BLIND SOURCE SEPARATION FOR CONVOLUTIVE MIXTURES EXPLOITING NONGAUSSIANITY, NONWHITENESS, AND NONSTATIONARITY
Herbert Buchner, Robert Aichner, Walter Kellermann · 2003
Generally, there are three types of approaches for blind source separation (BSS) on time series: exploitation of the nonwhiteness, the nonstationarity, and the nongaussianity of the source signals. While methods utilizing the first two properties are usually based on second order statistics (SOS), one needs higher order statistics (HOS) to take into account nongaussianity. In this paper, we combine all these three fundamental approaches (the three `Non's') for convolutive mixtures to one generic framework, the TRINICON algorithm ('Triple-N ICA for convolutive mixtures'). This is done by introducing an appropriate matrix formulation, combined with the use of multivariate probability densities for considering the time-dependencies of the source signals. It can be shown that our previously introduced generic SOS algorithm follows from the TRINICON as the optimum SOS algorithm. For the general HOS case, we introduce an efficient solution using models for correlated spherically invariant random processes (SIRPs) which are very well suited for a number of signals including speech. In this paper, we consider exclusively time-domain algorithms, but the framework can be extended to the frequency domain.