Blind Source Separation (eBook)

Yong Xiang received the B.E. and M.E. degrees from the University of Electronic Science and Technology of China, Chengdu, China, in 1983 and 1989, respectively. In 2003, he received the Ph.D. degree from The University of Melbourne, Melbourne, Australia. He was with the Southwest Institute of Electronic Equipment of China, Chengdu, from 1983 to 1986. In 1989, he joined the University of Electronic Science and Technology of China, where he was a Lecturer from 1989 to 1992 and an Associate Professor from 1992 to 1997. He was a Senior Communications Engineer with Bandspeed Inc., Melbourne, Australia, from 2000 to 2002. He is currently an Associate Professor with the School of Information Technology at Deakin University, Australia. His research interests include blind signal/system estimation, communication signal processing, information and network security, speech and image processing, and pattern recognition.Dezhong Peng received the B.S. degree in applied mathematics, the M.S. and Ph.D. degrees in computer software and theory from the University of Electronic Science and Technology of China, Chengdu, China, in 1998, 2001 and 2006, respectively. He was a Postdoctoral Research Fellow at the School of Engineering, Deakin University, Australia from 2007 to 2009. Currently, he is a Professor at the Machine Intelligence Laboratory, College of Computer Science, Sichuan University, Chengdu, China. His current research interests include blind signal processing and neural networks.Zuyuan Yang received the B.E. degree from Hunan University of Science and Technology, Xiangtan, China, and the Ph.D. degree from South China University of Technology, Guangzhou, China, in 2003 and 2010, respectively. He was a recipient of the Excellent Ph.D. Thesis Award of Guangdong Province in 2010. Dr Yang is currently a Researcher with the Faculty of Automation, Guangdong University of Technology, Guangzhou. His current research interests include blind source separation, compressed sensing, nonnegative matrix factorization, and image processing.

Preface 7
Acknowledgments 8
Contents 9
1 Introduction 11
1.1 Background of Blind Source Separation 11
1.2 Statistics Based Methods for Blind Source Separation 15
1.2.1 Higher-Order Statistics Based Methods 15
1.2.2 Second-Order Statistics Based Methods 17
1.3 Blind Source Separation via Dependent Component Analysis 18
1.3.1 Scenarios of Mutually Correlated Sources 18
1.3.2 Dependent Component Analysis Based Methods 20
References 24
2 Dependent Component Analysis Exploiting Nonnegativity and/or Time-Domain Sparsity 28
2.1 Nonnegative Sparse Representation Based Methods 28
2.1.1 Sparsity Measures for Nonnegative Signals 29
2.1.2 Estimation of Mixing Matrix and Source Signals 32
2.1.3 Uniqueness Conditions 36
2.2 Convex Geometry Analysis Based Methods 37
2.2.1 Geometric Features 38
2.2.2 Estimation of Source Signals 40
2.2.3 Source Identifiability Analysis 43
2.3 Nonnegative Matrix Factorization Based Methods 45
2.3.1 Nonnegative Matrix Factorization Models 45
2.3.2 Estimation of Mixing Matrix and Source Signals 48
2.3.3 Algorithm Analysis 53
References 53
3 Dependent Component Analysis Using Time-Frequency Analysis 57
3.1 Fundamentals of TFA 57
3.2 TFA-Based Methods for Mixing Matrix Estimation 60
3.2.1 System Model and Existing Works 60
3.2.2 Mixing Matrix Estimation Under Relaxed TF Sparsity 61
3.2.3 Mixing Matrix Estimation Under Local TF Sparsity 63
3.3 TFA-Based Methods for Source Recovery 64
3.3.1 Source Recovery Under Strong TF Sparsity 64
3.3.2 Source Recovery Under Relaxed TF Sparsity 67
3.3.3 Recovery of Non-sparse Dependent Sources 73
References 78
4 Dependent Component Analysis Using Precoding 80
4.1 Concept of Precoding Based Dependent Component Analysis 80
4.2 Precoding Based Time-Domain Method 81
4.3 Precoding Based Z-Domain Methods 87
4.3.1 Using Second-Order Precoders 87
4.3.2 Using First-Order Precoders 92
References 97
5 Future Work 98
5.1 Future Work for DCA Exploiting Nonnegativity and/or Time-Domain Sparsity 98
5.2 Future Work for DCA Exploiting Time-Frequency Analysis (TFA) 99
5.3 Future Work for DCA Exploiting Precoding 100
References 100