信號處理的小波導引（英文版）

定　價：￥65.00

作　者：	（法）Stephane Mallat著
出版社：	機械工業(yè)出版社
叢編項：	經(jīng)典原版書庫
標　簽：	通信技術(shù)理論與基礎(chǔ)

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ISBN：	9787111127680	出版時間：	2003-09-01	包裝：	膠版紙
開本：	24cm	頁數(shù)：	660	字數(shù)：

內(nèi)容簡介

　　本書取材于作者在多所國際知名大學講授”小波信號處理”課程時的講義，作者以信號處理的問題為背景，用淺顯的數(shù)學語言闡述小波理論及應用，使讀者可以透過復雜的數(shù)學公式來窺探小波的精髓，但又不致陷入小波純數(shù)學理論的迷宮。本書既可以讓計算機及電子工程系的學生了解工程問題的數(shù)學描述．又可以讓數(shù)學系的學生了解數(shù)學公式的工程意義，是一本極有價值的教材及參考書。作者簡介： Stephane Mallat是紐約大學Courant學院計算機科學系的教授，法國巴黎Ecole理工大學應用數(shù)學系的教授，并兼任麻省理工學院電子工程系以及特拉維夫大學應用數(shù)學系的客座教授。 Mallat博士還曾榮獲 ·1990年IEEE信號處理學會評選的論文獎。 ·1993年“斯隆”數(shù)學研究基金。 ·1997年SPIE光學儀器工程師學會評選的杰出成就獎。 ·1997年法國科學院評選的應用數(shù)學方面的“Blaise帕斯卡”獎。

作者簡介

　　Stephane Mallat是紐約大學Courant學院計算機科學系的教授，法國巴黎Ecole理工大學應用數(shù)學系的教授，并兼任麻省理工學院電子工程系以及特拉維夫大學應用數(shù)學系的客座教授。Mallat博士還曾榮獲·1990年IEEE信號處理學會評選的論文獎?！?993年“斯隆”數(shù)學研究基金?！?997年SPIE光學儀器工程師學會評選的杰出成就獎?！?997年法國科學院評選的應用數(shù)學方面的“Blaise帕斯卡”獎。

圖書目錄

PREFACE   xiii
PREFACE TO THE SECOND EDITION   xviii
NOTATION  xx
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 1
2.1.1  Impulse Response
2.1.2  Transfer Functions
2.2  Fourier Integrals l
2.2.1  Fourier Transform in L1(R)
2.2.2  Fourier Transform in L2(R)
2.2.3  Examples
2.3  Properties 1
2.3.1  Regularity and Decay
2.3.2  Uncertainty Principle
2.3.3  Total Variation
2.4  Two-Dimensional Fourier Transform 1
2.5  Problems
III
DISCRETE REVOLUTION
3.1  Sampling Analog Signals 1
3.1.1  Whittaker Sampling Theorem
3.1.2  Aliasing
3.1.3  General Sampling Theorems
3.2  Discrete Time-Invariant Filters 1
3.2.1  Impulse Response and Transfer Function
3.2.2  Fourier Series
3.3  Finite Signals 1
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 1
3.4.1  Two-Dimensional Sampling Theorem
3.4.2  Discrete Image Filtering
3.4.3  Circular Convolutions and Fourier Basis
3.5  Problems
IV
TIME MEETS FREQUENCY
4.1  Time-Frequency Atoms 1
4.2  Windowed Fourier Transform 1
4.2.1  Completeness and Stability
4.2.2  Choice of Window 2
4.2.3  Discrete Windowed Fourier Transform 2
4.3  Wavelet Transforms 1
4.3.1   Real Wavelets
4.3.2  Analytic Wavelets
4.3.3  Discrete Wavelets 2
4.4  Instantaneous Frequency 2
4.4.1  Windowed Fourier Ridges
4.4.2  Wavelet Ridges
4.5  Quadratic Tune-Frequency Energy 1
4.5.1   Wigner-Ville Distribution
4.5.2  Interferences and Positivity
4.5.3  Cohen's Class 2
4.5.4  Discrete Wigner-Ville Computations 2
4.6  Problems
V
FRAMES
5.1  Frame Theory 2
5.1.1   Frame Definition and SampLing
5.1.2  Pseudo Inverse
5.1.3  Inverse Frame Computations
5.1.4  Frame Projector and Noise Reduction
5.2  Windowed Fourier Frames 2
5.3  Wavelet Frames 2
5.4  Translation Invariance 1
5.5  Dyadic Wavelet Transform 2
5.5.1  Wavelet Design
5.5.2  "Algorithme a Trous"
5.5.3  Oriented Wavelets for a Vision 3
5.6  Problems
VI
WAVELET ZOOM
6.1  Lipschitz Regularity 1
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 2
6.2.1   Detection of Singularities
6.2.2  Reconstruction From Dyadic Maxima 3
6.3  Multiscale Edge Detection 2
6.3.1  Wavelet Maxima for Images 2
6.3.2  Fast Multiscale Edge Computations 3
6.4  Multifractals 2
6.4.1   Fractal Sets and Self-Similar Functions
6.4.2  Singularity Spectrum 3
6.4.3  Fractal Noises 3
6.5  Problems
VII
WAVELET BASES
7.1  Orthogonal Wavelet Bases 1
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 1
7.2.1  Choosing a Wavelet
7.2.2  Shannon, Meyer and Battle-Lemarie Wavelets
7.2.3  Daubechies Compactly Supported Wavelets
7.3  Wavelets and Filter Banks 1
7.3.1   Fast Orthogonal Wavelet Transform
7.3.2  Perfect Reconstruction Filter Banks
7.3.3  Biorthogonal Bases of I2(z) z
7.4  Biorthogonal Wavelet Bases 2
7.4.1  Construction of Biorthogonal Wavelet Bases
7.4.2  Biorthogonal Wavelet Design 2
7.4.3  Compactly Supported Biorthogonal Wavelets 2
7.4.4  Lifting Wavelets 3
7.5  Wavelet Bases on an Interval 2
7.5.1   Periodic Wavelets
IX
AN APPROXIMATION TOUR
9.1  Linear Approximations 1
9.1.1  Linear Approximation Error
9.1.2  Linear Fourier Approximations
9.1.3  Linear Multiresolution Approximations
9.1.4  Karhunen-Loeve Approximations 2
9.2  Non-Linear Approximations 1
9.2.1  Non-Linear Approximation Error
9.2.2  Wavelet Adaptive Grids
9.2.3  Besov Spaces 3
9.3  Image Approximations with Wavelets 1
9.4  Adaptive Basis Selection 2
9.4.1  Best Basis and Schur Concavity
9.4.2  Fast Best Basis Search in Trees
9.4.3  Wavelet Packet and Local Cosine Best Bases
9.5  Approximations with Pursuits 3
9.5.1  Basis Pursuit
9.5.2  Matching Pursuit
9.5.3  Orthogonal Matching Pursuit
9.6  Problems
X
ESTIMATIONS ARE APPROXIMATIONS
10.1 Bayes Versus Minimax 2
10.1.1 Bayes Estimation
10.1.2 Minimax Estimation
10.2 Diagonal Estimation in a Basis 2
10.2.1 Diagonal Estimation with Oracles
10.2.2 Thresholding Estimation
10.2.3 Thresholding Refinements 3
10.2.4 Wavelet Thresholding
10.2.5 Best Basis Thresholding 3
10.3 Minimax Optimality 3
10.3.1 Linear Diagonal Minimax Estimation
10.3.2 0rthosymmetric Sets
10.3.3 Nearly Minimax with Wavelets
10.4 Restoration3
10.4.1 Estimation in Arbitrary Gaussian Noise
10.4.2 Inverse Problems and Deconvolution
10.5 Coherent Estimation 3
1O.5. I Coherent Basis Thresholding
10.5.2 Coherent Matching Pursuit
10.6 Spectrum Estimation 2
10.6.1 Power Spectrum
10.6.2 Approximate Karhunen-Lotve Search 3
10.6.3 Locally Stationary Processes 3
10.7 Problems
Xl
TRANSFORM CODING
11.1 Signal Compression z
11.1.1 State of the Art
11.1.2 Compression in Orthonormal Bases
11.2 Distortion Rate of Quantization 2
11.2.1 Entropy Coding
11.2.2 Scalar Quantization
11.3 High Bit Rate Compression 2
11.3.1 Bit Allocation
11.3.2 Optimal Basis and Karhunen-Loeve
11.3.3 Transparent Audio Code
11.4 Image Compression 2
11.4.1 Deterministic Distortion Rate
11.4.2 Wavelet Image Coding
11.4.3 Block Cosine Image Coding
11.4.4 Embedded Transform Coding
11.4.5 Minimax Distortion Rate 3
11.5 Video Signals 2
11.5.1 Optical Flow
11.5.2 MPEG Video Compression
11.6 Problems
Appendix A
MATHEMATICAL COMPLEMENTS
A.1  Functions and Integration
A.2  Banach and Hilbert Spaces
A.3  Bases of Hilbert Spaces
A.4  Linear Operators
A.5  Separable Spaces and Bases
A.6  Random Vectors and Covariance Operators
A.7  Diracs
Appendix B
SOFTWARE TOOLBOXES
B.1  WAVELAB
B.2  LASTWAVE
B.3  Freeware Wavelet Toolboxes
BIBLIOGRAPHY
INDEX