Convolutive Blind Source Separation Methods

In this chapter, we provide an overview of existing algorithms for blind source separation of convolutive audio mixtures. We provide a taxonomy, wherein many of the existing algorithms can be organized, and we present published results from those algorithms that have been applied to real-world audio separation tasks

Independent vector analysis based on overlapped cliques of variable width for frequency-domain blind signal separation

A novel method is proposed to improve the performance of independent vector analysis (IVA) for blind signal separation of acoustic mixtures. IVA is a frequency-domain approach that successfully resolves the well-known permutation problem by applying a spherical dependency model to all pairs of frequency bins. The dependency model of IVA is equivalent to a single clique in an undirected graph; a clique in graph theory is defined as a subset of vertices in which any pair of vertices is connected by an undirected edge. Therefore, IVA imposes the same amount of statistical dependency on every pair of frequency bins, which may not match the characteristics of real-world signals. The proposed method allows variable amounts of statistical dependencies according to the correlation coefficients observed in real acoustic signals and, hence, enables more accurate modeling of statistical dependencies. A number of cliques constitutes the new dependency graph so that neighboring frequency bins are assigned to the same clique, while distant bins are assigned to different cliques. The permutation ambiguity is resolved by overlapped frequency bins between neighboring cliques. For speech signals, we observed especially strong correlations across neighboring frequency bins and a decrease in these correlations with an increase in the distance between bins. The clique sizes are either fixed, or determined by the reciprocal of the mel-frequency scale to impose a wider dependency on low-frequency components. Experimental results showed improved performances over conventional IVA. The signal-to-interference ratio improved from 15.5 to 18.8 dB on average for seven different source locations. When we varied the clique sizes according to the observed correlations, the stability of the proposed method increased with a large number of cliques.open4

On the indeterminacies of convolutive blind signal separation based on second-order statistics

Recently, several blind signal separation algorithms have been developed which are based on second order statistics. Little has been published however on whether second order statistics are sufficient to obtain a unique solution. Especially for applications that involve convolutive mixing and unmixing of signals that are correlated in time, there is a lack of knowledge on why and in what cases second order statistics suffice. This paper investigates the indeterminacies that are introduced when second order statistics are used and presents a theorem for the unmixing system to be uniquely found using second order statistics