Blind Source Separation: Theory and Applications

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 sty.

5.2.1 Concept of Independence of Random Variables.

Cover; Title Page; Copyright; Contents; About the Authors; Preface; Acknowledgements; Glossary; Chapter 1 Introduction; 1.1 Overview of Blind Source Separation; 1.2 History of BSS; 1.3 Applications of BSS; 1.3.1 Speech Signal Separation; 1.3.2 Data Communication and Array Signal Processing; 1.3.3 Image Processing and Recognition; 1.3.4 Geological Spatial Information Processing; 1.3.5 Biomedical Signal Processing; 1.3.6 Text Document Analysis; 1.4 Contents of the Book; References; Part I Basic Theory of BSS; Chapter 2 Mathematical Foundation of Blind Source Separation.

2.1 Matrix Analysis and Computing2.1.1 Determinant and Its Properties; 2.1.2 Concepts of Matrix; 2.1.3 Matrix Computation Formulas; 2.1.3.1 Matrix Inversion Lemma; 2.1.3.2 Properties of the Moore -- Penrose; 2.1.3.3 Mathematical Expectations of a Vector and a Matrix; 2.1.3.4 Kronecker Product of a Matrix; 2.1.3.5 The Symmetric Hessian Matrix; 2.1.3.6 Some Important Inequalities; 2.2 Foundation of Probability Theory for Higher-Order Statistics; 2.2.1 Moment; 2.2.2 Cumulant; 2.2.3 Properties of Moments and Cumulants; 2.3 Basic Concepts of Information Theory; 2.3.1 Entropy.

2.3.2 Differential Entropy, Maximum Entropy,…