这本经典教材的全新版本全面论述了稀疏表示的重要概念、技术和应用。反映了该主题在当今信
号处理领域所起的关键作用。书中清楚地给出了傅里叶、小波和时频变换的标准表示。以及用快速算法构造的正交基。作者在解释了稀疏的主要概念后将其运用于信号压缩、噪声衰减和逆问题。同时给出了冗余字典、超分辨和压缩感知中的稀疏表示。
全书以十分直观和近乎谈话的方式，以信号处理的问题为背景。叙述了小波的理论和应用，使读者可以透过复杂的数学公式来窥探小波的精髓，而又不致陷入小波纯数学理论的迷宫。本书是按研究生教材的要求编写的。既可以让应用数学系的学生了解数学公式的工程意义。也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。对于小波理论与应用的研究人员。本书更是一本**价值的参考书。

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

MaI Iat的教材是该领域元可争议的经典参考书，它是**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