Adaptive methods for score function modeling in blind source separation

Abstract

In signal processing and related fields, multichannel measurements are often encountered. Depending on the application, for instance, multiple antennas, multiple microphones or multiple biomedical sensors are used for the data acquisition. Such systems can be described using Multiple-Input Multiple-Output (MIMO) system models. In many cases, several source signals are present at the same time and there is only limited knowledge of their properties and how they contribute to each sensor output. If the source signals and the physical system are unknown and only the sensor outputs are observed, the processing methods developed for recovering the original signals are called blind.

In Blind Source Separation (BSS) the goal is to recover the source signals from the observed mixed signals (mixtures). Blindness means that neither the sources nor the mixing system is known. Separation can be based on the theoretically limiting but practically feasible assumption that the sources are statistically independent. This assumption connects BSS and Independent Component Analysis (ICA). The usage of mutual information as a measure of independence leads to iterative estimation of the score functions of the mixtures.

The purpose of this thesis is to develop BSS methods that can adapt to different source distributions. Adaptation makes it possible to separate sources without knowing the source distributions or even the characteristics of source distributions. Special attention is paid to methods that allow also asymmetric source distributions. Asymmetric distributions occur in important applications such as communications and biomedical signal processing. Adaptive techniques are proposed for the modeling of score functions or estimating functions. Three approaches based on the Pearson system, the Extended Generalized Lambda Distribution (EGLD) and adaptively combined fixed estimating functions are proposed. The Pearson system and the EGLD are parametric families of distributions and they are used to model the distributions of the mixtures. The strength of these parametric families is that they contain a wide class of distributions, including asymmetric distributions with positive and negative kurtosis, while the estimation of the parameters is still a relatively simple procedure. The methods may be implemented using existing ICA algorithms.

The reliable performance of the proposed methods is demonstrated in extensive simulations. In addition to symmetric source distributions, asymmetric distributions, such as Rayleigh and lognormal distribution, are utilized in simulations. The score adaptive methods outperform commonly used methods due to their ability to adapt to asymmetric distributions.