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Wavelets - Theory & Applications : Theory and Applications - A. K. Louis

Wavelets - Theory & Applications

Theory and Applications

Hardcover

Published: 7th October 1997
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With applications in pattern recognition, data compression and numerical analysis, the wavelet transform is a key area of modern mathematics that brings new approaches to the analysis and synthesis of signals. This book presents the central issues and emphasizes comparison, assessment and how to combine method and application. It reviews different approaches to guide researchers to appropriate classes of techniques.

Preface ix

Notation xi

Introduction xv

1 The Continuous Wavelet Transform 1

1.1. Definition and Elementary Properties 1

1.2 Affine Operators 10

1.3 Filter Properties of the Wavelet Transform 12

1.4 Approximation Properties 22

1.5 Decay Behaviour 32

1.6 Group-Theoretical Foundations and Generalizations 36

1.7 Extension of the One-Dimensional Wavelet Transform to Sobolev Spaces 59

Exercises 69

2 The Discrete Wavelet Transform 73

2.1 Wavelet Frames 73

2.2 Multiscale Analysis 97

2.3 Fast Wavelet Transform 121

2.4 One-Dimensional Orthogonal Wavelets 131

2.5 Two-Dimensional Orthogonal Wavelets 203

Exercises 226

3 Applications of the Wavelet Transform 231

3.1 Wavelet Analysis of One-Dimensional Signals 231

3.2 Quality Control of Texture 235

3.3 Data Compression in Digital Image Processing 239

3.4 Regularization of Inverse Problems 251

3.5 Wavelet – Galerkin Methods for Two-Point boundary Value Problems 259

3.6 Schwarz Iterations Based on Wavelet Decompositions 278

3.7 An Outlook on Two-Dimensional Boundary Value Problems 300

Exercises 306

Appendix The Fourier Transform 309

References 313

Index 321

ISBN: 9780471967927
ISBN-10: 0471967920
Series: Pure and Applied Mathematics: A Wiley Series of Texts, Monographs and Tract
Audience: Professional
Format: Hardcover
Language: English
Number Of Pages: 342
Published: 7th October 1997
Country of Publication: GB
Dimensions (cm): 23.9 x 16.0  x 2.6
Edition Number: 1