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

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Ⅰ INTRODUCTION TO A TRANSIENT WORLD2

1.1 Fourier Kingdom2

1.2 Time-Frequency Wedding2

1.2.1 Windowed Fourier Transform3

1.2.2 Wavelet Transform4

1.3 Bases of Time-Frequency Atoms6

1.3.1 Wavelet Bases and Filter Banks7

1.3.2 Tilings of Wavelet Packet and Local Cosine Bases9

1.4 Bases for What?11

1.4.1 Approximation12

1.4.2 Estimation14

1.4.3 Compression16

1.5.1 Reproducible Computational Science17

1.5 Travel Guide17

1.5.2 Road Map18

Ⅱ FOURIER KINGDOM20

2.1 Linear Time-Invariant Filtering120

2.1.1 Impulse Response21

2.1.2 Transfer Functions22

2.2 Fourier Integrals122

2.2.1 Fourier Transform in L1(R)23

2.2.2 Fourier Transform in L2(R)25

2.2.3 Examples27

2.3 Properties129

2.3.1 Regularity and Decay29

2.3.2 Uncertainty Principle30

2.3.3 Total Variation33

2.4 Two-Dimensional Fourier Transform138

2.5 Problems40

Ⅲ DISCRETE REVOLUTION42

3.1 Sampling Analog Signals142

3.1.1 Whittaker Sampling Theorem43

3.1.2 Aliasing44

3.1.3 General Sampling Theorems47

3.2 Discrete Time-Invariant Filters149

3.2.1 Impulse Response and Transfer Function49

3.2.2 Fourier Series51

3.3 Finite Signals154

3.3.1 Circular Convolutions55

3.3.2 Discrete Fourier Transform55

3.3.3 Fast Fourier Transform57

3.3.4 Fast Convolutions58

3.4 Discrete Image Processing159

3.4.1 Two-Dimensional Sampling Theorem60

3.4.2 Discrete Image Filtering61

3.4.3 Circular Convolutions and Fourier Basis62

3.5 Problems64

Ⅳ TIME MEETS FREQUENCY67

4.1 Time-Frequency Atoms167

4.2 Windowed Fourier Transform169

4.2.1 Completeness and Stability72

4.2.2 Choice of Window275

4.2.3 Discrete Windowed Fourier Transform277

4.3 Wavelet Transforms179

4.3.1 Real Wavelets80

4.3.2 Analytic Wavelets84

4.3.3 Discrete Wavelets289

4.4 Instantaneous Frequency291

4.4.1 Windowed Fourier Ridges94

4.4.2 Wavelet Ridges102

4.5 Quadratic Time-Frequency Energy1107

4.5.1 Wigner-Ville Distribution107

4.5.2 Interferences and Positivity112

4.5.3 Cohen s Class2116

4.5.4 Discrete Wigner-Ville Computations2120

4.6 Problems121

Ⅴ FRAMES125

5.1 Frame Theory2125

5.1.1 Frame Definition and Sampling125

5.1.2 Pseudo Inverse127

5.1.3 Inverse Frame Computations132

5.1.4 Frame Projector and Noise Reduction135

5.2 Windowed Fourier Frames2138

5.3 Wavelet Frames2143

5.4 Translation Invariance1146

5.5 Dyadic Wavelet Transform2148

5.5.1 Wavelet Design150

5.5.2 Algorithme ? Trous153

5.5.3 Oriented Wavelets for a Vision3156

5.6 Problems160

Ⅵ WAVELET ZOOM163

6.1 Lipschitz Regularity1163

6.1.1 Lipschitz Definition and Fourier Analysis164

6.1.2 Wavelet Vanishing Moments166

6.1.3 Regularity Measurements with Wavelets169

6.2.1 Detection of Singularities176

6.2 Wavelet Transform Modulus Maxima2176

6.2.2 Reconstruction From Dyadic Maxima3183

6.3 Multiscale Edge Detection2189

6.3.1 Wavelet Maxima for Images2189

6.3.2 Fast Multiscale Edge Computations3197

6.4 Multifractals2200

6.4.1 Fractal Sets and Self-Similar Functions200

6.4.2 Singularity Spectrum3205

6.4.3 Fractal Noises3211

6.5 Problems216

Ⅶ WAVELET BASES220

7.1 Orthogonal Wavelet Bases1220

7.1.1 Multiresolution Approximations221

7.1.2 Scaling Function224

7.1.3 Conjugate Mirror Filters228

7.1.4 In Which Orthogonal Wavelets Finally Arrive235

7.2 Classes of Wavelet Bases1241

7.2.1 Choosing a Wavelet241

7.2.2 Shannon, Meyer and Battle-Lemarié Wavelets246

7.2.3 Daubechies Compactly Supported Wavelets249

7.3 Wavelets and Filter Banks1255

7.3.1 Fast Orthogonal Wavelet Transform255

7.3.2 Perfect Reconstruction Filter Banks259

7.3.3 Biorthogonal Bases of 12(Z)2263

7.4 Biorthogonal Wavelet Bases2265

7.4.1 Construction of Biorthogonal Wavelet Bases265

7.4.2 Biorthogonal Wavelet Design2268

7.4.3 Compactly Supported Biorthogonal Wavelets2270

7.4.4 Lifting Wavelets3273

7.5 Wavelet Bases on an Interval2281

7.5.1 Periodic Wavelets282

7.5.2 Folded Wavelets284

7.5.3 Boundary Wavelets3286

7.6 Multiscale Interpolations2293

7.6.1 Interpolation and Sampling Theorems293

7.6.2 Interpolation Wavelet Basis3299

7.7 Separable Wavelet Bases1303

7.7.1 Separable Multiresolutions304

7.7.2 Two-Dimensional Wavelet Bases306

7.7.3 Fast Two-Dimensional Wavelet Transform310

7.7.4 Wavelet Bases in Higher Dimensions2313

7.8 Problems314

8.1.1 Wavelet Packet Tree322

8.1 Wavelet Packets2322

Ⅷ WAVELET PACKET AND LOCAL COSINE BASES322

8.1.2 Time-Frequency Localization327

8.1.3 Particular Wavelet Packet Bases333

8.1.4 Wavelet Packet Filter Banks336

8.2 Image Wavelet Packets2339

8.2.1 Wavelet Packet Quad-Tree339

8.2.2 Separable Filter Banks341

8.3 Block Transforms1343

8.3.1 Block Bases344

8.3.2 Cosine Bases346

8.3.3 Discrete Cosine Bases349

8.3.4 Fast Discrete Cosine Transforms2350

8.4 Lapped Orthogonal Transforms2353

8.4.1 Lapped Projectors353

8.4.2 Lapped Orthogonal Bases359

8.4.3 Local Cosine Bases361

8.4.4 Discrete Lapped Transforms364

8.5 Local Cosine Trees2368

8.5.1 Binary Tree of Cosine Bases369

8.5.2 Tree of Discrete Bases371

8.5.3 Image Cosine Quad-Tree372

8.6 Problems374

Ⅸ AN APPROXIMATION TOUR377

9.1 Linear Approximations1377

9.1.1 Linear Approximation Error377

9.1.2 Linear Fourier Approximations378

9.1.3 Linear Multiresolution Approximations382

9.1.4 Karhunen-Loève Approximations2385

9.2.1 Non-Linear Approximation Error389

9.2 Non-Linear Approximations1389

9.2.2 Wavelet Adaptive Grids391

9.2.3 Besov Spaces3394

9.3 Image Approximations with Wavelets1398

9.4 Adaptive Basis Selection2405

9.4.1 Best Basis and Schur Concavity406

9.4.2 Fast Best Basis Search in Trees411

9.4.3 Wavelet Packet and Local Cosine Best Bases413

9.5 Approximations with Pursuits3417

9.5.1 Basis Pursuit418

9.5.2 Matching Pursuit421

9.5.3 Orthogonal Matching Pursuit428

9.6 Problems430

10.1.1 Bayes Estimation435

10.1 Bayes Versus Minimax2435

Ⅹ ESTIMATIONS ARE APPROXIMATIONS435

10.1.2 Minimax Estimation442

10.2 Diagonal Estimation in a Basis2446

10.2.1 Diagonal Estimation with Oracles446

10.2.2 Thresholding Estimation450

10.2.3 Thresholding Refinements3455

10.2.4 Wavelet Thresholding458

10.2.5 Best Basis Thresholding3466

10.3 Minimax Optimality3469

10.3.1 Linear Diagonal Minimax Estimation469

10.3.2 Orthosymmetric Sets474

10.3.3 Nearly Minimax with Wavelets479

10.4.1 Estimation in Arbitrary Gaussian Noise486

10.4 Restoration3486

10.4.2 Inverse Problems and Deconvolution491

10.5 Coherent Estimation3501

10.5.1 Coherent Basis Thresholding502

10.5.2 Coherent Matching Pursuit505

10.6 Spectrum Estimation2507

10.6.1 Power Spectrum508

10.6.2 Approximate Karhunen-Loève Search3512

10.6.3 Locally Stationary Processes3516

10.7 Problems520

Ⅺ TRANSFORM CODING526

11.1 Signal Compression2526

11.1.1 State of the Art526

11.1.2 Compression in Orthonormal Bases527

11.2 Distortion Rate of Quantization2528

11.2.1 Entropy Coding529

11.2.2 Scalar Quantization537

11.3 High Bit Rate Compression2540

11.3.1 Bit Allocation540

11.3.2 Optimal Basis and Karhunen-Loève542

11.3.3 Transparent Audio Code544

11.4 Image Compression2548

11.4.1 Deterministic Distortion Rate548

11.4.2 Wavelet Image Coding557

11.4.3 Block Cosine Image Coding561

11.4.4 Embedded Transform Coding566

11.4.5 Minimax Distortion Rate3571

11.5 Video Signals2577

11.5.1 Optical Flow577

11.5.2 MPEG Video Compression585

11.6 Problems587

Appendix A MATHEMATICAL COMPLEMENTS591

A.1 Functions and Integration591

A.2 Banach and Hilbert Spaces593

A.3 Bases of Hilbert Spaces595

A.4 Linear Operators596

A.5 Separable Spaces and Bases598

A.6 Random Vectors and Covariance Operators599

A.7 Diracs601

Appendix B SOFTWARE TOOLBOXES603

B.1 WAVELAB603

8.2 LASTWAVE609

B.3 Freeware Wavelet Toolboxes610

BIBLIOGRAPHY612

INDEX629