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信号处理的小波导引 英文pdf电子书版本下载

信号处理的小波导引  英文
  • StephaneMallat编著 著
  • 出版社: 北京:机械工业出版社
  • ISBN:9787111288619
  • 出版时间:2010
  • 标注页数:807页
  • 文件大小:49MB
  • 文件页数:824页
  • 主题词:小波分析-应用-信号处理-英文

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图书目录

CHAPTER 1 Sparse Representations 1

1.1 Computational Harmonic Analysis 1

1.1.1 The Fourier Kingdom 2

1.1.2 Wavelet Bases 2

1.2 Approximation and Processing in Bases 5

1.2.1 Sampling with Linear Approximations 7

1.2.2 Sparse Nonlinear Approximations 8

1.2.3 Compression 11

1.2.4 Denoising 11

1.3 Time-Frequency Dictionaries 14

1.3.1 Heisenberg Uncertainty 15

1.3.2 Windowed Fourier Transform 16

1.3.3 Continuous Wavelet Transform 17

1.3.4 Time-Frequency Orthonormal Bases 19

1.4 Sparsity in Redundant Dictionaries 21

1.4.1 Frame Analysis and Synthesis 21

1.4.2 Ideal Dictionary Approximations 23

1.4.3 Pursuit in Dictionaries 24

1.5 Inverse Problems 26

1.5.1 Diagonal Inverse Estimation 27

1.5.2 Super-resolution and Compressive Sensing 28

1.6 Travel Guide 30

1.6.1 Reproducible Computational Science 30

1.6.2 Book Road Map 30

CHAPTER 2 The Fourier Kingdom 33

2.1 Linear Time-Invariant Filtering 33

2.1.1 Impulse Response 33

2.1.2 Transfer Functions 35

2.2 Fourier Integrals 35

2.2.1 Fourier Transform in L1(R) 35

2.2.2 Fourier Transform in L2(R) 38

2.2.3 Examples 40

2.3 Properties 42

2.3.1 Regularity and Decay 42

2.3.2 Uncertainty Principle 43

2.3.3 Total Variation 46

2.4 Two-Dimensional Fourier Transform 51

2.5 Exercises 55

CHAPTER 3 Discrete Revolution 59

3.1 Sampling Analog Signals 59

3.1.1 Shannon-Whittaker SamplingTheorem 59

3.1.2 Aliasing 61

3.1.3 General Sampling and Linear Analog Conversions 65

3.2 Discrete Time-Invariant Filters 70

3.2.1 Impulse Response and Transfer Function 70

3.2.2 Fourier Series 72

3.3 Finite Signals 75

3.3.1 Circular Convolutions 76

3.3.2 Discrete Fourier Transform 76

3.3.3 Fast Fourier Transform 78

3.3.4 Fast Convolutions 79

3.4 Discrete Image Processing 80

3.4.1 Two-Dimensional Sampling Theorems 80

3.4.2 Discrete Image Filtering 82

3.4.3 Circular Convolutions and Fourier Basis 83

3.5 Exercises 85

CHAPTER 4 Time Meets Frequency 89

4.1 Time-Frequency Atoms 89

4.2 Windowed Fourier Transform 92

4.2.1 Completeness and Stability 94

4.2.2 Choice of Window 98

4.2.3 Discrete Windowed Fourier Transform 101

4.3 Wavelet Transforms 102

4.3.1 Real Wavelets 103

4.3.2 Analytic Wavelets 107

4.3.3 Discrete Wavelets 112

4.4 Time-Frequency Geometry of Instantaneous Frequencies 115

4.4.1 Analytic Instantaneous Frequency 115

4.4.2 Windowed Fourier Ridges 118

4.4.3 Wavelet Ridges 129

4.5 Quadratic Time-Frequency Energy 134

4.5.1 Wigner-Ville Distribution 136

4.5.2 Interferences and Positivity 140

4.5.3 Cohen's Class 145

4.5.4 Discrete Wigner-Ville Computations 149

4.6 Exercises 151

CHAPTER 5 Frames 155

5.1 Frames and Riesz Bases 155

5.1.1 Stable Analysis and Synthesis Operators 155

5.1.2 Dual Frame and Pseudo Inverse 159

5.1.3 Dual-Frame Analysis and Synthesis Computations 161

5.1.4 Frame Projector and Reproducing Kernel 166

5.1.5 Translation-Invariant Frames 168

5.2 Translation-Invariant Dyadic Wavelet Transform 170

5.2.1 Dyadic Wavelet Design 172

5.2.2 Algorithme à Trous 175

5.3 Subsampled Wavelet Frames 178

5.4 Windowed Fourier Frames 181

5.4.1 Tight Frames 183

5.4.2 General Frames 184

5.5 Multiscale Directional Frames for Images 188

5.5.1 Directional Wavelet Frames 189

5.5.2 Curvelet Frames 194

5.6 Exercises 201

CHAPTER 6 Wavelet Zoom 205

6.1 Lipschitz Regularity 205

6.1.1 Lipschitz Definition and Fourier Analysis 205

6.1.2 Wavelet Vanishing Moments 208

6.1.3 Regularity Measurements with Wavelets 211

6.2 Wavelet Transform Modulus Maxima 218

6.2.1 Detection of Singularities 218

6.2.2 Dyadic Maxima Representation 224

6.3 Multiscale Edge Detection 230

6.3.1 Wavelet Maxima for Images 230

6.3.2 Fast Multiscale Edge Computations 239

6.4 Multifractals 242

6.4.1 Fractal Sets and Self-Similar Functions 242

6.4.2 Singularity Spectrum 246

6.4.3 Fractal Noises 254

6.5 Exercises 259

CHAPTER 7 Wavelet Bases 263

7.1 Orthogonal Wavelet Bases 263

7.1.1 Multiresolution Approximations 264

7.1.2 Scaling Function 267

7.1.3 Conjugate Mirror Filters 270

7.1.4 In Which Orthogonal Wavelets Finally Arrive 278

7.2 Classes of Wavelet Bases 284

7.2.1 Choosing a Wavelet 284

7.2.2 Shannon,Meyer,Haar,and Battle-Lemarié Wavelets 289

7.2.3 Daubechies Compactly Supported Wavelets 292

7.3 Wavelets and Filter Banks 298

7.3.1 Fast Orthogonal Wavelet Transform 298

7.3.2 Perfect Reconstruction Filter Banks 302

7.3.3 Biorthogonal Bases of l2(Z) 306

7.4 Biorthogonal Wavelet Bases 308

7.4.1 Construction of Biorthogonal Wavelet Bases 308

7.4.2 Biorthogonal Wavelet Design 311

7.4.3 Compactly Supported Biorthogonal Wavelets 313

7.5 Wavelet Bases on an Interval 317

7.5.1 Periodic Wavelets 318

7.5.2 Folded Wavelets 320

7.5.3 Boundary Wavelets 322

7.6 Multiscale Interpolations 328

7.6.1 Interpolation and Sampling Theorems 328

7.6.2 Interpolation Wavelet Basis 333

7.7 Separable Wavelet Bases 338

7.7.1 Separable Multiresolutions 338

7.7.2 Two-Dimensional Wavelet Bases 340

7.7.3 Fast Two-Dimensional Wavelet Transform 346

7.7.4 Wavelet Bases in Higher Dimensions 348

7.8 Lifting Wavelets 350

7.8.1 Biorthogonal Bases over Nonstationary Grids 350

7.8.2 Lifting Scheme 352

7.8.3 Quincunx WaveletBases 359

7.8.4 Wavelets on Bounded Domains and Surfaces 361

7.8.5 Faster Wavelet Transform with Lifting 367

7.9 Exercises 370

CHAPTER 8 Wavelet Packet and Local Cosine Bases 377

8.1 Wavelet Packets 377

8.1.1 Wavelet Packet Tree 377

8.1.2 Time-Frequency Localization 383

8.1.3 Particular Wavelet Packet Bases 388

8.1.4 Wavelet Packet Filter Banks 393

8.2 Image Wavelet Packets 395

8.2.1 Wavelet Packet Quad-Tree 395

8.2.2 Separable Filter Banks 399

8 3 Block Transforms 400

8.3.1 Block Bases 401

8.3.2 Cosine Bases 403

8.3.3 Discrete Cosine Bases 406

8.3.4 Fast Discrete Cosine Transforms 407

8.4 Lapped Orthogonal Transforms 410

8.4.1 LappedProjectors 410

8.4.2 Lapped Orthogonal Bases 416

8.4.3 Local Cosine Bases 419

8.4.4 Discrete Lapped Transforms 422

8.5 Local Cosine Trees 426

8.5.1 Binary Tree of Cosine Bases 426

8.5.2 Tree of Discrete Bases 429

8.5.3 Image Cosine Quad-Tree 429

8.6 Exercises 432

CHAPTER 9 Approximations in Bases 435

9.1 Linear Approximations 435

9.1.1 Sampling and Approximation Error 435

9.1.2 Linear Fourier Approximations 438

9.1.3 Multiresolution Approximation Errors with Wavelets 442

9.1.4 Karhunen-Loève Approximations 446

9.2 Nonlinear Approximations 450

9.2.1 Nonlinear Approximation Error 451

9.2.2 Wavelet Adaptive Grids 455

9.2.3 Approximations in Besov and Bounded Variation Spaces 459

9.3 Sparse Image Representations 463

9.3.1 Wavelet Image Approximations 464

9.3.2 Geometric Image Models and Adaptive Triangulations 471

9.3.3 Curvelet Approximations 476

9.4 Exercises 478

CHAPTER 10 Compression 481

10.1 Transform Coding 481

10.1.1 Compression State of the Art 482

10.1.2 Compression in Orthonormal Bases 483

10.2 Distortion Rate of Quantization 485

10.2.1 Entropy Coding 485

10.2.2 Scalar Quantization 493

10.3 High Bit Rate Compression 496

10.3.1 Bit Allocation 496

10.3.2 Optimal Basis and Karhunen-Loève 498

10.3.3 Transparent Audio Code 501

10.4 Sparse Signal Compression 506

10.4.1 Distortion Rate and Wavelet Image Coding 506

10.4.2 Embedded Transform Coding 516

10.5 Image-Compression Standards 519

10.5.1 JPEG Block Cosine Coding 519

10.5.2 JPEG-2000 Wavelet Coding 523

10.6 Exercises 531

CHAPTER 11 Denoising 535

11.1 Estimation with Additive Noise 535

11.1.1 Bayes Estimation 536

11.1.2 Minimax Estimation 544

11.2 Diagonal Estimationin a Basis 548

11.2.1 Diagonal Estimation with Ofacles 548

11.2.2 Thresholding Estimation 552

11.2.3 Thresholding Improvements 558

11.3 Thresholding Sparse Representations 562

11.3.1 Wavelet Thresholding 563

11.3.2 Wavelet and Curvelet Image Denoising 568

11.3.3 Audio Denoising by Time-Frequency Thresholding 571

11.4 Nondiagonal Block Thresholding 575

11.4.1 Block Thresholding in Bases and Frames 575

11.4.2 Wavelet Block Thresholding 581

11.4.3 Time-Frequency Audio Block Thresholding 582

11.5 Denoising Minimax Optimality 585

11.5.1 Linear Diagonal Minimax Estimation 587

11.5.2 Thresholding Optimality over Orthosymmetric Sets 590

11.5.3 Nearly Minimax with Wavelet Estimation 595

11.6 Exercises 606

CHAPTER 12 Sparsity in Redundant Dictionaries 611

12.1 Ideal Sparse Processing in Dictionaries 611

12.1.1 Best M-Term Approximations 612

12.1.2 Compression by Support Coding 614

12.1.3 Denoising by Support Selection in a Dictionary 616

12.2 Dictionaries of Orthonormal Bases 621

12.2.1 Approximation,Compression,and Denoising in a Best Basis 622

12.2.2 Fast Best-Basis Search in Tree Dictionaries 623

12.2.3 Wavelet Packet and Local Cosine Best Bases 626

12.2.4 Bandlets for Geometric Image Regularity 631

12.3 Greedy Matching Pursuits 642

12.3.1 Matching Pursuit 642

12.3.2 Orthogonal Matching Pursuit 648

12.3.3 Gabor Dictionaries 650

12.3.4 Coherent Matching Pursuit Denoising 655

12.4 11 Pursuits 659

12.4.1 Basis Pursuit 659

12.4.2 11 Lagrangian Pursuit 664

12.4.3 Computations of 11 Minimizations 668

12.4.4 Sparse Synthesis versus Analysis and Total Variation Regularization 673

12.5 Pursuit Recovery 677

12.5.1 Stability and Incoherence 677

12.5.2 Support Recovery with Matching Pursuit 679

12.5.3 Support Recovery with 11 Pursuits 684

12.6 Multichannel Signals 688

12.6.1 Approximation and Denoising by Thresholding in Bases 689

12.6.2 Multichannel Pursuits 690

12.7 Learning Dictionaries 693

12.8 Exercises 696

CHAPTER 13 Inverse Problems 699

13.1 Linear Inverse Estimation 700

13.1.1 Quadratic and Tikhonov Regularizations 700

13.1.2 Singular Value Decompositions 702

13.2 Thresholding Estimators for Inverse Problems 703

13.2.1 Thresholding in Bases of Almost Singular Vectors 703

13.2.2 Thresholding Deconvolutions 709

13.3 Super-resolution 713

13.3.1 Sparse Super-resolution Estimation 713

13.3.2 Sparse Spike Deconvolution 719

13.3.3 Recovery of Missing Data 722

13.4 Compressive Sensing 728

13.4.1 Incoherence with Random Measurements 729

13.4.2 Approximations with Compressive Sensing 735

13.4.3 Compressive Sensing Applications 742

13.5 Blind Source Separation 744

13.5.1 Blind Mixing Matrix Estimation 745

13.5.2 Source Separation 751

13.6 Exercises 752

APPENDIX Mathematical Complements 753

Bibliography 765

Index 795

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