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

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.

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 1…