Adaptive blind signal separation.

• Other Authors: Cheung, Chi-Chiu.
• Format: Others
• Language: English
• Published: 1997
• Subjects: Adaptive signal processing; Signal processing > Mathematics
• Online Access: http://library.cuhk.edu.hk/record=b5889133; http://repository.lib.cuhk.edu.hk/en/item/cuhk-322700

by Chi-Chiu Cheung. === Thesis (M.Phil.)--Chinese University of Hong Kong, 1997. === Includes bibliographical references (leaves 124-131). === Abstract --- p.i === Acknowledgments --- p.iii === Chapter 1 --- Introduction --- p.1 === Chapter 1.1 --- The Blind Signal Separation Problem --- p.1 === Chapter 1.2 --- Contributions of this Thesis --- p.3 === Chapter 1.3 --- Applications of the Problem --- p.4 === Chapter 1.4 --- Organization of the Thesis --- p.5 === Chapter 2 --- The Blind Signal Separation Problem --- p.7 === Chapter 2.1 --- The General Blind Signal Separation Problem --- p.7 === Chapter 2.2 --- Convolutive Linear Mixing Process --- p.8 === Chapter 2.3 --- Instantaneous Linear Mixing Process --- p.9 === Chapter 2.4 --- Problem Definition and Assumptions in this Thesis --- p.9 === Chapter 3 --- Literature Review --- p.13 === Chapter 3.1 --- Previous Works on Blind Signal Separation with Instantaneous Mixture --- p.13 === Chapter 3.1.1 --- Algebraic Approaches --- p.14 === Chapter 3.1.2 --- Neural approaches --- p.15 === Chapter 3.2 --- Previous Works on Blind Signal Separation with Convolutive Mixture --- p.20 === Chapter 4 --- The Information-theoretic ICA Scheme --- p.22 === Chapter 4.1 --- The Bayesian YING-YANG Learning Scheme --- p.22 === Chapter 4.2 --- The Information-theoretic ICA Scheme --- p.25 === Chapter 4.2.1 --- Derivation of the cost function from YING-YANG Machine --- p.25 === Chapter 4.2.2 --- Connections to previous information-theoretic approaches --- p.26 === Chapter 4.2.3 --- Derivation of the Algorithms --- p.27 === Chapter 4.2.4 --- Roles and Constraints on the Nonlinearities --- p.30 === Chapter 4.3 --- Direction and Motivation for the Analysis of the Nonlinearity --- p.30 === Chapter 5 --- Properties of the Cost Function and the Algorithms --- p.32 === Chapter 5.1 --- Lemmas and Corollaries --- p.32 === Chapter 5.1.1 --- Singularity of J(V) --- p.33 === Chapter 5.1.2 --- Continuity of J(V) --- p.34 === Chapter 5.1.3 --- Behavior of J(V) along a radially outward line --- p.35 === Chapter 5.1.4 --- Impossibility of divergence of the information-theoretic ICA al- gorithms with a large class of nonlinearities --- p.36 === Chapter 5.1.5 --- Number and stability of correct solutions in the 2-channel case --- p.37 === Chapter 5.1.6 --- Scale for the equilibrium points --- p.39 === Chapter 5.1.7 --- Absence of local maximum of J(V) --- p.43 === Chapter 6 --- The Algorithms with Cubic Nonlinearity --- p.44 === Chapter 6.1 --- The Cubic Nonlinearity --- p.44 === Chapter 6.2 --- Theoretical Results on the 2-Channel Case --- p.46 === Chapter 6.2.1 --- Equilibrium points --- p.46 === Chapter 6.2.2 --- Stability of the equilibrium points --- p.49 === Chapter 6.2.3 --- An alternative proof for the stability of the equilibrium points --- p.50 === Chapter 6.2.4 --- Convergence Analysis --- p.52 === Chapter 6.3 --- Experiments on the 2-Channel Case --- p.53 === Chapter 6.3.1 --- Experiments on two sub-Gaussian sources --- p.54 === Chapter 6.3.2 --- Experiments on two super-Gaussian sources --- p.55 === Chapter 6.3.3 --- Experiments on one super-Gaussian source and one sub-Gaussian source which are globally sub-Gaussian --- p.57 === Chapter 6.3.4 --- Experiments on one super-Gaussian source and one sub-Gaussian source which are globally super-Gaussian --- p.59 === Chapter 6.3.5 --- Experiments on asymmetric exponentially distributed signals .。 --- p.60 === Chapter 6.3.6 --- Demonstration on exactly and nearly singular initial points --- p.61 === Chapter 6.4 --- Theoretical Results on the 3-Channel Case --- p.63 === Chapter 6.4.1 --- Equilibrium points --- p.63 === Chapter 6.4.2 --- Stability --- p.66 === Chapter 6.5 --- Experiments on the 3-Channel Case --- p.66 === Chapter 6.5.1 --- Experiments on three pairwise globally sub-Gaussian sources --- p.67 === Chapter 6.5.2 --- Experiments on three sources consisting of globally sub-Gaussian and globally super-Gaussian pairs --- p.67 === Chapter 6.5.3 --- Experiments on three pairwise globally super-Gaussian sources --- p.69 === Chapter 7 --- Nonlinearity and Separation Capability --- p.71 === Chapter 7.1 --- Theoretical Argument --- p.71 === Chapter 7.1.1 --- Nonlinearities that strictly match the source distribution --- p.72 === Chapter 7.1.2 --- Nonlinearities that loosely match the source distribution --- p.72 === Chapter 7.2 --- Experiment Verification --- p.76 === Chapter 7.2.1 --- Experiments on reversed sigmoid --- p.76 === Chapter 7.2.2 --- Experiments on the cubic root nonlinearity --- p.77 === Chapter 7.2.3 --- Experimental verification of Theorem 2 --- p.77 === Chapter 7.2.4 --- Experiments on the MMI algorithm --- p.78 === Chapter 8 --- Implementation with Mixture of Densities --- p.80 === Chapter 8.1 --- Implementation of the Information-theoretic ICA scheme with Mixture of Densities --- p.80 === Chapter 8.1.1 --- The mixture of densities --- p.81 === Chapter 8.1.2 --- Derivation of the algorithms --- p.82 === Chapter 8.2 --- Experimental Verification on the Nonlinearity Adaptation --- p.84 === Chapter 8.2.1 --- Experiment 1: Two channels of sub-Gaussian sources --- p.84 === Chapter 8.2.2 --- Experiment 2: Two channels of super-Gaussian sources --- p.85 === Chapter 8.2.3 --- Experiment 3: Three channels of different signals --- p.89 === Chapter 8.3 --- Seeking the Simplest Workable Mixtures of Densities ......... .。 --- p.91 === Chapter 8.3.1 --- Number of components --- p.91 === Chapter 8.3.2 --- Mixture of two densities with only biases changeable --- p.93 === Chapter 9 --- ICA with Non-Kullback Cost Function --- p.97 === Chapter 9.1 --- Derivation of ICA Algorithms from Non-Kullback Separation Functionals --- p.97 === Chapter 9.1.1 --- Positive Convex Divergence --- p.97 === Chapter 9.1.2 --- Lp Divergence --- p.100 === Chapter 9.1.3 --- De-correlation Index --- p.102 === Chapter 9.2 --- Experiments on the ICA Algorithm Based on Positive Convex Divergence --- p.103 === Chapter 9.2.1 --- Experiments on the algorithm with fixed nonlinearities --- p.103 === Chapter 9.2.2 --- Experiments on the algorithm with mixture of densities --- p.106 === Chapter 10 --- Conclusions --- p.107 === Chapter A --- Proof for Stability of the Equilibrium Points of the Algorithm with Cubic Nonlinearity on Two Channels of Signals --- p.110 === Chapter A.1 --- Stability of Solution Group A --- p.110 === Chapter A.2 --- Stability of Solution Group B --- p.111 === Chapter B --- Proof for Stability of the Equilibrium Points of the Algorithm with Cubic Nonlinearity on Three Channels of Signals --- p.119 === Chapter C --- Proof for Theorem2 --- p.122 === Bibliography --- p.124