advanced signal and image analysis, time series analysis, statistical signal estimation and data compression.

Introductions to Wavelets

• Dl  C. S. Burrus and R. A. Gopinath, "A Tutorial Overview of Wavelets, Filter Banks and Interrelationships"
• Dl  T. Edwards, "Discrete Wavelet Transforms: Theory and Application."
• Dl  E. Gootman and M. Wickerhauser, "Elementary Wavelets."
• A. Graps, "An Introduction To Wavelets."
• Dl  C. Heil and D. Walnut, "Continuous and Discrete Wavelet Transforms."
• Dl  B. Jawerth and W. Sweldens, "An Overview of Wavelet Based Multiresolution Analysis". An abstract is also available.
• Dl  J. Lewalle, "Tutorial on Wavelet Analysis of Experimental Data" local miror
• Dl  P. Schröder and W. Sweldens, "Building Your Own Wavelets at Home." An abstract is also available.
• Dl  G. Strang, "Wavelets"
• Dl  G. Strang "Wavelets and dilation equations: a brief introduction."
• Dl  B. Vidakovic, "Wavelets for Kids," also part 2.

General Theory

• L. Andersson, N. Hall, B. Jawerth and G. Peters, "Wavelets on Closed Subsets of the Real Line"
• Dl  P. Auscher, G. Weiss and M. V. Wickerhauser, "Local Sine and Cosine Bases of Coifman and Meyer and the Construction of Smooth Wavelets"
• C. Basdevant and V. Perrier, "Besov Norms in Terms of Continuous Wavelet Transforms and Application to Structure Functions."
• B.E. Bassil, G.J. Dickson and D.M. Monro, "Orthonormal Wavelets With Balanced Uncertainty".
• G. Beylkin and N. Saito, "Multiresolution Representations using the Autocorrelation Functions of Compactly Supported Wavelets."
• Dl  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."
• A. G. Bruce, H. Gao and D. Ragozin, "Non-smooth Wavelets: Graphing Functions Unbounded on Every Interval."
• C. Cabrelli, C. Heil, and U. Molter, "Accuracy of Lattice Translates of Several Multidimensional Refinable Functions."
• R. C. Calderbank, I. Daubechies, W. Sweldens and B. Yeo "Wavelet Transforms that Map Integers to Integers." There is also an uncompressed version.
• 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.
• Dl  S. Chen and D. Donoho, "Atomic Decomposition by Basis Pursuit."
• A. Cohen, W. Dahmen and R. DeVore, "Multiscale Decompositions on Bounded Domains."
• J. Cohen, "The Foot Problem in Wavelet Packet Splitting." A Mathematica notebook converted to Postscript.
• J. Cohen, "Schauder Basis for [0,1]." A Mathematica notebook converted to Postscript.
• J. Cohen, "The Littlewood-Paley-Stein Wavelet." A Mathematica notebook converted to Postscript.
• J. Cohen, "Battle-Lemarie Wavelets." A Mathematica notebook converted to Postscript.
• J. Cohen, "The Daubechies Minimum Phase Wavelets." A Mathematica notebook converted to Postscript.
• J. Cohen, "Meyer Wavelets." A Mathematica notebook converted to Postscript.
• Dl  R. Coifman and M. V. Wickerhauser, "Entropy-Based Algorithms for Best Basis Selection"
• Dl  R. Coifman and M. Wickerhauser, "Best-adapted Wave Packet Bases."
• Dl  R. Coifman(?), "Numerical Harmonic Analysis."
• Dl  R. Coifman, Y. Meyer and M. Wickerhauser, "Size Properties of Wavelets Packets."
• Dl  R. Coifman and Y. Meyer, "Orthonormal Wave Packet Bases."
• Dl  R. Coifman and M. V. Wickerhauser, "Wavelets and Adapted Waveform Analysis"
• Dl  R. Coifman, Y. Meyer and M. Wickerhauser, "Adapted Wave Form Analysis, Wavelet Packets and Applications."
• D. Colella and C. Heil, "Matrix Refinement Equations: Existence and Accuracy."
• S. Dahlke, W. Dahmen, E. Schmitt and I. Weinreich, "Multiresolution Analysis and Wavelets on S^2 and S^3."
• W. Dahmen, "Stability of Multiscale Transformations."
• W. Dahmen and C. A. Micchelli, "Biorthogonal Wavelet Expansions."
• Dl  G. Davis, S. Mallat and Z. Zhang, "Adaptive Nonlinear Approximations."
• Dl  G. Davis, "Adaptive Nonlinear Approximations."
• Dl  G. Davis, S. Mallat and Z. Zhang, "Adaptive Time-Frequency Approximations with Matching Pursuits."
• I. Daubechies and W. Sweldens, . An abstract is also available.
• C. deBoor, R. DeVore and R. Amos, "On the Construction of Multivariate (Pre)Wavelets."
• R. L. deQueiroz, "On Lapped Transforms."
• M. Girardi and W. Sweldens, "A New Class of Unbalanced Haar Wavelets That Form an Unconditional Basis for Lp on General Measure Spaces." An abstract is also available.
• S. Haykin and S. Mann, "The Chirplet Transform: A New Signal Analysis Technique Based on Affine Relationships in the Time-Frequency Plane." This about 3.5 MB. Access denied. Dl  There is short html-version: Chirplet transform: Physical Consideration and local mirror
• C. Heil, G. Strang and V. Strela, "Approximation By Translates of Refinable Functions."
• C. Heil and G. Strang, "Continuity of the Joint Spectral Radius: Application to Wavelets."
• Dl  B. Jawerth and W. Sweldens, "Biorthogonal Smooth Local Trigonometric Bases." An abstract is also available.
• B. Jawerth and W. Sweldens, "Weighted Multiwavelets on General Domains."
• 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."
• J. Lippus, "Wavelet Coefficients of Functions of Generalized Lipschitz Classes."
• Dl  S. Mallat and Z. Zhang, "Matching Pursuit with Time-Frequency Dictionaries."
• E. J. McCoy, D. B. Percival and A. T. Walden, "On the Phase of Least-Asymmetric Scaling and Wavelet Filters."
• R. Piessens and W. Sweldens, "Wavelet Sampling Techniques." An abstract is also available.
• J. Shen and G. Strang, "The zeros of the Daubechies polynomials."
• J. Shen and G. Strang, "Asymptotics of Daubechies Filters, Scaling Functions and Wavelets."
• M. J. Shensa, "An Inverse DWT for Nonorthogonal Wavelets"
• W. Sweldens, "Compactly Supported Wavelets which are Biorthogonal to a Weighted Inner Product." An abstract is also available.
• W. Sweldens, "The Lifting Scheme: A Custom-Design Construction of Biorthogonal Wavelets." An abstract is also available.
• W. Sweldens, "The Lifting Scheme: A Construction of Second Generation Wavelets." An abstract is also available.
• B. Suter and X. Xia, "Vector Valued Wavelets and Vector Filter Banks."
• Dl  C. Taswell, "Wavelet Transform Algorithms for Finite Duration Discrete-Time Signals."
• C. Taswell, "Near-Best Basis Selection Algorithms with Non-Additive Information Cost Functions."
• K. Urban, "On Divergence-Free Wavelets."
• Dl  R. O. Wells Jr., "Recent Advances in Wavelet Technology" ps-file without figures
• Dl  M. V. Wickerhauser(?), "Entropy of a Vector Relative to a Decomposition."
• Dl  M. V. Wickerhauser, "Lectures on Wavelet Packet Algorithms"
• Dl  M. V. Wickerhauser, "Smooth Localized Orthonormal Bases"
• C. Zarowski, "Notes on Orthogonal Wavelets and Wavelet Packets"
• V. Zavadsky, "Multiresolution Approximations of Banach Spaces."
• V. Zavadsky, "Wavelet Approximation of Sampled Functions."

Frame Decompositions

• J. Benedetto, C. Heil, and D. Walnut, "Differentiation and the Balian-Low Theorem."
• O. Christensen and C. Heil, "Perturbations of Banach Frames and Atomic 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, "On the Correlation Structure of Multiplicity M Scaling Functions"
• 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

• D. E. Ashpis and J. Lewalle, "Transport in bypass transition: mapping the active time scales using wavelet techniques"
• D.E. Ashpis and J. Lewalle, "Demonstration of wavelet techniques in the spectral analysis of bypass transition data"
• Dl  C. Basdevant, V. Perrier and T. Philipovitch, "Wavelet Spectra Compared to Fourier Spectra."
• J.P. Bonnet, J. Lewalle and M.N. Glauser, "Coherent Structures: Past, Present and Future."
• G. Buresti, J. Lewalle and P. Petagna, "Wavelet statistics and the near-field structure of coaxial jets"
• Dl  C. S. Burrus and R. A. Gopinath, "Wavelet-Based Lowpass/Bandpass Interpolation"
• C. S. Burrus, R. A. Gopinath and J. E. Odegard, "Design of Linear Phase Cosine Modulated Filter Banks for Subband Image Compression"
• Dl  S. Cabrera, V. Krienovich and O. Sirisaengtaksin, "Wavelets Compress Better Than All Other Methods: A 1-D Theorem."
• Dl  S. Cabrera, V. Krienovich and O. Sirisaengtaksin, "Wavelet Nerual Networks are Optimal Approximators for Functions of One Variable."
• R. Carmona, W. L. Hwang and B. Torresani, "Characterization of Signals by the Ridges of Their Wavelet Transforms."
• R. Carmona, W. L. Hwang and B. Torresani, "Multi-Ridge Detection and Time-Frequency Reconstruction."
• R. Coifman, "Adapted Multiresolution Analysis, Computation, Signal Processing and Operator Theory"
• Dl  R. Coifman, Y. Meyer, S. Quake and M. Wickerhauser, "Signal Processing and Compression with Wave Packets."
• Dl  . Coifman, Y. Meyer and M. V. Wickerhauser, "Wavelet Analysis and Signal Processing"
• P. Crane, H. Higuchi and J. Lewalle, "On the structure of two-dimensional wakes behind a pair of flat plates"
• 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., J. Lu, J. B. Weaver and Y. Xu, "Noise Reduction With Multiscale Edge Representation and Perceptual Criteria."
• D. M. Healy, Jr. and J. Lu, "Contrast Enhancement via Multiscale Gradient Transformations."
• W. Hwang and S. Mallat, "Singularity Detection and Processing with Wavelets."
• Dl  B Jawerth, Y. Liu and W. Sweldens, "Signal Compression with Smooth Local Trigonometric Bases." An abstract is also available.
• M. M. Lankhorst and M. D. van der Laan, "Wavelet-Based Signal Approximation with Genetic Algorithms."
• J. Lewalle, K. Read and M. T. Schobeiri, "Effect of unsteady wake-passing frequency on boundary layer transition --- experimental investigation and wavelet analysis"
• J. Lewalle, S.J. Murphy and F.W. Peek, "Wavelet analysis of olfactory nerve response to stimulus"
• J. Lewalle, "Wavelet analysis of experimental data: some methods and the underlying physics"
• G. Strang, "Eigenvalues of (!2)H and convergence of the cascade algorithm."
• Dl  G. Strang, "Creating and comparing wavelets."
• A. R. Tate, "Pattern Recognition Analysis of in vivo Magnetic Resonance Spectra"
• 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."
• E. H. Adelson, W. T. Freeman, D. J. Heeger and E. P. Simoncelli, "Shiftable Multi-Scale Transforms."
• E. H. Adelson and E. P. Simoncelli, "Subband Transforms."
• V.R. Algazi, R.R. Estes and J. Lu, "Comparison of wavelet image coders using the Picture Quality Scale (PQS)."
• 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."
• R. A. Carmona, R. D. Frostig and W. L. Hwang, "Wavelet Analysis for Brain Function Imaging."
• H. Chao and P. Fisher, "An Approach of Fast Integer Reversible Wavelet Transforms for Image Compression."
• B. Deng, B. D. Jawerth, G. Peters and W. Sweldens, "Wavelet Probing for Compression Based Segmentation". An abstract is also available.
• J. Fan and A. Laine, "An Adaptive Approach for Texture Segmentation by Multi-Channel Wavelet Frames.".
• W. T. Freeman and E. P. Simoncelli, "The Steerable Pyramid: A Flexible Architecture for Multi-Scale Derivative Computation." / C Source Code (75k)
• A. Grzeszczak, M. K. Mandal, S. Panchanathan and T. Yeap, "VLSI Implementation of Discrete Wavelet Transform."
• O. Guleryuz, M. T. Orchard and Z. Xiong, "A DCT-based Embedded Image Coder."
• D. M. Healy, Jr., J. Lu and J. B. Weaver, "Contrast Enhancement of Medical Images Using Multiscale Edge Representation."
• C. Heil, P. N. Heller, G. Strang, V. Strela, and P. Topiwala, "Accuracy of Lattice Translates of Several Multidimensional Refinable Functions."
• C. Herley, M. T. Orchard, K. Ramchandran and Z. Xiong, "Flexible Tree-structured Signal Expansions for Compression Using Time-Varying Filter Banks."
• M. L. Hilton, B. D. Jawerth and A. Sengupta, "Compressing Still and Moving Images with Wavelets" with figure.
• P. Kovesi, "Image Features from Phase Congruency"
• B. Lin, "Wavelet Phase Filter for Denoising Tomographic Image Reconstruction"
• M. Louys, F. Murtagh and J. L. Stark, "Astronomical Image Compression Using the Pyramidal Median Transform." Also summary version.
• M. K. Mandal, T. Aboulnasr and S. Panchanathan, "Image Indexing Using Moments and Wavelets."
• M. K. Mandal, E. Chan, X. Wang and S. Panchanathan, "Multiresolution Motion Estimation Techniques for Video Compression."
• M. K. Mandal, S. Panchanathan and T. Aboulnasr, "Choice of Wavelets for Image Compression."
• D.M. Monro and B.G. Sherlock, "Psychovisually Tuned Wavelet Fingerprint Compression".
• D.M. Monro and B.G. Sherlock, "Optimised Wavelets for Fingerprint Compression".
• 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.
• M. T. Orchard, Z. Xiong and Y. Zhang, "A Simple Deblocking Algorithm for JPEG Compressed Images Using Overcomplete Wavelet Representations."
• M. T. Orchard, K. Ramchandran and Z. Xiong, "Wavelet Packets Image Coding Using Space-Frequency Quantization."
• M. T. Orchard, K. Ramchandran and Z. Xiong, "Space-frequency Quantization for Wavelet Image Coding."
• H. Pan, "Uniform Full-Information Image Matching Using Complex Conjugate Wavelet Pyramids", with figures.
• H.Pan, "General Stereo Image Matching Using Symmetric Complex Wavelets," presented at SPIE Conference: Wavelet Applications in Signal and Image Processing, VI. Denver, August 1996, Published in SPIE Proceedings, vol. 2825.
• P. Schröder and W. Sweldens, "Spherical wavelets: Efficiently representing functions on the sphere." An abstract is also available.
• P. Schröder and W. Sweldens, "Spherical Wavelets: Texture Processing." An abstract is also available.
• J. A. Solomon, J. Villasenor, A. B. Watson and G. Y. Yang, "Visual Thresholds For Wavelet Quantization Error."
• V. Strela, P. Heller, G. Strang, P. Topiwala and C. Heil, "The application of multiwavelet filter banks to signal and image processing."
• 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"
• Z. Xiong, "Representation and Coding of Images Using Wavelets."

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 Nonexpansive Symmetric Extension Transforms for Multirate Filter Banks"
• C. M. Brislawn, "Fingerprints Go Digital"
• C. M. Brislawn, "Preservation of Subband Symmetry in Multirate Signal Coding."
• "The FBI Wavelet/Scalar Quantization Fingerprint Image Compression Standard."

Wavelets and Speech Processing

• J. Berger, "The Center for Studies in Music Technology" at Yale.
• 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." An abstract is also available.
• P. Monasse and V. Perrier, "Ondelettes sur l'Intervalle pour la Prise en Compte de Conditions aux Limites."
• 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

• A. Averbuch, G. Beylkin R. R. Coifman and M. Israeli, "Multiscale Inversion of Elliptic Operators."
• E. Bacry, S. Mallat and G. Papanicolaou, "A Wavelet Based Space-Time Adaptive Numerical Method for Partial Differential Equations"
• G. Beylkin and N. Coult, "A Multiresolution Strategy for Reduction of Elliptic PDE's and Eigenvalue Problems."
• G. Beylkin and J. H. Keiser, "On the Adaptive Numerical Solution of Nonlinear Partial Differential Equations in Wavelet Bases."
• D. M. Bond and S. A. Vavasis, "Fast Wavelet Transforms for Matrices Arising From Boundary Element Methods."
• T. Chan, W. Tang and W. Wan, .
• P. Charton and V. Perrier, "Factorisation sur Bases d'Ondelettes du Noyeau de la Chaleur et Algorithmes Matriciels Rapides Associes."
• P. Charton and V. Perrier, "Towards a Wavelet Based Numerical Scheme for the Two-Dimensional Navier-Stokes Equations."
• P. Charton and V. Perrier, "A Pseudo-Wavelet Scheme for the Two-Dimensional Navier-Stokes Equations."
• S. Dahlke and A. Kunoth, "Biorthogonal Wavelets and Multigrid."
• S. Dahlke and I. Weinreich, "Wavelet-Galerkin Methods: An Adapted Biorthogonal Wavelet Basis."
• S. Dahlke and I. Weinreich, "Wavelet Bases Adapted to Pseudo-Differential Operators."
• W. Dahmen and A. Kunoth, "Multilevel Preconditioning."
• W. Dahmen, A. Kunoth and K. Urban "A Wavelet-Galerkin Method for the Stokes-Equations," also full version with pictures.
• 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"
• A. Jiang, .
• J. H. Keiser, "On I. Wavelet Based Approach to Numerical Solution on Nonlinear Partial Differential Equations and II. Nonlinear Waves in Fully Discrete Dynamical Systems."
• A. Kunoth, "Multilevel Preconditioning -- Appending Boundary Conditions by Lagrange Multipliers."
• G. Leaf and J. M. Restrepo, "Wavelet-Galerkin Discretization of Hyperbolic Equations."
• J. Lewalle, "Wavelet Transforms of some Equations of Fluid Mechanics"
• J. Lewalle, "Energy Dissipation in the Wavelet-Transformed Navier-Stokes Equations"
• J. Lewalle, "On the effect of boundary conditions on the multifractal statistics of incompressible turbulence"
• J. Lewalle, "Diffusion is Hamiltonian".
• J. Lewalle, "Gaussian Wavelets as Green's functions".
• D. Lu, T. Ohyoshi and L. Zhu, "Treatment of Boundary Conditions in the Application of Wavelet-Galerkin Method to a SH Wave Problem"
• P. Monasse and V. Perrier, "Orthonormal Wavelet Bases Adapted for Partial Differential Equations with Boundary Conditions."
• 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"
• K. Urban, "A Wavelet-Galerkin Algorithm for the Driven-Cavity-Stokes-Problem in Two Space Dimensions."
• 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."
• P. Charton and V. Perrier, "Produits Rapides Matrices-Vecteur en Bases d'Ondelettes: Application a la Resolution Numerique d'Equation aux Derivees Partielles."
• P. Charton, "Produits de Matrices Rapides en Bases d'Ondelettes: Application a la Resolution Numerique d'Equation aux Derivees Partielles."
• N. H. Getz, "A Fast Discrete Periodic Wavelet Transform." An associated toolbox of Matlab routines is also available.
• L. Jameson, "On the Spline-Based Wavelet Differentiation Matrix."
• L. Jameson, "On the Differention Matrix for Daubechies-Based Wavelets on an Interval."
• L. Jameson, "On the Daubechies-Based Wavelet Differentiation Matrix."
• L. Jameson, "On the Wavelet Optimized Finite Difference Method."
• 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." An abstract is also available.
• R. Piessens and W. Sweldens, "Asymptotic Error Expansion of Wavelet Approximations of Smooth Functions II." An abstract is also available.
• 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

• E. H. Adelson and E. P. Simoncelli, "Noise Removal via Bayesian Wavelet Coring."
• A. G. Bruce, D. L.Donoho, H. Gao and R. D. Martin, "Denoising and Robust Non-linear Wavelet Analysis."
• A. G. Bruce and H. Gao, "WaveShrink: Shrinkage Functions and Thresholds."
• A. G. Bruce and H. Gao, "WaveShrink with Semisoft Shrinkage."
• A. G. Bruce and H. Gao, "Understanding WaveShrink: Variance and Bias Estimation."
• A. G. Bruce, H. Gao and D. Ragozin, "S+WAVELETS: An Object-Oriented Toolkit for Wavelet Analysis."
• A. G. Bruce and H. Gao, "S+WAVELETS: Algorithms and Technical Details."
• J. Buckheit and D. Donoho, "WaveLab and Reproducible Research."
• R. Coifman and N. Saito, "Local Discriminant Bases."
• R. Coifman and F. Majid, "Adapted Waveform Analysis and Denoising."
• R. Coifman and D. Donoho, "Translation-Invariant De-Noising."
• A. Davis, A. Marshak and W. Wiscombe, "Wavelet-Based Multifractal Analysis of Non-Stationary and/or Intermittent Geophysical Signals." with figures.
• B. Deylon and A. Juditsky, "Wavelet Estimators. Global Error Mesures Revisited."
• D. Donoho, "Nonlinear Solution of Linear Inverse Problems by Wavelet-Vaguelette Decomposition"
• Dl  D. Donoho, "Smooth Wavelet Decompositions with Blocky Coefficient Kernels"
• Dl  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"
• Dl  D. Donoho and I. Johnstone, "Adapting to Unknown Smoothness by Wavelet Shrinkage"
• Dl  D. Donoho and I. Johnstone, "Ideal Spatial Adaptation via Wavelet Shrinkage"
• Dl  D. Donoho and I. Johnstone, "Minimax Estimation via Wavelet Shrinkage"
• Dl  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"
• Dl  D. Donoho, I. Johnstone, G. Kerkyacharian and D. Picard, "Wavelet Shrinkage: Asymptopia?"
• Dl  D. Donoho and I. Johnstone, "Ideal Denoising in an Orthonormal Basis Chosen From a Library of Bases."
• H. Y. Gao, "Choice of Thresholds for Wavelet Shrinkage Estimate of the Spectrum."
• P. Goel and B. Vidakovic, "Wavelet Transformations as Diversity Enhancers"
• I. Johnstone, "Minimax Bayes, Asymptotic Minimax and Sparse Wavelet Priors"
• I. M. Johnstone and B. W. Silverman, "Wavelet Threshold Estimators for Data with Correlated Noise."
• A. Juditsky, "Wavelet Estimators. Adapting To Unkown Smoothness."
• A. Juditsky and F. Leblanc, "Computing Wavelet Density Estimators for Stochastic Processes."
• G. Katul and B. Vidakovic, "Partitioning eddy motion using Lorentz wavelet filtering."
• P. Moulin, "Wavelet Thresholding Techniques for Power Spectrum Estimation."
• G.P. Nason and B. W. Silverman, "The Discrete Wavelet Transform in S."
• G.P. Nason and B. W. Silverman, "the Stationary Wavelet Transform and some Statistical Applications."
• G.P. Nason, "Wavelet Regression by Cross-Validation"
• A. B. Owen, "Monte Carlo Variance of Scrambled Equidistribution Quadrature."
• D. B. Percival, "On the Estimation of the Wavelet Variance."
• A. Pinheiro and B. Vidakovic, "Estimating the Square Root of a Density Via Compactly Supported Wavelets."
• N. Saito, "Local Feature Extraction and Its Appplications Using a Library of Bases."
• 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."
• A. T. Walden, D. B. Percival and E. J. McCoy, "Spectrum Estimation by Wavelet Thresholding of Multitaper Estimators."
• 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."
• M. J. Jensen, "OLS Estimate of the Fractional Differencing Parameter Using Wavelets Derived From Smoothing Kernels."

Wavelets and Fractals

• A. Davis, A. Marshak and W. Wiscombe, "Wavelet-Based Multifractal Analysis of Non-Stationary and/or Intermittent Geophysical Signals." with figures.
• C. Jones, 2-D Wavelet Packet Analysis of Structural Self-Organization and Morphogenic Regulation in Filamentous Fungal Colonies.
• J. Lewalle, "Wavelet Transforms of the Navier-Stokes Equations and the Generalized Dimensions of Turbulence"
• W. Hwang and S. Mallat, "Characterization of Self-Similar Multifractals with Wavelet Maxima."

Wavelets and Communication Theory

• J. Dill and A. R. Lindsey, "Wavelet Packet Modulation: A Generalized Method for Orthogonally Multiplexed Communication."
• R. Learned, H. Krim, B. Claus, A. S. Willsky, and W. C. Karl, "Wavelet-Packet-Based Multiple Access Communication."
• A. R. Lindsey, "Multidimensional Signaling via Wavelet Packets."
• A. R. Lindsey, Generalized Orthogonally Multiplexed Communication via Wavelet Packet Bases, chapter 1, chapter 2, chapter 3, chapter 4, chapter 5, chapter 6. Also with appendix and references.

Wavelets and Computer Graphics

• M. Cohen, S. Gortler, P. Hanrahan and P. Schröder, "Wavelet Radiosity." With figure 12 and figure 14 .
• M. Cohen, S. Gortler, P. Hanrahan and P. Schröder, "Wavelet Projections for Radiosity."
• A. Dreger, M. H. Gross R. Koch and L. Lippert, "A New Method to Approximate the Volume Rendering Equation using Wavelet Bases and Piecewise Polynomials," with figures 5-6, figures 7-10, and figures 11-13. Also abstract available. Technical Report No. 220, Computer Science Department, ETH Zürich, 1994.
• A. Fournier, "Wavelets and their Applications in Computer Graphics." This is 2.5 MB compressed.
• M. H. Gross and L. Lippert, "Fast Wavelet Based Volume Rendering by Accumulation of Tranparent Texture Maps." With figure 6, figure 7, figure 8, figure 9, figure 10 and figure 11. Also abstract available. Technical Report No. 228, Computer Science Department, ETH Zürich, 1995.
• M. H. Gross and R. Koch, "Visualization of Multidimensional Shape and Texture Features in Laser Range Data using Complex-Valued Gabor Wavelets."
• M. H. Gross and L. Lippert, "Ray-tracing of Multiresolution B-Spline Volumes." Also abstract available. Technical Report No. 239, Computer Science Department, ETH Zürich, 1996.
• P. Hanrahan and P. Schröder, "Wavelet Methods for Radiance Computations." With figure 8, figure 9 left, figure 9 right, figure 10, figure 10 top left and figure 10 top right.
• C. Herley, "Exact Interpolation and Iterative Subdivision Schemes."
• P. Schröder, W. Sweldens and D. Zorin, "Interpolating Subdivision for Meshes with Arbitrary Topology". An abstract is also available.

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."
• Dl  J. C. Cohen and T. Chen, "Fundamentals of the Discrete Wavelet Transform for Seismic Data Processing."
• A. Fournier, "Wavelet Analysis of Observed Geopotential and Wind: Blocking and Local Energy Coupling Across Scales."
• A. Fournier, "Wavelet Multiresolution Analysis of Numerically Simulated 3d Radiative Convection."
• A. Fournier, "Wavelet Representation of Lower-Atmospheric Long Nonlinear Wave Dynamics, Governed by the Benjamin-Davis-Ono-Burgers Equation."
• F. Hermann, "A scaling medium representation, a discussion on well-logs, fractals and waves." An abstract is also available.
• I. Pierce and L. Watkins, "Modelling optical pulse propagation in nonlinear media using wavelets."
• W. C. Shann, "Finite Element Methods for Maxwell's Equations with Stationary Magnetic Fields and Galerkin-wavelet Methods for Two Point Boundary Value Problems," with separate abstract and table of contents.
• L. R. Watkins and Y. R. Zhou, "Modelling Propagation in Optical Fibres using Wavelets."
• Dl  R. O. Wells, "Adaptive Wave Propogation Modelling."
• L. Zubair, "Studies in Turbulence using Wavelet Transforms for Data Compression and Scale-Separation."

Hardware and Software 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."
• J. Lu, "Computation of 2-D Wavelet Transform on the Massively Parallel Computer for Image Processing."

This page was modified October 23, 1997
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