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| 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。
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| 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 |
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