Blind separation of L sources from M mixtures of speech signals

Abstract

In many real-world applications of blind source separation, the number of mixture signals, L, available for analysis often differs from the number of sources, M, which may be present. In this paper, we extend a successful and efficient kurtosis maximization algorithm used in speech separation of two sources from two linear mixtures for use in problems with arbitrary numbers of sources and mixtures. We examine three cases: underdetermined (M<L), critically determined (M=L), and overdetermined (M>L). In each of these cases, we present simulation results (using the TIMIT speech corpus) and discuss separation matrix initialization issues and observed algorithm limitations. We find that in the critically determined case, the algorithm performs well (20–40 dB SIR) at separating four sources from four mixtures. For the other cases, our results are mixed. In the overdetermined case (two sources, three mixtures), the algorithm performs well (20–40 dB SIR) and we find that the extra mixtures do not result in better SIR measurements. In the underdetermined case (three sources, two mixtures), we are able to separate out at least one source (sometimes two) with the other output signals each containing pairs of the remaining sources.