Wavelet Tour of Signal Processing (eBook)

Stephane Mallat (Autor)

eBook Download: PDF

1999 | 2. Auflage
620 Seiten
Elsevier Science (Verlag)
978-0-08-052083-4 (ISBN)

Infos

This book is intended to serve as an invaluable reference for anyone concerned with the application of wavelets to signal processing. It has evolved from material used to teach wavelet signal processing courses in electrical engineering departments at Massachusetts Institute of Technology and Tel Aviv University, as well as applied mathematics departments at the Courant Institute of New York University and ?cole
Polytechnique in Paris.

Key Features
* Provides a broad perspective on the principles and applications of transient signal processing with wavelets
* Emphasizes intuitive understanding, while providing the mathematical foundations and description of fast algorithms
* Numerous examples of real applications to noise removal, deconvolution, audio and image compression, singularity and edge detection,
multifractal analysis, and time-varying frequency measurements
* Algorithms and numerical examples are implemented in Wavelab, which is a Matlab toolbox freely available over the Internet
* Content is accessible on several level of complexity, depending on the individual reader's needs
New to the Second Edition
* Optical flow calculation and video compression algorithms
* Image models with bounded variation functions
* Bayes and Minimax theories for signal estimation
* 200 pages rewritten and most illustrations redrawn
* More problems and topics for a graduate course in wavelet signal processing, in engineering and applied mathematics

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This book is intended to serve as an invaluable reference for anyone concerned with the application of wavelets to signal processing. It has evolved from material used to teach "e;wavelet signal processing"e; courses in electrical engineering departments at Massachusetts Institute of Technology and Tel Aviv University, as well as applied mathematics departments at the Courant Institute of New York University and EcolePolytechnique in Paris. - Provides a broad perspective on the principles and applications of transient signal processing with wavelets- Emphasizes intuitive understanding, while providing the mathematical foundations and description of fast algorithms- Numerous examples of real applications to noise removal, deconvolution, audio and image compression, singularity and edge detection, multifractal analysis, and time-varying frequency measurements- Algorithms and numerical examples are implemented in Wavelab, which is a Matlab toolbox freely available over the Internet- Content is accessible on several level of complexity, depending on the individual reader's needs New to the Second Edition- Optical flow calculation and video compression algorithms- Image models with bounded variation functions- Bayes and Minimax theories for signal estimation- 200 pages rewritten and most illustrations redrawn- More problems and topics for a graduate course in wavelet signal processing, in engineering and applied mathematics

Inhalt

Cover 1
Contents 8
Preface 16
Preface to the Second Edition 21
Notation 23
CHAPTER I. INTRODUCTION TO A TRANSIENT WORLD 26
1.1 Fourier Kingdom 27
1.2 Time-Frequency Wedding 27
1.3 Bases of Time-Frequency Atoms 31
1.4 Bases for What? 36
1.5 Travel Guide 42
CHAPTER II. FOURIER KINGDOM 45
2.1 Linear Time-Invariant Filtering 45
2.2 Fourier Integrals 47
2.3 Properties 54
2.4 Two-Dimensional Fourier Transform 63
2.5 Problems 65
CHAPTER III. DISCRETE REVOLUTION 67
3.1 Sampling Analog Signals 67
3.2 Discrete Time-Invariant Filters 74
3.3 Finite Signals 79
3.4 Discrete Image Processing 84
3.5 Problems 89
CHAPTER IV. TIME MEETS FREQUENCY 92
4.1 Time-Frequency Atoms 92
4.2 Windowed Fourier Transform 94
4.3 Wavelet Transforms 104
4.4 Instantaneous Frequency 116
4.5 Quadratic Time-Frequency Energy 132
4.6 Problems 146
CHAPTER V. FRAMES 150
5.1 Frame Theory 150
5.2 Windowed Fourier Frames 163
5.3 Wavelet Frames 168
5.4 Translation Invariance 171
5.5 Dyadic Wavelet Transform 173
5.6 Problems 185
CHAPTER VI. WAVELET ZOOM 188
6.1 Lipschitz Regularity 188
6.2 Wavelet Transform Modulus Maxima 201
6.3 Multiscale Edge Detection 214
6.4 Multifractals 225
6.5 Problems 241
CHAPTER VII. WAVELET BASES 245
7.1 Orthogonal Wavelet Bases 245
7.2 Classes of Wavelet Bases 266
7.3 Wavelets and Filter Banks 280
7.4 Biorthogonal Wavelet Bases 290
7.5 Wavelet Bases on an Interval 306
7.6 Multiscale Interpolations 318
7.7 Separable Wavelet Bases 328
7.8 Problems 339
CHAPTER VIII. WAVELET PACKET AND LOCAL COSINE BASES 346
8.1 Wavelet Packets 347
8.2 Image Wavelet Packets 364
8.3 Block Transforms 368
8.4 Lapped Orthogonal Transforms 378
8.5 Local Cosine Trees 393
8.6 Problems 399
CHAPTER IX. AN APPROXIMATION TOUR 401
9.1 Linear Approximations 402
9.2 Non-Linear Approximations 414
9.3 Image Approximations with Wavelets 423
9.4 Adaptive Basis Selection 430
9.5 Approximations with Pursuits 442
9.6 Problems 455
CHAPTER X. ESTIMATIONS ARE APPROXIMATIONS 459
10.1 Bayes Versus Minimax 460
10.2 Diagonal Estimation in a Basis 471
10.3 Minimax Optimality 494
10.4 Restoration 511
10.5 Coherent Estimation 526
10.6 Spectrum Estimation 532
10.7 Problems 545
CHAPTER XI. TRANSFORM CODING 550
11.1 Signal Compression 551
11.2 Distortion Rate of Quantization 553
11.3 High Bit Rate Compression 565
11.4 Image Compression 573
11.5 Video Signals 602
11.6 Problems 612
APPENDIX A. MATHEMATICAL COMPLEMENTS 616
A.1 Functions and Integration 616
A.2 Banach and Hilbert Spaces 618
A.3 Bases of Hilbert Spaces 620
A.4 Linear Operators 621
A.5 Separable Spaces and Bases 623
A.6 Random Vectors and Covariance Operators 624
A.7 Diracs 626
APPENDIX B. SOFTWARE TOOLBOXES 628
B.1 Wavelas 628
B.2 Lastwave 634
B.3 Freeware Wavelet Toolboxes 635
Bibliography 637
Index 654

Produkt-Details

• Erscheint lt. Verlag: 14.9.1999
• Sprache: englisch
• Themenwelt: Informatik ► Software Entwicklung ► User Interfaces (HCI)
• Themenwelt: Informatik ► Theorie / Studium ► Algorithmen
• Themenwelt: Mathematik / Informatik ► Mathematik ► Analysis
• Themenwelt: Mathematik / Informatik ► Mathematik ► Angewandte Mathematik
• Themenwelt: Sozialwissenschaften ► Pädagogik ► Berufspädagogik
• Themenwelt: Technik ► Elektrotechnik / Energietechnik
• Themenwelt: Technik ► Nachrichtentechnik
• Themenwelt: Wirtschaft
• ISBN-10: 0-08-052083-9 / 0080520839
• ISBN-13: 978-0-08-052083-4 / 9780080520834