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Wavelets: tools for science & technology

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Bibliographic Details
Previous Title:	Meyer, Yves Wavelets
Main Authors:	Jaffard, Stéphane (Author), Meyer, Yves (Author), Ryan, Robert D. (Author)
Format:	Book
Language:	English
Published:	Philadelphia Soc. for Industrial and Applied Mathematics 2001
Edition:	Rev. ed.
Subjects:	Ondelettes Wavelets Wavelets (Mathematics) Wavelet
Online Access:	Inhaltsverzeichnis
Physical Description:	XIII, 256 S. graph. Darst.
ISBN:	0898714486

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MARC


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adam_text	WAVELETS TOOLS FOR SCIENCE & TECHNOLOGY STEPHANE JAFFARD UNIVERSITE PARIS XII INSTITUT UNIVERSITAIRE DE FRANCE YVES MEYER ECOLE NORMALE SUPERIEURE DE CACHAN ACADEMIE DES SCIENCES ROBERT D. RYAN PARIS, FRANCE EIAJTL SOCIETY FOR INDUSTRIAL AND APPLIED MATHEMATICS PHILADELPHIA CONTENTS PREFACE TO REVISED EDITION IX PREFACE FROM THE FIRST EDITION XIII CHAPTER 1. SIGNALS AND WAVELETS 1 1.1 WHAT IS A SIGNAL? 1 1.2 THE LANGUAGE AND GOALS OF SIGNAL AND IMAGE PROCESSING 2 1.3 STATIONARY SIGNALS, TRANSIENT SIGNALS, AND ADAPTIVE CODING 6 1.4 GROSSMANNMORLET TIME-SCALE WAVELETS 8 1.5 TIME-FREQUENCY WAVELETS FROM GABOR TO MALVAR AND WILSON 9 1.6 OPTIMAL ALGORITHMS IN SIGNAL PROCESSING 10 1.7 OPTIMAL REPRESENTATION ACCORDING TO MARR 12 1.8 TERMINOLOGY 13 1.9 READER S GUIDE 13 CHAPTER 2. WAVELETS FROM A HISTORICAL PERSPECTIVE 15 2.1 INTRODUCTION 15 2.2 FROM FOURIER (1807) TO HAAR (1909), FREQUENCY ANALYSIS BECOMES SCALE ANALYSIS 16 2.3 NEW DIRECTIONS OF THE 1930S: PAUL LEVY AND BROWNIAN MOTION .... 20 2.4 NEW DIRECTIONS OF THE 1930S: LITTLEWOOD AND PALEY 21 2.5 NEW DIRECTIONS OF THE 1930S: THE FRANKLIN SYSTEM 23 2.6 NEW DIRECTIONS OF THE 1930S: THE WAVELETS OF LUSIN 25 2.7 ATOMIC DECOMPOSITIONS FROM 1960 TO 1980 26 2.8 STROMBERG S WAVELETS 28 2.9 A FIRST SYNTHESIS: WAVELET ANALYSIS 29 2.10 THE ADVENT OF SIGNAL PROCESSING 31 2.11 CONCLUSIONS 32 CHAPTER 3. QUADRATURE MIRROR FILTERS 35 3.1 INTRODUCTION 35 3.2 SUBBAND CODING: THE CASE OF IDEAL FILTERS 36 3.3 QUADRATURE MIRROR FILTERS 37 3.4 TREND AND FLUCTUATION 40 3.5 THE TIME-SCALE ALGORITHM OF MALLAT AND THE TIME-FREQUENCY ALGORITHM OF GALAND 40 3.6 TRENDS AND FLUCTUATIONS WITH ORTHONORMAL WAVELET BASES 42 VI CONTENTS 3.7 CONVERGENCE TO WAVELETS 43 3.8 THE WAVELETS OF DAUBECHIES 46 3.9 CONCLUSIONS 46 CHAPTER 4. PYRAMID ALGORITHMS FOR NUMERICAL IMAGE PROCESSING 49 4.1 INTRODUCTION 49 4.2 THE PYRAMID ALGORITHMS OF BURT AND ADELSON 50 4.3 EXAMPLES OF PYRAMID ALGORITHMS 54 4.4 PYRAMID ALGORITHMS AND IMAGE COMPRESSION 55 4.5 PYRAMID ALGORITHMS AND MULTIRESOLUTION ANALYSIS 57 4.6 THE ORTHOGONAL PYRAMIDS AND WAVELETS 58 4.7 BIORTHOGONAL WAVELETS 63 CHAPTER 5. TIME-FREQUENCY ANALYSIS FOR SIGNAL PROCESSING 67 5.1 INTRODUCTION 67 5.2 THE COLLECTIONS F2 OF TIME-FREQUENCY ATOMS 69 5.3 MALLAT S MATCHING PURSUIT ALGORITHM 71 5.4 BEST-BASIS SEARCH 72 5.5 THE WIGNER-VILLE TRANSFORM 72 5.6 PROPERTIES OF THE WIGNER-VILLE TRANSFORM 74 5.7 THE WIGNER-VILLE TRANSFORM AND PSEUDODIFFERENTIAL CALCULUS 76 5.8 RETURN TO THE DEFINITION OF TIME-FREQUENCY ATOMS 79 5.9 THE WIGNER-VILLE TRANSFORM AND INSTANTANEOUS FREQUENCY 79 5.10 THE WIGNER-VILLE TRANSFORM OF ASYMPTOTIC SIGNALS 81 5.11 INSTANTANEOUS FREQUENCY AND THE MATCHING PURSUIT ALGORITHM . . . . 83 5.12 MATCHING PURSUIT AND THE WIGNER-VILLE TRANSFORM 84 5.13 SEVERAL SPECTRAL LINES 85 5.14 CONCLUSIONS 86 5.15 HISTORICAL REMARKS 86 CHAPTER 6. TIME-FREQUENCY ALGORITHMS USING MALVARWILSON WAVELETS 89 6.1 INTRODUCTION 89 6.2 MALVAR-WILSON WAVELETS: A HISTORICAL PERSPECTIVE 90 6.3 WINDOWS WITH VARIABLE LENGTHS 92 6.4 MALVAR-WILSON WAVELETS AND TIME-SCALE WAVELETS 94 6.5 ADAPTIVE SEGMENTATION AND THE SPLIT-AND-MERGE ALGORITHM 95 6.6 THE ENTROPY OF A VECTOR WITH RESPECT TO AN ORTHONORMAL BASIS . . . . 96 6.7 THE ALGORITHM FOR FINDING THE OPTIMAL MALVAR-WILSON BASIS 97 6.8 AN EXAMPLE WHERE THIS ALGORITHM WORKS 99 6.9 THE DISCRETE CASE 99 6.10 MODULATED MALVAR-WILSON BASES 100 6.11 EXAMPLES 102 6.12 CONCLUSIONS 104 CHAPTER 7. TIME-FREQUENCY ANALYSIS AND WAVELET PACKETS 105 7.1 HEURISTIC CONSIDERATIONS 105 7.2 THE DEFINITION OF BASIC WAVELET PACKETS 108 7.3 GENERAL WAVELET PACKETS ILL 7.4 SPLITTING ALGORITHMS 112 CONTENTS VII 7.5 CONCLUSIONS 114 CHAPTER 8. COMPUTER VISION AND HUMAN VISION 117 8.1 MARR S PROGRAM 117 8.2 THE THEORY OF ZERO-CROSSINGS 120 8.3 A COUNTEREXAMPLE TO MARR S CONJECTURE 121 8.4 MALLAT S CONJECTURE 122 8.5 THE TWO-DIMENSIONAL VERSION OF MALLAT S ALGORITHM 124 8.6 CONCLUSIONS 125 CHAPTER 9. WAVELETS AND TURBULENCE 127 9.1 INTRODUCTION 127 9.2 THE STATISTICAL THEORY OF TURBULENCE AND FOURIER ANALYSIS 128 9.3 MULTIFRACTAL PROBABILITY MEASURES AND TURBULENT FLOWS 130 9.4 MULTIFRACTAL MODELING OF THE VELOCITY FIELD 131 9.5 COHERENT STRUCTURES 137 9.6 COUDER S EXPERIMENTS 139 9.7 MARIE FARGE S NUMERICAL EXPERIMENTS 140 9.8 MODELING AND DETECTING CHIRPS IN TURBULENT FLOWS 141 9.9 WAVELETS, PARAPRODUCTS, AND NAVIER-STOKES EQUATIONS 145 9.10 HAUSDORFF MEASURE AND DIMENSION 147 CHAPTER 10. WAVELETS AND MULTIFRACTAL FUNCTIONS 149 10.1 INTRODUCTION 149 10.2 THE WEIERSTRASS FUNCTION 150 10.3 REGULAR POINTS IN AN IRREGULAR BACKGROUND 152 10.4 THE RIEMANN FUNCTION 157 10.4.1 HOLDER REGULARITY AT IRRATIONALS 158 10.4.2 RIEMANN S FUNCTION NEAR X 0 = 1 163 10.5 CONCLUSIONS AND COMMENTS 164 CHAPTER 11. DATA COMPRESSION AND RESTORATION OF NOISY IMAGES 167 11.1 INTRODUCTION 167 11.2 NONLINEAR APPROXIMATION AND SPARSE WAVELET EXPANSIONS 168 11.3 DENOISING 177 11.4 MODELING IMAGES 181 11.5 RIDGELETS 184 11.6 CONCLUSIONS 185 CHAPTER 12. WAVELETS AND ASTRONOMY 187 12.1 THE HUBBLE SPACE TELESCOPE AND DECONVOLVING ITS IMAGES 187 12.1.1 THE MODEL 187 12.1.2 DISCOVERING AND FIXING THE PROBLEM 188 12.1.3 IDEA 189 12.2 DATA COMPRESSION 194 12.2.1 HLCOMPRESS 194 12.2.2 SMOOTH RESTORATION 196 12.2.3 COMMENTS 197 12.3 THE HIERARCHICAL ORGANIZATION OF THE UNIVERSE 197 12.3.1 A FRACTAL UNIVERSE 200 VIII CONTENTS 12.4 CONCLUSIONS 201 APPENDIX A. FILTER FUNDAMENTALS 203 A.I THE 1 2 (Z) THEORY AND DEFINITIONS 203 A.2 THE GENERAL TWO-CHANNEL FILTER BANK 205 APPENDIX B. WAVELET TRANSFORMS 209 B.I THE L 2 THEORY 209 B.2 INVERSION FORMULAS 210 B.2.1 L 2 INVERSION 211 B.2.2 INVERSION WITH THE LUSIN WAVELET 213 B.3 GENERALIZATIONS 215 APPENDIX C. A COUNTEREXAMPLE 219 C.I INTRODUCTION 219 C.2 THE FUNCTION 6 220 C.3 REPRESENTATIONS OF /O * 8 P AND ITS DERIVATIVES 221 C.4 HUNTING THE ZEROS OF (/ 0 * 0 P ) 223 C.5 THE FUNCTIONS R, R6 P , (R6 P ) , AND (R0 P ) 225 C.6 (R 6 P ) AND (R * B P ) VANISH AT THE ZEROS OF (/ 0 * 9 P ) 225 C.7 THE BEHAVIOR OF (R* 0 P ) /{F 0 * 9 P ) 226 C.8 REMARKS 227 C.9 A CASE OF PERFECT RECONSTRUCTION 229 APPENDIX D. HOLDER SPACES AND BESOV SPACES 233 D.I HOLDER SPACES 233 D.2 BESOV SPACES 234 D.3 EXAMPLES 235 BIBLIOGRAPHY 237 AUTHOR INDEX 249 SUBJECT INDEX 253
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author	Jaffard, Stéphane Meyer, Yves Ryan, Robert D.
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subject_GND	(DE-588)4215427-3
title	Wavelets tools for science & technology
title_auth	Wavelets tools for science & technology
title_exact_search	Wavelets tools for science & technology
title_full	Wavelets tools for science & technology Stéphane Jaffard ; Yves Meyer ; Robert D. Ryan
title_fullStr	Wavelets tools for science & technology Stéphane Jaffard ; Yves Meyer ; Robert D. Ryan
title_full_unstemmed	Wavelets tools for science & technology Stéphane Jaffard ; Yves Meyer ; Robert D. Ryan
title_old	Meyer, Yves Wavelets
title_short	Wavelets
title_sort	wavelets tools for science technology
title_sub	tools for science & technology
topic	Ondelettes Wavelets gtt Wavelets (Mathematics) Wavelet (DE-588)4215427-3 gnd
topic_facet	Ondelettes Wavelets Wavelets (Mathematics) Wavelet
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work_keys_str_mv	AT jaffardstephane waveletstoolsforsciencetechnology AT meyeryves waveletstoolsforsciencetechnology AT ryanrobertd waveletstoolsforsciencetechnology

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