Wavelet Resources
Acknowledgment: This page was copied from Wavelet Resources on August 9, 1995.
Introductions to Wavelets
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C. S. Burrus and R. A. Gopinath,
"A Tutorial Overview of Wavelets, Filter Banks and Interrelationships"
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R. DeVore and B. Lucier,
"Wavelets."
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T. Edwards,
"Discrete Wavelet Transforms: Theory and Application."
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E. Gootman and M. Wickerhauser,
"Elementary Wavelets."
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A. Graps,
"An Introduction To Wavelets."
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B. Jawerth and W. Sweldens,
"An Overview of Wavelet Based Multiresolution Analysis."
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P. Schroeder and W. Sweldens,
"Building Your Own Wavelets at Home."
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B. Vidakovic,
"Wavelets for Kids," also
part 2.
General Theory
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L. Andersson, N. Hall, B. Jawerth and G. Peters,
"Wavelets on Closed Subsets of the Real Line"
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P. Auscher, G. Weiss and M. V. Wickerhauser,
"Local Sine and Cosine Bases of Coifman and
Meyer and the Construction of Smooth Wavelets"
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G. Beylkin and N. Saito,
"Multiresolution Representations using the Autocorrelation Functions of Compactly
Supported Wavelets."
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G. Beylkin and N. Saito,
"Wavelets, their Autocorrelation Functions and Multiresolution Analysis of Signals."
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G. Beylkin and B. Torrésani,
"Implementation of Operators via Filter Banks, Autocorrelation Shell and Hardy Wavelets."
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D. Chen,
"Extended Families of Cardinal Spline Wavelets."
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D. Chen,
"Spline Wavelets of Small Support."
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D. Chen,
"Characterization of Biorthogonal Cardinal Spline Wavelet Bases."
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D. Chen,
"Cardinal Spline Wavelets", dissertation. Also
part 2,
part 3,
part 4,
part 5 and
part 6.
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S. Chen and D. Donoho,
"Atomic Decomposition by Basis Pursuit."
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A. Cohen, W. Dahmen and R. DeVore,
"Multiscale Decompositions on Bounded Domains."
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J. Cohen,
"The Foot Problem in Wavelet Packet Splitting." A Mathematica notebook converted to Postscript.
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J. Cohen,
"Schauder Basis for [0,1]." A Mathematica notebook converted to Postscript.
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J. Cohen,
"The Littlewood-Paley-Stein Wavelet." A Mathematica notebook converted to Postscript.
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J. Cohen,
"Battle-Lemarie Wavelets." A Mathematica notebook converted to Postscript.
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J. Cohen,
"The Daubechies Minimum Phase Wavelets." A Mathematica notebook converted to Postscript.
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J. Cohen,
"Meyer Wavelets." A Mathematica notebook converted to Postscript.
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R. Coifman and M. V. Wickerhauser,
"Entropy-Based Algorithms for Best Basis Selection"
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R. Coifman and M. Wickerhauser,
"Best-adapted Wave Packet Bases."
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R. Coifman(?),
"Numerical Harmonic Analysis."
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R. Coifman, Y. Meyer and M. Wickerhauser,
"Size Properties of Wavelets Packets."
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R. Coifman and Y. Meyer,
"Orthonormal Wave Packet Bases."
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R. Coifman and M. V. Wickerhauser,
"Wavelets and Adapted Waveform Analysis"
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R. Coifman, Y. Meyer and M. Wickerhauser,
"Adapted Wave Form Analysis, Wavelet
Packets and Applications."
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D. Colella and C. Heil,
"Matrix Refinement Equations: Existence and Accuracy."
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S. Dahlke, W. Dahmen, E. Schmitt and I. Weinreich,
Multiresolution Analysis and Wavelets on S^2 and S^3."
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G. Davis, S. Mallat and Z. Zhang,
"Adaptive Nonlinear Approximations."
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G. Davis,
"Adaptive Nonlinear Approximations."
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G. Davis, S. Mallat and Z. Zhang,
"Adaptive Time-Frequency Approximations with Matching Pursuits."
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C. deBoor, R. DeVore and R. Amos,
"On the Construction of Multivariate (Pre)Wavelets."
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R. L. deQueiroz,
"On Lapped Transforms."
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M. Girardi and W. Sweldens,
"A New Class of Unbalanced Haar Wavelets That Form an Unconditional Basis for Lp on
General Measure Spaces."
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B. Jawerth and W. Sweldens,
"Weighted Multiwavelets on General Domains."
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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.
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C. Heil, G. Strang and V. Strela,
"Approximation By Translates of Refinable Functions."
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C. Heil and G. Strang,
"Continuity of the Joint Spectral Radius: Application to Wavelets."
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B. Jawerth and W. Sweldens,
"Biorthogonal Smooth Local Trigonometric Bases."
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M. K. Kwong and P. T. Peter Tang,
"W-Matrices, Nonorthogonal Multiresolution Analysis and Finite Signals of Arbitrary
Length."
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G. Leaf, J. M. Restrepo and G. Schlossnagle,
"Periodized Daubechies Wavelets."
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J. Lippus,
"Wavelet Coefficients of Functions of Generalized Lipschitz Classes."
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S. Mallat and Z. Zhang,
"Matching Pursuit with Time-Frequency Dictionaries."
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R. Piessens and W. Sweldens,
"Wavelet Sampling Techniques."
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M. J. Shensa,
"An Inverse DWT for Nonorthogonal Wavelets"
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W. Sweldens,
"Compactly Supported Wavelets which are Biorthogonal to a Weighted Inner Product."
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W. Sweldens,
"The Lifting Scheme: A Custom-Design Construction of Biorthogonal Wavelets."
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W. Sweldens,
"The Lifting Scheme: A Construction of Second Generation Wavelets."
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B. Suter and X. Xia,
"Vector Valued Wavelets and Vector Filter Banks."
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C. Taswell,
"Wavelet Transform Algorithms for Finite Duration Discrete-Time Signals."
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C. Taswell,
"Near-Best Basis Selection Algorithms with Non-Additive Information Cost Functions."
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R. O. Wells Jr.,
"Recent Advances in Wavelet Technology"
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vM. Wickerhauser(?),
"Entropy of a Vector Relative to a Decomposition."
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M. V. Wickerhauser,
"Lectures on Wavelet Packet Algorithms"
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M. V. Wickerhauser,
"Smooth Localized Orthonormal Bases"
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V. Zavadsky,
"Multiresolution Approximations of Banach Spaces."
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V. Zavadsky,
"Wavelet Approximation of Sampled Functions."
Frame Decompositions
M-Band Wavelets and Filter Banks
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C. S. Burrus and R. A. Gopinath,
"On the Correlation Structure of Multiplicity M Scaling Functions"
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C. S. Burrus and R. A. Gopinath,
"Wavelets and Filter Banks"
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C. S. Burrus and R. A. Gopinath,
"Unitary FIR Filter Banks and Symmetry"
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C. S. Burrus and R. A. Gopinath,
"Theory of Modulated Filter Banks and Modulated Wavelet Tight Frames"
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C. S. Burrus and R. A. Gopinath,
"Factorization Approach to Time-Varying Unitary Filter Bank Trees and Wavelets"
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R. Gopinath,
"Wavelets and Filter Banks - New Results and Applications."
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C. Herley,
"Boundary Filters for Finite-Length Signals and Time-Varying Filter Banks."
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P. Steffen, P. Heller, R. A. Gopinath and C. S. Burrus,
"The Theory of Regular M-Band Wavelets"
Wavelets and General Signal Processing
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C. S. Burrus and R. A. Gopinath,
"Wavelet-Based Lowpass/Bandpass Interpolation"
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C. S. Burrus, R. A. Gopinath and J. E. Odegard,
"Design of Linear Phase Cosine Modulated Filter Banks for Subband Image Compression"
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S. Cabrera, V. Krienovich and O. Sirisaengtaksin,
"Wavelets Compress Better Than All Other Methods: A 1-D Theorem."
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S. Cabrera, V. Krienovich and O. Sirisaengtaksin,
"Wavelet Nerual Networks are Optimal Approximators for Functions of One Variable."
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R. Carmona, W. L. Hwang and B. Torresani,
"Characterization of Signals by the Ridges of Their Wavelet Transforms."
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R. Carmona, W. L. Hwang and B. Torresani,
"Multi-Ridge Detection and Time-Frequency Reconstruction."
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R. Coifman,
"Adapted Multiresolution Analysis, Computation, Signal Processing and Operator Theory"
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R. Coifman, Y. Meyer, S. Quake and M. Wickerhauser,
"Signal Processing and Compression with
Wave Packets."
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R. Coifman, Y. Meyer and M. V. Wickerhauser,
"Wavelet Analysis and Signal Processing"
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M. Goldburg,
"Applications of Wavelets to Quantization and Random Process Representations." About 1.1 MB.
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D. M. Healy, Jr., J. Lu and J. B. Weaver,
"Signal Recovery and Wavelet Reproducing Kernels."
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D. M. Healy, Jr., J. Lu, J. B. Weaver and Y. Xu,
"Noise Reduction With Multiscale Edge Representation and Perceptual Criteria."
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D. M. Healy, Jr. and J. Lu,
"Contrast Enhancement via Multiscale Gradient Transformations."
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W. Hwang and S. Mallat,
"Singularity Detection and Processing with Wavelets."
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B Jawerth, Y. Liu and W. Sweldens,
"Signal Compression with Smooth Local Trigonometric Bases."
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M. M. Lankhorst and M. D. van der Laan,
"Wavelet-Based Signal Approximation with Genetic Algorithms."
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G. Uytterhoeven,
"Design and Implementation of Compression Algorithms using Multiwavelets."
Wavelets and Image Processing
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E. Adelson and E. Simoncelli,
"Subband Image Coding with Three-tap Pyramids."
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V.R. Algazi, R.R. Estes and J. Lu,
"Comparison of wavelet image coders using the Picture Quality Scale (PQS)."
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M. Bhatia, W. C. Karl, and A. S. Willsky,
"A Wavelet-Based Method for
Multiscale Tomographic Reconstruction."
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M. Bhatia, W. C. Karl, and A. S. Willsky,
"Using Natural Wavelet Bases
and Multiscale Stochastic Models for Tomographic Reconstruction."
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A. Bijaoui, B. Lopez, C. Perrier and J. L. Stark,
"Image Reconstruction by the Wavelet Transform Applied to Aperture Synthesis."
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A. Bijaoui, F. Murtagh and J. L. Stark,
"Image Restoration with Noise Suppression Using a Wavelet Transform and a Multiresolution
Support Constraint," with
figures.
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A. Bijaoui, F. Murtagh and J. L. Stark,
"Restauration des Images Multi-Echelles par l'Algorithm a Trous." Be forwarned: this is 4 MB.
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A. Bijaoui, F. Murtagh and J. L. Stark,
"Multiresolution Support Applied to Image Filtering and Restoration."
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A. Bijaoui, F. Murtagh and J. L. Stark,
"Multiresolution and Astronomical Image Processing."
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A. Bijaoui, F. Murtagh and J. L. Stark,
"Image Restoration with Noise Suppression Using a Multiresolution Analysis Support."
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A. Bijaoui, F. Murtagh ,J. L. Stark and W. Zeilinger,
"Object Detection Using Multiresolution Analysis."
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R. A. Carmona, R. D. Frostig and W. L. Hwang,
"Wavelet Analysis for Brain Function Imaging."
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B. Deng, B. D. Jawerth, G. Peters and W. Sweldens,
"Wavelet Probing for Compression Based Segmentation".
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J. Fan and A. Laine,
"An Adaptive Approach for Texture Segmentation by Multi-Channel Wavelet Frames.".
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D. M. Healy, Jr., J. Lu and J. B. Weaver,
"Contrast Enhancement of Medical Images Using Multiscale Edge Representation."
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M. L. Hilton, B. D. Jawerth and A. Sengupta,
"Compressing Still and Moving Images with Wavelets" with
figure.
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P. Kovesi,
"Image Features from Phase Congruency"
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B. Lin,
"Wavelet Phase Filter for Denoising Tomographic Image Reconstruction"
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M. Louys, F. Murtagh and J. L. Stark,
"Astronomical Image Compression Using the Pyramidal Median Transform." Also
summary version.
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P. Moulin,
"A Multiscale Relaxation Algorithm for SNR Maximization in 2-D
Nonorthogonal Subband Coding."
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F. Murtagh and J. L. Stark,
"Multiresolution Image Analysis Using Wavelets."
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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.
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P. Schroeder and W. Sweldens,
"Spherical wavelets: Efficiently representing functions on the sphere."
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P. Schroeder and W. Sweldens,
"Spherical Wavelets: Texture Processing."
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G. Weiss,
"Time-Frequency and Time-Scaling Methods in Signal and Image Processing"
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M. Wickerhauser,
"Picture Compression by Best-Basis Subband Coding."
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M. V. Wickerhauser,
"High-Resolution Still Picture Compression"
The FBI Wavelet Fingerprint Compression Standard
Wavelets and Speech Processing
Wavelets and Ordinary Differential Equations
Wavelets and Partial Differential Equations
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E. Bacry, S. Mallat and G. Papanicolaou,
"A Wavelet Based Space-Time Adaptive Numerical Method for Partial Differential
Equations"
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D. M. Bond and S. A. Vavasis,
"Fast Wavelet Transforms for Matrices Arising From Boundary Element Methods."
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R. Glowinski, T. Pan , R. O. Wells, Jr. and X. Zhou,
"Wavelet and Finite Element Solutions for the Neumann Problem Using
Fictitious Domains"
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R. Glowinski, A. Rieder, R. O. Wells, Jr. and X. Zhou,
"A Wavelet Multigrid
Preconditioner for Dirichlet Boundary Value Problems in General Domains."
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R. Glowinski, A. Rieder, R. O. Wells, Jr. and X. Zhou,
"A Preconditioned CG-Method for Wavelet-Galerkin Discretizations of Elliptic
Problems"
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F. Heurtaux, F. Planchon and M. V. Wickerhauser,
"Scale Decomposition in Burgers' Equation"
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G. Leaf and J. M. Restrepo,
"Wavelet-Galerkin Discretization of Hyperbolic Equations."
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A. Rieder and X. Zhou,
"On the Robustness of the Damped V-Cycle of the Wavelet Frequency Decompositions
Multigrid Method"
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A. Rieder, R. O. Wells, Jr. and X. Zhou,
"A Wavelet Approach to Robust Multilevel
Solvers for Anisotropic Elliptic Problems."
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A. Rieder, R. O. Wells, Jr. and X. Zhou,
"On the Wavelet Frequency Decomposition Method"
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R. O. Wells, Jr. and X. Zhou,
"Wavelet Solutions for the Dirichlet Problem"
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R. O. Wells, Jr. and X. Zhou,
"Wavelet Interpolation and Approximate Solution of Elliptic Partial Differential
Equations"
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R. O. Wells, Jr. and X. Zhou,
"Representing the Geometry of Domains by Wavelets with Applications
to Partial Differential Equations"
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R. O. Wells, Jr.,
"Multiscale Applications of Wavelets to Solutions of Partial Differential
Equations"
Wavelets and Numerical Analysis
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G. Beylkin, R. Coifman and V. Rokhlin,
"Fast Wavelet Transforms and Numerical
Algorithms I."
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G. Beylkin,
"On the Representation of Operators in Bases of Compactly Supported Wavelets."
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G. Beylkin,
"On the Fast Algorithm for Multiplication of Functions in the Wavelet Bases."
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G. Beylkin,
"Wavelets and Fast Numerical Algorithms." Lecture notes for an AMS short course, 1993.
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G. Beylkin,
"Wavelets, Multiresolution Analysis and Fast Numerical Algorithms." Draft of INRIA lectures,
May 1991.
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G. Beylkin and M. E. Brewster,
"A Multiresolution Strategy for Numerical Homogenization."
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L. Jameson,
"On the Spline-Based Wavelet Differentiation Matrix."
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L. Jameson,
"On the Differention Matrix for Daubechies-Based Wavelets on an Interval."
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L. Jameson,
"On the Daubechies-Based Wavelet Differentiation Matrix."
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L. Jameson,
"On the Wavelet Optimized Finite Difference Method."
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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.
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R. Piessens and W. Sweldens,
"Quadrature Formulae and Asymptotic Error Expansion of Wavelet Approximations
of Smooth Functions."
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R. Piessens and W. Sweldens,
"Asymptotic Error Expansion of Wavelet Approximations of Smooth Functions II."
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W. C. Shann,
"Quadratures Involving Polynomials and Daubechies' Wavelets."
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W. Sweldens,
"Construction and Application of Wavelets in Numerical Analysis."
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M. Wickerhauser,
"Nonstandard Matrix Multiplication."
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M. V. Wickerhauser,
"Computation with Adapted Time-Frequency Atoms"
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M. V. Wickerhauser,
"Wavelet Approximations to Jacobians and the Inversion of Complicated
Maps"
Wavelets and Statistics
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J. Buckheit and D. Donoho,
"WaveLab and Reproducible Research."
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R. Coifman and N. Saito,
"Local Discriminant Bases."
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R. Coifman and F. Majid,
"Adapted Waveform Analysis and Denoising."
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R. Coifman and D. Donoho,
"Translation-Invariant De-Noising."
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A. Davis, A. Marshak and W. Wiscombe,
"Wavelet-Based Multifractal Analysis of
Non-Stationary and/or Intermittent Geophysical Signals."
with
figures.
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B. Deylon and A. Juditsky,
"Wavelet Estimators. Global Error Mesures Revisited."
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D. Donoho,
"Nonlinear Solution of Linear Inverse Problems by
Wavelet-Vaguelette Decomposition"
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D. Donoho,
"Smooth Wavelet Decompositions with Blocky Coefficient Kernels"
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D. Donoho,
"De-noising by Soft Thresholding"
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D. Donoho,
"Interpolating Wavelet Transforms"
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D. Donoho,
"Unconditional Bases are Optimal Bases for Data Compression and for
Statistical Estimation"
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D. Donoho and I. Johnstone,
"Adapting to Unknown Smoothness by Wavelet Shrinkage"
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D. Donoho and I. Johnstone,
"Ideal Spatial Adaptation via Wavelet Shrinkage"
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D. Donoho and I. Johnstone,
"Minimax Estimation via Wavelet Shrinkage"
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D. Donoho and I. Johnstone,
"Minimax Risk over l_p Balls"
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D. Donoho, I. Johnstone, G. Kerkyacharian and D. Picard,
"Density Estimation via Wavelet Shrinkage"
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D. Donoho, I. Johnstone, G. Kerkyacharian and D. Picard,
"Wavelet Shrinkage: Asymptopia?"
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D. Donoho and I. Johnstone,
"Ideal Denoising in an Orthonormal Basis Chosen From a Library of Bases."
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H. Y. Gao,
"Choice of Thresholds for Wavelet Shrinkage Estimate of the Spectrum."
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P. Goel and B. Vidakovic,
"Wavelet Transformations as Diversity Enhancers"
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I. Johnstone,
"Minimax Bayes, Asymptotic Minimax and Sparse Wavelet Priors"
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I. M. Johnstone and B. W. Silverman,
"Wavelet Threshold Estimators for Data with Correlated Noise."
-
A. Juditsky,
"Wavelet Estimators. Adapting To Unkown Smoothness."
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A. Juditsky and F. Leblanc,
"Computing Wavelet Density Estimators for Stochastic Processes."
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G. Katul and B. Vidakovic,
"Partitioning eddy motion using Lorentz wavelet filtering."
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P. Moulin,
"Wavelet Thresholding Techniques for Power Spectrum Estimation."
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G.P. Nason and B. W. Silverman,
"The Discrete Wavelet Transform in S."
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G.P. Nason and B. W. Silverman,
"the Stationary Wavelet Transform and some Statistical Applications."
-
G.P. Nason,
"Wavelet Regression by Cross-Validation"
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A. B. Owen,
"Monte Carlo Variance of Scrambled Equidistribution Quadrature."
-
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."
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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
Wavelets and Fractals
Wavelets and Communication Theory
Wavelets and Computer Graphics
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A. Fournier,
"Wavelets and their Applications in Computer Graphics." This is 2.5 MB compressed.
-
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.
-
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.
-
M. H. Gross and R. Koch,
"Visualization of Multidimensional Shape and Texture Features in Laser Range
Data using Complex-Valued Gabor Wavelets."
-
C. Herley,
"Exact Interpolation and Iterative Subdivision Schemes."
Wavelets and Physics
Hardware and Software Implementation of Wavelet Transforms