Blind Signal Processing: Theory and Practice

Cover......Page 1
Blind Signal Processing......Page 4
ISBN 9783642113468......Page 5
Preface......Page 6
Table of Content......Page 10
Symbols......Page 14
1.2 Blind Source Separation......Page 16
1.2.1 Linear Instantaneous Mixing Problem......Page 17
1.2.2 Separation of Convolutive Mixtures......Page 23
1.3 Independent Component Analysis(ICA)......Page 24
1.4 The Historical Development and Research Prospect of Bl ind Signal Processing......Page 26
References......Page 35
2.1.1 Random Process......Page 42
2.1.2 Random Variable and Distribution......Page 44
2.1.3 Non-Correlativity and Statistical Independence......Page 47
2.2.1 Basic Concept......Page 49
2.2.2 Maximum Likelihood Estimation......Page 50
2.2.3 Linear Mean Square Estimation......Page 52
2.2.4 Least-Squares Estimation......Page 53
2.2.5 Bayesian Estimation......Page 54
2.3.1 Entropy......Page 55
1. Differential entropy......Page 56
3. Negentropy......Page 57
2.3.3 Mutual Information......Page 58
2.4.1 Moment and Cumulant......Page 59
2. 4. 2 Moment and Cumulant of Stationary Process......Page 62
2.5.1 Zero Meaning of Signal......Page 63
2.5.2 Whitening of Signal......Page 64
2.6 Complex Nonlinear Function......Page 68
2.6.2 Decorrelation Lemma for Two Complex Random Vectors......Page 69
2.6.3 Proper (inherent) Property of Complex Random Vector......Page 70
2.6.4 Principle of Selection of Complex Nonlinear Function......Page 71
References......Page 73
3.1 Problem Statement and Assumptions......Page 76
3.2 Contrast Functions......Page 78
1. Maximum likelihood estimation contrast function......Page 79
3. Other contrast functions......Page 81
3.2.2 Computation of Contrast Function......Page 82
3.3 Information Maximization Method of ICA......Page 83
3.4 Maximum Likelihood Method and Common Learning Rule......Page 86
3.5 FastICA Algorithm......Page 87
3.6 Natural Gradient Method......Page 90
1. Hidden Markov Model......Page 93
2. Generative Model......Page 96
References......Page 98
4.1 Principal Component Analysis & Infinitesimal Analysis......Page 100
4.2 Nonlinear PCA and Blind Source Separation......Page 103
4.3 Kernel PCA......Page 105
4.4.2 Nonlinear PCA......Page 107
4.4.3 Complex Nonlinear PCA......Page 109
References......Page 111
5.1 Nonlinear Model and Source Separation......Page 114
5.2 Learning Algorithm......Page 116
5.3 Extended Gaussianization Method of Post Nonlinear Blind Separation......Page 117
5.4 Neural Network Method for Nonlinear ICA......Page 120
5.5 Genetic Algorithm of Nonlinear ICA Solution......Page 122
5.6 Application Examples of Nonlinear ICA......Page 123
References......Page 127
6.1 Description of Issues......Page 130
6.2 Convolutive Mixtures in Time-Domain......Page 131
6.3 Convolutive Mixtures Algorithms in Frequency-Domain......Page 132
6.4 Frequency-Domain Blind Separation of Speech Convolutive Mixtures......Page 139
6.5 Bussgang Method......Page 143
6.6 Multi-channel Blind Deconvolution......Page 145
References......Page 147
7.1 Advancing the Problem......Page 150
7.2 Nonparametric Estimation of Probability Density Function......Page 151
7.2.1 Kernel Function Method of Probability Density Estimation......Page 152
7.2.2 Experiential Bandwidth Selection of Kernel Function Method......Page 157
7.2.3 Sheather-Jones Bandwidth Selection of Kernel Function Method......Page 158
7.3 Estimation of Evaluation Function......Page 159
7.4 Blind Separation Algorithm Based on Probability Density Estimation......Page 160
7.4.1 Mixtures Case of Hybrid Signals......Page 161
7.4.2 Comparison of Density Estimation-Based Algorithm and EXTICA Algorithm......Page 166
7.5 Probability Density Estimation of Gaussian Mixtures Model......Page 168
7.6 Blind Deconvolution Algorithm Based on Probability Density Function Estimation......Page 173
7.6.1 Evaluation Criterion in Blind Deconvolution......Page 174
7.6.2 Blind Deconvolution Simulation......Page 175
7.6.3 Sub-Gaussian Mixtures Case......Page 176
7.6.4 Super-Gaussian Mixtures Case......Page 177
7.6.5 Hybrid Mixed Signals Case......Page 179
7.7 On-line Algorithm of Nonparametric Density Estimation......Page 181
References......Page 190
8.1 Introduction......Page 194
8.2 JAD Algorithm of Frequency-Domain Feature......Page 195
8.3 JAD Algorithm of Time-Frequency Feature......Page 200
8.4 Joint Approximate Block Diagonalization Algorithm of Convolutive Mixtures......Page 203
8.5 JAD Method Based on Cayley Transformation......Page 207
8.6 Joint Diagonalization and Joint Non-Diagonalization Method......Page 209
8.7 Nonparametric Density Estimating Separating Method Based on Time-Frequency Analysis......Page 212
1. Mixing model......Page 213
2. Noise reduction in the time-frequency domain......Page 214
3. Time-frequency nonparametric density estimation ICA algorithm (TFNPICA)......Page 216
4. Simulation experiment......Page 218
Appendix:......Page 220
References......Page 221
9.1 Blind Signal Extraction......Page 224
9.2.1 Introduction......Page 227
9.2.2 Projection Pursuit and Blind Separation......Page 229
9.2.3 Signal Source Probability Density and Joint Estimation of Demixing Matrix......Page 231
9.2.4 Optimization Algorithm and Global Convergence......Page 232
9.3.1 Introduction......Page 234
9.3.2 Identification Condition......Page 235
9.3.3 Time-Domain Algorithm......Page 239
9.3.4 Frequency-Domain Algorithm......Page 242
9.4 Blind Separation for Fewer Sensors than Sources—Underdetermined Model......Page 244
9.4.1 Underdetermined Model......Page 247
1. Linear algorithm and underdetermined model......Page 249
9.4.3 Performance of Algorithms and Evaluation Index......Page 250
1. Comparison of the real mixing matrix and its estimation......Page 251
2. Comparison of source signals and their estimation......Page 252
1. Bayesian method of statistical model......Page 253
2. Gaussian mixtures model based Bayesian analysis......Page 257
9.4.5 Underdetermined Model and Bayesian Filter in Convolutive Mixtures......Page 264
9.5 FastICA Separation Algorithm of Complex Numbers in Convolutive Mixtures......Page 271
9.6 On-line Complex ICA Algorithm Based on Uncorrelated Characteristics of Complex Vectors......Page 278
2. On-line enhancing CICA algorithms......Page 279
3. Simulation......Page 280
9.7 ICA-Based Wigner-Ville Distribution......Page 283
9.8.1 Basic Concept of ICA Feature Extraction......Page 288
9.8.2 ICA Feature Extraction and Characteristics Analysis of Speech and Music Signals......Page 290
9.9.1 Introduction......Page 297
9.9.2 Algorithm......Page 298
9.9.3 Applications and Discussions......Page 300
9.10.1 Introduction......Page 301
9.10.2 Problem Statement......Page 302
9.10.3 Particle Filtering......Page 303
9.10.4 Experiment and Analysis......Page 305
2. Nonlinear and noisy determined ICA......Page 307
9.10.5 Conclusion......Page 308
References......Page 309
10.1.1 Introduction......Page 320
1. Analysis of active sonar data......Page 321
2. Target enhancement procedure by BSS......Page 323
1. Separation algorithm......Page 324
2. Correct permutation......Page 326
10.1.4 Experiments and analysis......Page 328
10.2.1 Artifacts Rejection in EEG of Little Animal......Page 331
10.2.2 ICA-Based ECG Artifact Rejection in Clinical EEG......Page 333
10.3.1 Experiment Setup......Page 336
10.3.3 Data Analysis......Page 337
10.4 ICA in Human Face Recognition......Page 339
10.5 ICA in Data Compression......Page 343
10.5.1 Plenoptic-Illumination Function and Image-Based Relighting......Page 344
2. ICA decomposition for IAI dataset......Page 345
3. IBI-based relighting......Page 346
2. Implementation......Page 347
10.5.4 Results and Discussions......Page 348
2. Overall compression results......Page 349
10.6.1 FMRI and Its Data Analysis......Page 352
10.6.2 ICA-Based fMRI Data Analysis......Page 355
10.6.3 Huge Data Compression Issue......Page 356
10.6.4 Results of sICA and tICA......Page 358
10.6.5 Summary......Page 360
10.7.1 Problems of Using Conventional ICA for Speech Signal Separation......Page 361
10.7.2 Null Beamforming-Based Initialization......Page 363
10.7.3 Minimal Distortion Principle for Speech Signal ICA Separation......Page 364
10.7.4 Evaluations......Page 366
10.8 Independent Component Analysis of Microarray Gene Expression Data in the Study of Alzheimer’s Disease (AD)......Page 370
10.8.1 Gene Expression in ICA Model......Page 371
1. ICA decomposed AD microarray data into biological processes......Page 372
2. ICA improved clustering results of AD samples......Page 373
3. ICA identi ed signi cant genes for AD......Page 375
10.8.3 Discussions......Page 377
References......Page 378
Index......Page 386