信号处理的小波导引

PREFACE

PREFACE TO THE SECOND EDITION

NOTATION

I INTRODUCTION TO A TRANSIENT WORLD

1.1 Fourier Kingdom

1.2 Time-Frequency Wedding

1.2.1 Windowed Fourier Transform

1.2.2 Wavelet Transform

1.3 Bases of Time-Frequency Atoms

1.3.1 Wavelet Bases and Filter Banks

1.3.2 Tilings of Wavelet Packet and Local Cosine Bases

1.4 Bases for What

1.4.1 Approximation

1.4.2 Estimation

1.4.3 Compression

1.5 Travel Guide

1.5.1 Reproducible Computational Science

1.5.2 Road Map

II FOURIER KINGDOM

2.1 Linear Time-Invariant Filtering

2.1.1 Impulse Response

2.1.2 Transfer Functions

2.2 Fourier Integrals

2.2.1 Fourier Transform in L1(R)

2.2.2 Fourier Transform in L2(R)

2.2.3 Examples

2.3 Properties

2.3.1 Regularity and Decay

2.3.2 Uncertainty Principle

2.3.3 Total Variation

2.4 Two-Dimensional Fourier Transform

2.5 Problems

III DISCRETE REVOLUTION

3.1 Sampling Analog Signals

3.1.1 Whittaker Sampling Theorem

3.1.2 Aliasing

3.1.3 General Sampling Theorems

3.2 Discrete Time-Invariant Filters

3.2.1 Impulse Response and Transfer Function

3.2.2 Fourier Series

3.3 Finite Signals

3.3.1 Circular Convolutions

3.3.2 Discrete Fourier Transform

3.3.3 Fast Fourier Transform

3.3.4 Fast Convolutions

3.4 Discrete Image Processing

3.5 Problems

IV TIME MEETS FREQUENCY

4.1 Time-Frequency Atoms

4.2 Windowed Fourier Transform

4.2.1 Completeness and Stability

4.2.2 Choice of Window 2

4.2.3 Discrete Windowed Fourier Transform

4.3 Wavelet Transforms

4.3.1 Real Wavelets

4.3.2 Analytic Wavelets

4.3.3 Discrete Wavelets

4.4 Instantaneous Frequency

4.5 Quadratic Tune-Frequency Energy

4.6 Problems

V FRAMES

5.1 Frame Theory

5.2 Windowed Fourier Frames

5.3 Wavelet Frames

5.4 Translation Invariance

5.5 Dyadic Wavelet Transform

5.6 Problems

VI WAVELET ZOOM

6.1 Lipschitz Regularity

6.2 Wavelet Transform Modulus Maxima

6.3 Multiscale Edge Detection

6.4 Multifractals

6.5 Problems

VII WAVELET BASES

7.1 Orthogonal Wavelet Bases

7.2 Classes of Wavelet Bases

7.3 Wavelets and Filter Banks

7.4 Biorthogonal Wavelet Bases

7.5 Wavelet Bases on an Interval

IX AN APPROXIMATION TOUR

9.1 Linear Approximations

9.2 Non-Linear Approximations

9.3 Image Approximations with Wavelets

9.4 Adaptive Basis Selection

ESTIMATIONS ARE APPROXIMATIONS

XI TRANSFORM CODING

Appendix A MATHEMATICAL COMPLEMENTS

Appendix B SOFTWARE TOOLBOXES

BIBLIOGRAPHY

INDEX

本书取材于作者在多所国际知名大学讲授”小波信号处理”课程时的讲义，作者以信号处理的问题为背景，用浅显的数学语言阐述小波理论及应用，使读者可以透过复杂的数学公式来窥探小波的精髓，但又不致陷入小波纯数学理论的迷宫。 本书既可以让计算机及电子工程系的学生了解工程问题的数学描述．又可以让数学系的学生了解数学公式的工程意义，是一本极有价值的教材及参考书。【作者简介】作者：(法国)马拉特Stephane Mallat是纽约大学Courant学院计算机科学系的教授，法国巴黎Ecole理工大学应用数学系的教授，并兼任麻省理工学院电子工程系以及特拉维夫大学应用数学系的客座教授。 Mallat博士还曾荣获 ·1990年IEEE信号处理学会评选的论文奖。 ·1993年“斯隆”数学研究基金。 ·1997年SPIE光学仪器工程师学会评选的杰出成就奖。 ·1997年法国科学院评选的应用数学方面的“Blaise帕斯卡”奖。