The General Blind Source SeparationModel And A Bayesian Approach

This paper describes the general linear synthesis blind source separation problem and presents a Bayesian statistical approach with correlated sources. This is a generalization of the methods in Rowe (1999). The blind separation of sources model is extended to the general case where the mixing matrix is allowed to change over time, the sources are allowed to be time delayed, and both the observed mixed signal vectors and the unobserved source signal vectors could be correlated. For simplicity , it is assumed that the mixing matrix is constant over the time interval of interest. Further, correlation simpliications are explored for the observed mixed signals and the unobserved sources. The problem addressed by blind source separation is that of separating unobservable source signals when mixed signals are observed. A linear synthesis model is adopted where the observations are linear combinations of the sources and a Bayesian statistical approach is adopted. To motivate the blind separation of sources model, the context of the \cock-tail party problem" is adopted. At a cocktail party, there are p microphones that record or observe m partygoers or speakers at n time increments. The observed conversations consist of mixtures of true unobservable conversations. The p-dimensional mixed signal vectors x i = (x i1 ; : : : ; x ip) 0 are observed and the goal is to separate these observed signal vectors into m-dimensional true