信号处理的小波导引 英文PDF|Epub|txt|kindle电子书版本网盘下载

信号处理的小波导引 英文PDF格式电子书版下载

注意：本站所有压缩包均有解压码： 点击下载压缩包解压工具

CHAPTER 1 Sparse Representations1

1.1 Computational Harmonic Analysis1

1.1.1 The Fourier Kingdom2

1.1.2 Wavelet Bases2

1.2 Approximation and Processing in Bases5

1.2.1 Sampling with Linear Approximations7

1.2.2 Sparse Nonlinear Approximations8

1.2.3 Compression11

1.2.4 Denoising11

1.3 Time-Frequency Dictionaries14

1.3.1 Heisenberg Uncertainty15

1.3.2 Windowed Fourier Transform16

1.3.3 Continuous Wavelet Transform17

1.3.4 Time-Frequency Orthonormal Bases19

1.4 Sparsity in Redundant Dictionaries21

1.4.1 Frame Analysis and Synthesis21

1.4.2 Ideal Dictionary Approximations23

1.4.3 Pursuit in Dictionaries24

1.5 Inverse Problems26

1.5.1 Diagonal Inverse Estimation27

1.5.2 Super-resolution and Compressive Sensing28

1.6 Travel Guide30

1.6.1 Reproducible Computational Science30

1.6.2 Book Road Map30

CHAPTER 2 The Fourier Kingdom33

2.1 Linear Time-Invariant Filtering33

2.1.1 Impulse Response33

2.1.2 Transfer Functions35

2.2 Fourier Integrals35

2.2.1 Fourier Transform in L1(R)35

2.2.2 Fourier Transform in L2(R)38

2.2.3 Examples40

2.3 Properties42

2.3.1 Regularity and Decay42

2.3.2 Uncertainty Principle43

2.3.3 Total Variation46

2.4 Two-Dimensional Fourier Transform51

2.5 Exercises55

CHAPTER 3 Discrete Revolution59

3.1 Sampling Analog Signals59

3.1.1 Shannon-Whittaker SamplingTheorem59

3.1.2 Aliasing61

3.1.3 General Sampling and Linear Analog Conversions65

3.2 Discrete Time-Invariant Filters70

3.2.1 Impulse Response and Transfer Function70

3.2.2 Fourier Series72

3.3 Finite Signals75

3.3.1 Circular Convolutions76

3.3.2 Discrete Fourier Transform76

3.3.3 Fast Fourier Transform78

3.3.4 Fast Convolutions79

3.4 Discrete Image Processing80

3.4.1 Two-Dimensional Sampling Theorems80

3.4.2 Discrete Image Filtering82

3.4.3 Circular Convolutions and Fourier Basis83

3.5 Exercises85

CHAPTER 4 Time Meets Frequency89

4.1 Time-Frequency Atoms89

4.2 Windowed Fourier Transform92

4.2.1 Completeness and Stability94

4.2.2 Choice of Window98

4.2.3 Discrete Windowed Fourier Transform101

4.3 Wavelet Transforms102

4.3.1 Real Wavelets103

4.3.2 Analytic Wavelets107

4.3.3 Discrete Wavelets112

4.4 Time-Frequency Geometry of Instantaneous Frequencies115

4.4.1 Analytic Instantaneous Frequency115

4.4.2 Windowed Fourier Ridges118

4.4.3 Wavelet Ridges129

4.5 Quadratic Time-Frequency Energy134

4.5.1 Wigner-Ville Distribution136

4.5.2 Interferences and Positivity140

4.5.3 Cohen's Class145

4.5.4 Discrete Wigner-Ville Computations149

4.6 Exercises151

CHAPTER 5 Frames155

5.1 Frames and Riesz Bases155

5.1.1 Stable Analysis and Synthesis Operators155

5.1.2 Dual Frame and Pseudo Inverse159

5.1.3 Dual-Frame Analysis and Synthesis Computations161

5.1.4 Frame Projector and Reproducing Kernel166

5.1.5 Translation-Invariant Frames168

5.2 Translation-Invariant Dyadic Wavelet Transform170

5.2.1 Dyadic Wavelet Design172

5.2.2 Algorithme à Trous175

5.3 Subsampled Wavelet Frames178

5.4 Windowed Fourier Frames181

5.4.1 Tight Frames183

5.4.2 General Frames184

5.5 Multiscale Directional Frames for Images188

5.5.1 Directional Wavelet Frames189

5.5.2 Curvelet Frames194

5.6 Exercises201

CHAPTER 6 Wavelet Zoom205

6.1 Lipschitz Regularity205

6.1.1 Lipschitz Definition and Fourier Analysis205

6.1.2 Wavelet Vanishing Moments208

6.1.3 Regularity Measurements with Wavelets211

6.2 Wavelet Transform Modulus Maxima218

6.2.1 Detection of Singularities218

6.2.2 Dyadic Maxima Representation224

6.3 Multiscale Edge Detection230

6.3.1 Wavelet Maxima for Images230

6.3.2 Fast Multiscale Edge Computations239

6.4 Multifractals242

6.4.1 Fractal Sets and Self-Similar Functions242

6.4.2 Singularity Spectrum246

6.4.3 Fractal Noises254

6.5 Exercises259

CHAPTER 7 Wavelet Bases263

7.1 Orthogonal Wavelet Bases263

7.1.1 Multiresolution Approximations264

7.1.2 Scaling Function267

7.1.3 Conjugate Mirror Filters270

7.1.4 In Which Orthogonal Wavelets Finally Arrive278

7.2 Classes of Wavelet Bases284

7.2.1 Choosing a Wavelet284

7.2.2 Shannon,Meyer,Haar,and Battle-Lemarié Wavelets289

7.2.3 Daubechies Compactly Supported Wavelets292

7.3 Wavelets and Filter Banks298

7.3.1 Fast Orthogonal Wavelet Transform298

7.3.2 Perfect Reconstruction Filter Banks302

7.3.3 Biorthogonal Bases of l2(Z)306

7.4 Biorthogonal Wavelet Bases308

7.4.1 Construction of Biorthogonal Wavelet Bases308

7.4.2 Biorthogonal Wavelet Design311

7.4.3 Compactly Supported Biorthogonal Wavelets313

7.5 Wavelet Bases on an Interval317

7.5.1 Periodic Wavelets318

7.5.2 Folded Wavelets320

7.5.3 Boundary Wavelets322

7.6 Multiscale Interpolations328

7.6.1 Interpolation and Sampling Theorems328

7.6.2 Interpolation Wavelet Basis333

7.7 Separable Wavelet Bases338

7.7.1 Separable Multiresolutions338

7.7.2 Two-Dimensional Wavelet Bases340

7.7.3 Fast Two-Dimensional Wavelet Transform346

7.7.4 Wavelet Bases in Higher Dimensions348

7.8 Lifting Wavelets350

7.8.1 Biorthogonal Bases over Nonstationary Grids350

7.8.2 Lifting Scheme352

7.8.3 Quincunx WaveletBases359

7.8.4 Wavelets on Bounded Domains and Surfaces361

7.8.5 Faster Wavelet Transform with Lifting367

7.9 Exercises370

CHAPTER 8 Wavelet Packet and Local Cosine Bases377

8.1 Wavelet Packets377

8.1.1 Wavelet Packet Tree377

8.1.2 Time-Frequency Localization383

8.1.3 Particular Wavelet Packet Bases388

8.1.4 Wavelet Packet Filter Banks393

8.2 Image Wavelet Packets395

8.2.1 Wavelet Packet Quad-Tree395

8.2.2 Separable Filter Banks399

8 3 Block Transforms400

8.3.1 Block Bases401

8.3.2 Cosine Bases403

8.3.3 Discrete Cosine Bases406

8.3.4 Fast Discrete Cosine Transforms407

8.4 Lapped Orthogonal Transforms410

8.4.1 LappedProjectors410

8.4.2 Lapped Orthogonal Bases416

8.4.3 Local Cosine Bases419

8.4.4 Discrete Lapped Transforms422

8.5 Local Cosine Trees426

8.5.1 Binary Tree of Cosine Bases426

8.5.2 Tree of Discrete Bases429

8.5.3 Image Cosine Quad-Tree429

8.6 Exercises432

CHAPTER 9 Approximations in Bases435

9.1 Linear Approximations435

9.1.1 Sampling and Approximation Error435

9.1.2 Linear Fourier Approximations438

9.1.3 Multiresolution Approximation Errors with Wavelets442

9.1.4 Karhunen-Loève Approximations446

9.2 Nonlinear Approximations450

9.2.1 Nonlinear Approximation Error451

9.2.2 Wavelet Adaptive Grids455

9.2.3 Approximations in Besov and Bounded Variation Spaces459

9.3 Sparse Image Representations463

9.3.1 Wavelet Image Approximations464

9.3.2 Geometric Image Models and Adaptive Triangulations471

9.3.3 Curvelet Approximations476

9.4 Exercises478

CHAPTER 10 Compression481

10.1 Transform Coding481

10.1.1 Compression State of the Art482

10.1.2 Compression in Orthonormal Bases483

10.2 Distortion Rate of Quantization485

10.2.1 Entropy Coding485

10.2.2 Scalar Quantization493

10.3 High Bit Rate Compression496

10.3.1 Bit Allocation496

10.3.2 Optimal Basis and Karhunen-Loève498

10.3.3 Transparent Audio Code501

10.4 Sparse Signal Compression506

10.4.1 Distortion Rate and Wavelet Image Coding506

10.4.2 Embedded Transform Coding516

10.5 Image-Compression Standards519

10.5.1 JPEG Block Cosine Coding519

10.5.2 JPEG-2000 Wavelet Coding523

10.6 Exercises531

CHAPTER 11 Denoising535

11.1 Estimation with Additive Noise535

11.1.1 Bayes Estimation536

11.1.2 Minimax Estimation544

11.2 Diagonal Estimationin a Basis548

11.2.1 Diagonal Estimation with Ofacles548

11.2.2 Thresholding Estimation552

11.2.3 Thresholding Improvements558

11.3 Thresholding Sparse Representations562

11.3.1 Wavelet Thresholding563

11.3.2 Wavelet and Curvelet Image Denoising568

11.3.3 Audio Denoising by Time-Frequency Thresholding571

11.4 Nondiagonal Block Thresholding575

11.4.1 Block Thresholding in Bases and Frames575

11.4.2 Wavelet Block Thresholding581

11.4.3 Time-Frequency Audio Block Thresholding582

11.5 Denoising Minimax Optimality585

11.5.1 Linear Diagonal Minimax Estimation587

11.5.2 Thresholding Optimality over Orthosymmetric Sets590

11.5.3 Nearly Minimax with Wavelet Estimation595

11.6 Exercises606

CHAPTER 12 Sparsity in Redundant Dictionaries611

12.1 Ideal Sparse Processing in Dictionaries611

12.1.1 Best M-Term Approximations612

12.1.2 Compression by Support Coding614

12.1.3 Denoising by Support Selection in a Dictionary616

12.2 Dictionaries of Orthonormal Bases621

12.2.1 Approximation,Compression,and Denoising in a Best Basis622

12.2.2 Fast Best-Basis Search in Tree Dictionaries623

12.2.3 Wavelet Packet and Local Cosine Best Bases626

12.2.4 Bandlets for Geometric Image Regularity631

12.3 Greedy Matching Pursuits642

12.3.1 Matching Pursuit642

12.3.2 Orthogonal Matching Pursuit648

12.3.3 Gabor Dictionaries650

12.3.4 Coherent Matching Pursuit Denoising655

12.4 11 Pursuits659

12.4.1 Basis Pursuit659

12.4.2 11 Lagrangian Pursuit664

12.4.3 Computations of 11 Minimizations668

12.4.4 Sparse Synthesis versus Analysis and Total Variation Regularization673

12.5 Pursuit Recovery677

12.5.1 Stability and Incoherence677

12.5.2 Support Recovery with Matching Pursuit679

12.5.3 Support Recovery with 11 Pursuits684

12.6 Multichannel Signals688

12.6.1 Approximation and Denoising by Thresholding in Bases689

12.6.2 Multichannel Pursuits690

12.7 Learning Dictionaries693

12.8 Exercises696

CHAPTER 13 Inverse Problems699

13.1 Linear Inverse Estimation700

13.1.1 Quadratic and Tikhonov Regularizations700

13.1.2 Singular Value Decompositions702

13.2 Thresholding Estimators for Inverse Problems703

13.2.1 Thresholding in Bases of Almost Singular Vectors703

13.2.2 Thresholding Deconvolutions709

13.3 Super-resolution713

13.3.1 Sparse Super-resolution Estimation713

13.3.2 Sparse Spike Deconvolution719

13.3.3 Recovery of Missing Data722

13.4 Compressive Sensing728

13.4.1 Incoherence with Random Measurements729

13.4.2 Approximations with Compressive Sensing735

13.4.3 Compressive Sensing Applications742

13.5 Blind Source Separation744

13.5.1 Blind Mixing Matrix Estimation745

13.5.2 Source Separation751

13.6 Exercises752

APPENDIX Mathematical Complements753

Bibliography765

Index795