| MaI Iat的教材是该领域元可争议的经典参考书，它是唯一一本能够从深度和广度全面覆盖该领域关键资料的著作。 ——Laurent Demanet，斯坦福大学 |
| Stephane Mallat目前是法国巴黎综合理工大学应用数学系教授。曾供职于纽约大学库朗数学科学研究所。他还创立了一家图像处理半导体公司。并担任该公司的CEO。 |
| Preface to the Sparse Edition Notations CHAPTER 1 Sparse Representations 1.1 Computational Harmonic Analysis 1.1.1 The Fourier Kingdom 1.1.2 Wavelet Bases 1.2 Approximation and Processing in Bases 1.2.1 Sampling with Linear Approximations 1.2.2 Sparse Nonlinear Approximations 1.2.3 Compression 1.2.4 Denoising 1.3 Time-Frequency Dictionaries 1.3.1 Heisenberg Uncertainty 1.3.2 Windowed Fourier Transform 1.3.3 Continuous Wavelet Transform 1.3.4 Time-Frequency Orthonormal Bases 1.4 Sparsity in Redundant Dictionaries 1.4.1 Frame Analysis and Synthesis 1.4.2 Ideal I)ictionary Approximations 1.4.3 Pursuit in Dictionaries 1.5 Inverse Problems 1.5.1 Diagonal Inverse Estimation 1.5.2 Super-resolution and Compressive Sensing 1.6 Travel Guide 1.6.1 Reproducible Computational Science 1.6.2 Book Road Map CHAPTER 2 The 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 TotalVariation 2.4 Two-Dimensional Fourier Transform 2.5 Exercises CHAPTER 3 Discrete Revolution 3.1 Sampling Analog Signals 3.1.1 Shannon-Whittaker Sampling Theorem 3.1.2 Aliasing 3.1.3 General Sampling and Linear Analog Conversions 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 3.4.1 Two-Dimensional Sampling Theorems 3.4.2 Discrete Image Filtering 3.4.3 Circular Convolutions and Fourier Basis 3.5 Exercises CHAPTER 4 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 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 Time-Frequency Geometry of Instantaneous Frequencies 4.4.1 Analytic Instantaneous Frequency 4.4.2 Windowed Fourier Ridges 4.4.3 Wavelet Ridges 4.5 Quadratic Time-Frequency Energy 4.5.1 Wigner-Ville Distribution 4.5.2 Interferences and Positivity 4.5.3 Cohen's Class 4.5.4 Discrete Wigner-Ville Computations 4.6 Exercises CHAPTER 5 Frames CHAPTER 6 Wavelet Zoom CHAPTER 7 Wavelet Bases CHAPTER 8 Wavelet Packet and Local Cosine Bases CHAPTER 9 Approximations in Bases CHAPTER 10 Compression CHAPTER 11 Denoising CHAPTER 12 Sparsity in Redundant Dictionaries CHAPTER 13 Inverse Problems APPENDIX Mathematical Complements Bibliography Index |
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