Contributions to theory and algorithms of independent component analysis and signal separation

Abstract

This thesis addresses the problem of blind signal separation (BSS) using independent component analysis (ICA). In blind signal separation, signals from multiple sources arrive simultaneously at a sensor array, so that each sensor array output contains a mixture of source signals. Sets of sensor outputs are processed to recover the source signals or to identify the mixing system. The term blind refers to the fact that no explicit knowledge of source signals or mixing system is available. Independent component analysis approach uses statistical independence of the source signals to solve the blind signal separation problems. Application domains for the material presented in this thesis include communications, biomedical, audio, image, and sensor array signal processing.

In this thesis reliable algorithms for ICA-based blind source separation are developed. In blind source separation problem the goal is to recover all original source signals using the observed mixtures only. The objective is to develop algorithms that are either adaptive to unknown source distributions or do not need to utilize the source distribution information at all. Two parametric methods that can adapt to a wide class of source distributions including skewed distributions are proposed. Another nonparametric technique with desirable large sample properties is also proposed. It is based on characteristic functions and thereby avoids the need to model the source distributions. Experimental results showing reliable performance are given on all of the presented methods.

In this thesis theoretical conditions under which instantaneous ICA-based blind signal processing problems can be solved are established. These results extend the celebrated results by Comon of the traditional linear real-valued model. The results are further extended to complex-valued signals and to nonlinear mixing systems. Conditions for identification, uniqueness, and separation are established both for real and complex-valued linear models, and for a proposed class of non-linear mixing systems.