《信號處理的小波導引》是2010年機械工業出版社出版的書籍，作者是馬拉特。
基本介紹
- 書名：東方出版社
- 作者：馬拉特
- ISBN：9787111288619
- 定價：￥69.00
- 出版社：機械工業出版社
- 出版時間：2010-1-1
內容簡介,目錄,作者簡介,
內容簡介
本書以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套用，使讀者可以透過複雜的數學公式來窺探小波的精髓，而又不致陷入小波純數學理論的迷宮。本書是按研究生教材的要求編寫的。既可以讓套用數學系的學生了解數學公式的工程意義。也可以讓計算機及電子工程系的學生了解工程問題的數學描述。對於小波理論與套用的研究人員，本書更是一本極具價值的參考書。
這本經典教材的全新版本全面論述了稀疏表示的重要概念、技術和套用。反映了該主題在當今信號處理領域所起的關鍵作用。書中清楚地給出了傅立葉、小波和時頻變換的標準表示。以及用快速算法構造的正交基。作者在解釋了稀疏的主要概念後將其運用於信號壓縮、噪聲衰減和逆問題。同時給出了冗餘字典、超分辨和壓縮感知中的稀疏表示。
目錄
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
作者簡介
Stephane Mallat目前是法國巴黎綜合理工大學套用數學系教授。曾供職於紐約大學庫朗數學科學研究所。他還創立了一家圖像處理半導體公司。並擔任該公司的CEO。
