信號處理的小波導(dǎo)引

內(nèi)容概要

這本經(jīng)典教材的全新版本全面論述了稀疏表示的重要概念、技術(shù)和應(yīng)用。反映了該主題在當今信號處理領(lǐng)域所起的關(guān)鍵作用。書中清楚地給出了傅里葉、小波和時頻變換的標準表示。以及用快速算法構(gòu)造的正交基。作者在解釋了稀疏的主要概念后將其運用于信號壓縮、噪聲衰減和逆問題。同時給出了冗余字典、超分辨和壓縮感知中的稀疏表示。    全書以十分直觀和近乎談話的方式，以信號處理的問題為背景。敘述了小波的理論和應(yīng)用，使讀者可以透過復(fù)雜的數(shù)學(xué)公式來窺探小波的精髓，而又不致陷入小波純數(shù)學(xué)理論的迷宮。本書是按研究生教材的要求編寫的。既可以讓應(yīng)用數(shù)學(xué)系的學(xué)生了解數(shù)學(xué)公式的工程意義。也可以讓計算機及電子工程系的學(xué)生了解工程問題的數(shù)學(xué)描述。對于小波理論與應(yīng)用的研究人員。本書更是一本極具價值的參考書。

作者簡介

Stephane Mallat目前是法國巴黎綜合理工大學(xué)應(yīng)用數(shù)學(xué)系教授。曾供職于紐約大學(xué)庫朗數(shù)學(xué)科學(xué)研究所。他還創(chuàng)立了一家圖像處理半導(dǎo)體公司。并擔(dān)任該公司的CEO。

書籍目錄

Preface to the Sparse EditionNotationsCHAPTER 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 MapCHAPTER 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  ExercisesCHAPTER 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  ExercisesCHAPTER 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  ExercisesCHAPTER 5  FramesCHAPTER 6  Wavelet ZoomCHAPTER 7  Wavelet BasesCHAPTER 8  Wavelet Packet and Local Cosine BasesCHAPTER 9  Approximations in BasesCHAPTER 10  CompressionCHAPTER 11  DenoisingCHAPTER 12  Sparsity in Redundant DictionariesCHAPTER 13  Inverse ProblemsAPPENDIX Mathematical ComplementsBibliographyIndex

媒體關(guān)注與評論

　　MaI Iat的教材是該領(lǐng)域元可爭議的經(jīng)典參考書，它是唯一一本能夠從深度和廣度全面覆蓋該領(lǐng)域關(guān)鍵資料的著作。　　——Laurent Demanet，斯坦福大學(xué)

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