Signal Separation

The problem of signal separation is a very broad and fundamental one. A powerful paradigm within which signal separation can be achieved is the assumption that the signals/sources are statistically independent of one another. This is known as Independent Component Analysis (ICA). In this thesis, the theoretical aspects and derivation of ICA are examined, from which disparate approaches to signal separation are drawn together in a unifying framework. This is followed by a review of signal separation techniques based on ICA. Second order statistics based output decorrelation methods are employed to try to solve the challenging problem of separating convolutively mixed signals, in the context of mainly audio source separation and the Cocktail Party Problem. Various optimisation techniques are devised to implement second order signal separation of both artificially mixed signals and real mixtures. A study of the advantages and limitations of decorrelation methods is made and some theoretical insights are drawn into a major identifiability problem associated with convolutive source separation using second order statistics only. Motivated by the fact that many signals in real life, especially audio signals, exhibit large degrees of non-stationarity, decorrelation algorithms that take into consideration aspects of non-stationarity are devised. Next, a model based approach to source separation is considered. The problem of nonstationary ICA (nsICA) is addressed, where the mixing system is scalar but time-varying. The density of the sources are modelled as finite mixtures of Gaussians. Simulation based Bayesian methods, notably Markov Chain Monte Carlo (MCMC) techniques, are employed to separate both synthetic and real data that have been mixed by non-stationary mixing matrices. Satisfactory results have been obtained with very few data points, using batch methods, such as Gibbs sampling. The techniques of Sequential Monte Carlo (SMC) methods, or particle filtering, are employed to this problem as well, in the context of both blind and semi-blind signal separation, which involve tracking the time varying mixing system. The thesis concludes with an overview of the main contributions and possible directions for future research.