A systematic exploration of both classic and contemporary algorithms in blind source separation with practical case studies   

The book presents an overview of Blind Source Separation, a relatively new signal processing method.  Due to the multidisciplinary nature of the subject, the book has been written so as to appeal to an audience from very different backgrounds. Basic mathematical skills (e.g. on matrix algebra and foundations of probability theory) are essential in order to understand the algorithms, although the book is written in an introductory, accessible style.

This book offers a general overview of the basics of Blind Source Separation, important solutions and algorithms, and in-depth coverage of applications in image feature extraction, remote sensing image fusion, mixed-pixel decomposition of SAR images, image object recognition fMRI medical image processing, geochemical and geophysical data mining, mineral resources prediction and geoanomalies information recognition. Firstly, the background and theory basics of blind source separation are introduced, which provides the foundation for the following work. Matrix operation, foundations of probability theory and information theory basics are included here. There follows the fundamental mathematical model and fairly new but relatively established blind source separation algorithms, such as Independent Component Analysis (ICA) and its improved algorithms (Fast ICA, Maximum Likelihood ICA, Overcomplete ICA, Kernel ICA, Flexible ICA, Non-negative ICA, Constrained ICA, Optimised ICA). The last part of the book considers the very recent algorithms in BSS e.g. Sparse Component Analysis (SCA) and Non-negative Matrix Factorization (NMF). Meanwhile, in-depth cases are presented for each algorithm in order to help the reader understand the algorithm and its application field.

• A systematic exploration of both classic and contemporary algorithms in blind source separation with practical case studies
• Presents new improved algorithms aimed at different applications, such as image feature extraction, remote sensing image fusion, mixed-pixel decomposition of SAR images, image object recognition, and MRI medical image processing
• With applications in geochemical and geophysical data mining, mineral resources prediction and geoanomalies information recognition
• Written by an expert team with accredited innovations in blind source separation and its applications in natural science
• Accompanying website includes a software system providing codes for most of the algorithms mentioned in the book, enhancing the learning experience

Essential reading for postgraduate students and researchers engaged in the area of signal processing, data mining, image processing and recognition, information, geosciences, life sciences.

Xianchuan Yu, Beijing Normal University, P. R. China

Dan Hu, Beijing Normal University, P. R. China

Jindong Xu, Beijing Normal University, P. R. China

About the Authors xiii

Preface xv

Acknowledgements xvii

Glossary xix

1 Introduction 1

1.1 Overview of Blind Source Separation 1

1.2 History of BSS 4

1.3 Applications of BSS 8

1.4 Contents of the Book 10

References 11

Part I BASIC THEORY OF BSS

2 Mathematical Foundation of Blind Source Separation 19

2.1 Matrix Analysis and Computing 19

2.2 Foundation of Probability Theory for Higher-Order Statistics 28

2.3 Basic Concepts of Information Theory 33

2.4 Distance Measure 37

2.5 Solvability of the Signal Blind Source Separation Problem 40

Further Reading 41

3 General Model and Classical Algorithm for BSS 43

3.1 Mathematical Model 43

3.2 BSS Algorithm 46

References 51

4 Evaluation Criteria for the BSS Algorithm 53

4.1 Evaluation Criteria for Objective Functions 53

4.2 Evaluation Criteria for Correlations 57

4.3 Evaluation Criteria for Signal-to-Noise Ratio 57

References 58

Part II INDEPENDENT COMPONENT ANALYSIS AND APPLICATIONS

5 Independent Component Analysis 61

5.1 History of ICA 61

5.2 Principle of ICA 65

5.3 Chapter Summary 82

References 83

6 Fast Independent Component Analysis and Its Application 85

6.1 Overview 85

6.2 FastICA Algorithm 89

6.3 Application and Analysis 92

6.4 Conclusion 118

References 119

7 Maximum Likelihood Independent Component Analysis and Its Application 121

7.1 Overview 121

7.2 Algorithms for Maximum Likelihood Estimation 123

7.3 Application and Analysis 130

7.4 Chapter Summary 133

References 133

8 Overcomplete Independent Component Analysis Algorithms and Applications 135

8.1 Overcomplete ICA Algorithms 135

8.2 Applications and Analysis 139

8.3 Chapter Summary 143

References 144

9 Kernel Independent Component Analysis 145

9.1 KICA Algorithm 145

9.2 Application and Analysis 147

9.3 Concluding Remarks 149

References 152

10 Natural Gradient Flexible ICA Algorithm and Its Application 153

10.1 Natural Gradient Flexible ICA Algorithm 153

10.2 Application and Analysis 156

10.3 Chapter Summary 166

References 166

11 Non-negative Independent Component Analysis and Its Application 167

11.1 Non-negative Independent Component Analysis 168

11.2 Application and Analysis 169

11.3 Chapter Summary 182

References 182

12 Constraint Independent Component Analysis Algorithms and Applications 183

12.1 Overview 183

12.2 CICA Algorithm 185

12.3 Application and Analysis 189

12.4 Chapter Summary 196

References 196

13 Optimized Independent Component Analysis Algorithms and Applications 199

13.1 Overview 199

13.2 Optimized ICA Algorithm 200

13.3 Application and Analysis 205

13.4 Chapter Summary 221

References 222

14 Supervised Learning Independent Component Analysis Algorithms and Applications 225

14.1 Overview 225

14.2 Mathematical Model 226

14.3 Principles of SL-ICA 227

14.4 SL-ICA Implementation Process 230

14.5 The Experiment 230

14.6 Chapter Summary 239

Appendix 14.A Polarization Channel SAR Images of Beijing and the Decomposition Results using SL-ICA 239

References 242

Part III ADVANCES AND APPLICATIONS OF BSS

15 Non-negative Matrix Factorization Algorithms and Applications 247

15.1 Introduction 247

15.2 NMF Algorithms 251

15.3 Applications and Analysis 276

15.4 Chapter Summary 309

References 310

16 Sparse Component Analysis and Applications 313

16.1 Overview 314

16.2 Linear Clustering SCA (LC-SCA) 321

16.3 Plane Clustering SCA (PC-SCA) 332

16.4 Over-Complete SCA Based on Plane Clustering (PCO-SCA) 336

16.5 Blind Image Separation Based on Wavelets and SCA (WL-SCA) 340

16.6 New BSS Algorithm Based on Feedback SCA 343

16.7 Remote Sensing Image Classification Based on SCA 351

16.8 Chapter Summary 357

References 357

Index 361