Blind Source Separation : Theory and Applications.
Title:
Blind Source Separation : Theory and Applications.
Author:
Yu, Xianchuan.
ISBN:
9781118679869
Personal Author:
Edition:
1st ed.
Physical Description:
1 online resource (388 pages)
Contents:
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 Computing -- 2.1.1 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, and Negentropy -- 2.3.3 Mutual Information -- 2.3.4 Relative Entropy (Kullback--Leibler Divergence) -- 2.3.5 Important Inequality -- 2.4 Distance Measure -- 2.4.1 Geometric Distance Measure -- 2.4.2 The Distance between Datasets -- 2.4.3 Distance Measures -- 2.5 Solvability of the Signal Blind Source Separation Problem -- 2.5.1 Partitioned Matrix -- 2.5.2 Decomposability of Mixing Matrix -- Further Reading -- Chapter 3 General Model and Classical Algorithm for BSS -- 3.1 Mathematical Model -- 3.1.1 Linear Mixing Models.
3.1.1.1 Instantaneous Linear Mixing -- 3.1.1.2 Linear Convolution Mixing Model -- 3.1.2 Nonlinear Mixing Model -- 3.2 BSS Algorithm -- 3.2.1 BSS Algorithm for Instantaneous Linear Mixing -- 3.2.2 Nonlinear Principle Component Analysis (PCA) -- 3.2.2.1 Introduction -- 3.2.2.2 Kernel PCA -- 3.2.3 Separation Algorithm for Nonlinear Mixing -- 3.2.3.1 Separation of Post Nonlinear (PNL) Mixtures -- 3.2.3.2 General Separation Methods for Nonlinear Mixtures -- 3.2.3.3 Nonlinear ICA Neural Networks -- 3.2.4 Fashionable BSS -- 3.2.4.1 Sparse Component Analysis (SCA) -- 3.2.4.2 Nonnegative Matrix Factorization (NMF) -- References -- Chapter 4 Evaluation Criteria for the BSS Algorithm -- 4.1 Evaluation Criteria for Objective Functions -- 4.1.1 Mutual Information Minimization -- 4.1.2 Negentropy Maximization -- 4.1.3 Maximum Likelihood -- 4.1.4 Information Maximization -- 4.1.5 Permanent Model Objective Function -- 4.1.6 Higher-Order Cumulant Objective Function -- 4.2 Evaluation Criteria for Correlations -- 4.3 Evaluation Criteria for Signal-to-Noise Ratio -- References -- Part II Independent Component Analysis and Applications -- Chapter 5 Independent Component Analysis -- 5.1 History of ICA -- 5.2 Principle of ICA -- 5.2.1 Concept of Independence of Random Variables -- 5.2.2 ICA Definition -- 5.2.3 ICA Estimation Principle -- 5.2.3.1 ICA Assumptions -- 5.2.3.2 ICA Mathematical Model -- 5.2.3.3 ICA Unmixing Model -- 5.2.4 Uncertainty of ICA -- 5.2.5 Relationship between ICA and BSS, PCA, and Whitening -- 5.2.5.1 ICA and BSS -- 5.2.5.2 ICA and PCA -- 5.2.5.3 ICA and Whitening -- 5.2.6 Basic Methods for ICA -- 5.2.6.1 Objective Function of ICA -- 5.2.6.2 ICA Optimization Algorithm -- 5.2.7 Impact of the Statistical Properties of the Signal on the Algorithm.
5.2.7.1 Symmetrical Distribution Assumptions of Traditional ICA -- 5.2.7.2 Non-symmetrical Distribution and Skewness -- 5.3 Chapter Summary -- References -- Chapter 6 Fast Independent Component Analysis and Its Application -- 6.1 Overview -- 6.1.1 Deflation Method -- 6.1.2 Symmetry Method -- 6.2 FastICA Algorithm -- 6.2.1 Ordinary FastICA -- 6.2.2 Optimization of FastICA -- 6.3 Application and Analysis -- 6.3.1 Whitening Preprocessing -- 6.3.2 Separation of Blind Signals -- 6.3.3 Separation of Image Signals -- 6.3.4 ICA Algorithm for Geochemical Exploration Data Analysis -- 6.3.5 FastICA Algorithm Used for Remote Sensing Image Classification -- 6.3.6 Application of the ICA Algorithm to Image Noise Reduction -- 6.3.7 M-FastICA for Face Recognition -- 6.3.8 FastICA for Extracting Image Information -- 6.4 Conclusion -- References -- Chapter 7 Maximum Likelihood Independent Component Analysis and Its Application -- 7.1 Overview -- 7.1.1 Likelihood Estimation -- 7.1.2 Probability Density Estimation -- 7.2 Algorithms for Maximum Likelihood Estimation -- 7.2.1 Gradient Algorithms -- 7.2.2 A Fast Fixed-Point Algorithm -- 7.3 Application and Analysis -- 7.3.1 Blind Signal Separation -- 7.3.2 Image Signal Separation -- 7.4 Chapter Summary -- References -- Chapter 8 Overcomplete Independent Component Analysis Algorithms and Applications -- 8.1 Overcomplete ICA Algorithms -- 8.1.1 Classic Overcomplete ICA Algorithm -- 8.1.2 Algebraic Overcomplete ICA Algorithm -- 8.1.3 Geometric Overcomplete ICA Algorithm -- 8.2 Applications and Analysis -- 8.2.1 Overcomplete ICA Facial Feature Representation -- 8.2.2 Experiments and Conclusions -- 8.3 Chapter Summary -- References -- Chapter 9 Kernel Independent Component Analysis -- 9.1 KICA Algorithm -- 9.1.1 Object Function of KICA -- 9.1.2 KCCA Algorithm -- 9.1.3 KGV Algorithm.
9.2 Application and Analysis -- 9.3 Concluding Remarks -- References -- Chapter 10 Natural Gradient Flexible ICA Algorithm and Its Application -- 10.1 Natural Gradient Flexible ICA Algorithm -- 10.1.1 Basic Algorithm for Flexible ICA -- 10.1.2 Related Improvement of the Flexible ICA Basic Algorithm -- 10.1.3 Determination of ai -- 10.2 Application and Analysis -- 10.2.1 Experimental Data -- 10.2.2 Traditional Image Denoising Algorithm -- 10.2.2.1 Median Filtering -- 10.2.2.2 Mean Filtering -- 10.2.3 ICA Denoising Algorithm -- 10.2.3.1 FastICA Denoising -- 10.2.3.2 ERICA Denoising -- 10.2.3.3 Natural Gradient Flexible ICA Speckle Noise Reduction Based on the Natural Gradient -- 10.2.4 Analysis of Results -- 10.3 Chapter Summary -- References -- Chapter 11 Non-negative Independent Component Analysis and Its Application -- 11.1 Non-negative Independent Component Analysis -- 11.2 Application and Analysis -- 11.2.1 Mixed-Signal Separation Experiment -- 11.2.2 Remote Sensing Image Fusion Experiments -- 11.2.2.1 Experimental Data -- 11.2.2.2 Remote Sensing Image Fusion Based on Ordered Non-negative ICA -- 11.2.2.3 Comparative Analysis of Experimental Results -- 11.3 Chapter Summary -- References -- Chapter 12 Constraint Independent Component Analysis Algorithms and Applications -- 12.1 Overview -- 12.2 CICA Algorithm -- 12.2.1 CICA Algorithm Based on Negative Entropy -- 12.2.1.1 Target Functions -- 12.2.1.2 Optimization Algorithm -- 12.2.2 CICA Algorithm Based on Kurtosis -- 12.3 Application and Analysis -- 12.3.1 CICA of Voice Signals -- 12.3.2 CICA for Prediction of Mineral Resources -- 12.4 Chapter Summary -- References -- Chapter 13 Optimized Independent Component Analysis Algorithms and Applications -- 13.1 Overview -- 13.2 Optimized ICA Algorithm.
13.2.1 The Weighted Iterative Algorithm for Optimized ICA -- 13.2.2 Optimized ICA Weighted Iterative Algorithm -- 13.2.3 Choice of Number of Independent Components -- 13.3 Application and Analysis -- 13.3.1 Separation Simulation for an Artificial Mixed Signal -- 13.3.2 Optimized ICA for fMRI Data Analysis -- 13.3.2.1 Independent Component Related to the Task -- 13.3.2.2 Instantaneous Task-Related Independent Component -- 13.3.2.3 Signal Independent Component of Head Movements -- 13.3.2.4 Independent Component of Class Periodic Signals -- 13.3.2.5 Independent Component of the Noise Signal -- 13.3.2.6 Component with a Special Meaning -- 13.4 Chapter Summary -- References -- Chapter 14 Supervised Learning Independent Component Analysis Algorithms and Applications -- 14.1 Overview -- 14.2 Mathematical Model -- 14.2.1 Mathematical Model for Mixed Pixels in SAR Images -- 14.2.2 ICA Model -- 14.3 Principles of SL-ICA -- 14.3.1 Centering -- 14.3.2 Whitening -- 14.3.3 Objective Function of SL-ICA -- 14.3.4 Optimized Algorithm -- 14.4 SL-ICA Implementation Process -- 14.4.1 Iterative Process of SL-ICA -- 14.4.1.1 Initialization -- 14.4.1.2 Recursive Operation -- 14.4.1.3 Post Processing -- 14.4.2 Flowchart of SL-ICA Algorithm -- 14.5 The Experiment -- 14.5.1 Computer Simulated Multi-polarization SAR Images -- 14.5.2 Real Multi-polarization Channel SAR Images -- 14.6 Chapter Summary -- Appendix 14.A Polarization Channel SAR Images of Beijing and the Decomposition Results using SL-ICA -- References -- Part III Advances and Applications of BSS -- Chapter 15 Non-negative Matrix Factorization Algorithms and Applications -- 15.1 Introduction -- 15.1.1 The Origin of Non-negative Matrix Factorization Theory -- 15.1.2 Characteristics of NMF Theory -- 15.1.3 Application Fields of NMF Theory -- 15.2 NMF Algorithms.
15.2.1 The Mathematical Model of NMF.
Abstract:
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.
Local Note:
Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2017. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.
Subject Term:
Genre:
Electronic Access:
Click to View