基本信息·出版社：机械工业出版社 ·页码：805 页 ·出版日期：2010年01月 ·ISBN：9787111286615 ·条形码：9787111286615 ·版本：第3版 ·装帧：平装 ...
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信号处理的小波导引(英文版.第3版) |
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信号处理的小波导引(英文版.第3版) |
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基本信息·出版社：机械工业出版社
·页码：805 页
·出版日期：2010年01月
·ISBN：9787111286615
·条形码：9787111286615
·版本：第3版
·装帧：平装
·开本：32
·正文语种：英语
·丛书名：经典原版书库
·外文书名：A Wavelet Tour of Signal Processing:The Sparse Way,Third Edition
·图书品牌：华章图书
内容简介 《信号处理的小波导引(英文版.第3版)》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。《信号处理的小波导引(英文版.第3版)》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。《信号处理的小波导引(英文版.第3版)》更是一本极具价值的参考书。
作者简介 马拉特（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。
媒体推荐 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
编辑推荐 《信号处理的小波导引(英文版.第3版)》全新版的新增内容：
·字典中的稀疏信号表示。
·压缩感知、超分辨和源分离。
·曲线波和条带波的几何图像处理。
·提升小波变换用于计算机图像处理。
·时频语音信号处理和去噪。
·JPEG 2000图像压缩。
·新增和修订的练习。
目录 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
5.1 Frames and Riesz Bases
5.1.1 Stable Analysis and Synthesis Operators
5.1.2 Dual Frame and Pseudo Inverse
5.1.3 Dual-Frame Analysis and Synthesis Computations
5.1.4 Frame Projector and Reproducing Kernel
5.1.5 Translation-Invariant Frames
5.2 Translation-Invariant Dyadic Wavelet Transform
5.2.1 Dyadic Wavelet Design
5.2.2 Algorithme a Trous
5.3 Subsampled Wavelet Frames
5.4 Windowed Fourier Frames
5.4.1 Tight Frames
5.4.2 General Frames
5.5 Multiscale Directional Frames for Images
5.5.1 Directional Wavelet Frames
5.5.2 Curvelet Frames
5.6 Exercises
CHAPTER 6 Wavelet Zoom
6. l Lipschitz Regularity
6.1.1 Lipschitz Definition and Fourier Analysis
6.1.2 Wavelet Vanishing Moments
6.1.3 Regularity Measurements with Wavelets
6.2 Wavelet Transform Modulus Maxima
6.2.1 Detection of Singularities
6.2.2 Dyadic Maxima Representation
6.3 Multiscale Edge Detection
6.3.1 Wavelet Maxima for Images
6.3.2 Fast Multiscale Edge Computations
6.4 Multifractals
6.4.1 Fractal Sets and Self-Similar Functions
6.4.2 Singularity Spectrum
6.4.3 Fractal Noises
6.5 Exercises
CHAPTER 7 Wavelet Bases
7.1 Orthogonal Wavelet Bases
7.1.1 Multiresolution Approximations
7.1.2 Scaling Function
7.1.3 Conjugate Mirror Filters
7.1.4 In Which Orthogonal Wavelets Finally Arrive
7.2 Classes of Wavelet Bases
7.2.1 Choosing a Wavelet
7.2.2 Shannon, Meyer, Haar, and Battle-Lemarie Wavelets
7.2.3 Daubechies Compactly Supported Wavelets
7.3 Wavelets and Filter Banks
7.3.1 Fast Orthogonal Wavelet Transform
7.3.2 Perfect Reconstruction Filter Banks
7.3.3 Biorthogonal Bases of e2 (z)
7.4 Biorthogonal Wavelet Bases
7.4.1 Construction of Biorthogonal Wavelet Bases
7.4.2 Biorthogonal Wavelet Design
7.4.3 Compactly Supported Biorthogonal Wavelets
7.5 Wavelet Bases on an Interval
7.5.1 Periodic Wavelets
7.5.2 Folded Wavelets
7.5.3 Boundary Wavelets
7.6 Multiscale Interpolations
7.6.1 Interpolation and Sampling Theorems
7.6.2 Interpolation Wavelet Basis
7.7 Separable Wavelet Bases
7.7.1 Separable Multiresolutions
7.7.2 Two-Dimensional Wavelet Bases
7.7.3 Fast Two-Dimensional Wavelet Transform
7.7.4 Wavelet Bases in Higher Dimensions
7.8 Lifting Wavelets
7.8.1 Biorthogonal Bases over Nonstationary Grids
7.8.2 Lifting Scheme
7.8.3 Quincunx Wavelet Bases
7.8.4 Wavelets on Bounded Domains and Surfaces
7.8.5 Faster Wavelet Transform with Lifting
7.9 Exercises
CHAPTER 8 Wavelet Packet and Local Cosine Bases
8. 1 Wavelet Packets
8.1.1 Wavelet Packet Tree
8.1.2 Time-Frequency Localization
8.1.3 Particular Wavelet Packet Bases
8.1.4 Wavelet Packet Filter Banks
8.2 Image Wavelet Packets
8.2.1 Wavelet Packet Quad-Tree
8.2.2 Separable Filter Banks
8.3 Block Transforms
8.3.1 Block Bases
8.3.2 Cosine Bases
8.3.3 Discrete Cosine Bases
8.3.4 Fast Discrete Cosine Transforms
……
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
……
文摘 插图：
Signal singularities have specific scaling invariance characterized by Lipschitz exponents. Chapter 6 relates the point-wise regularity of f to the asymptotic decay of the wavelet transform amplitude when s goes to zero. Singularities are detected by following the local maxima of the wavelet transform across scales.
In images, wavelet local maxima indicate the position of edges, which are sharp variations of image intensity. It defines scale-space approximation support of from which precise image approximations are reconstructed. At different scales, the geometry of this local maxima support provides contours of image structures of varying sizes. This multiscale edge detection is particularly effective for pattern recognition in computer vision.
The zooming capability of the wavelet transform not only locates isolated singular events, but can also characterize more complex multifractal signals having nonisolated singularities. Mandelbrot [41] was the first to recognize the existence of multifractals in most corners of nature. Scaling one part of a multifractal produces a signal that is statistically similar to the whole. This self-similarity appears in the continuous wavelet transform, which modifies the analyzing scale. From global measurements of the wavelet transform decay, Chapter 6 measures the singular- ity distribution of multifractals. This is particularly important in analyzing their properties and testing multifractal models in physics or in financial time series.
