Eliminating the Permutation Ambiguity of Convolutive Blind Source Separation by Using Coupled Frequency Bins

Blind source separation (BSS) is a typical unsupervised learning method that extracts latent components from their observations. In the meanwhile, convolutive BSS (CBSS) is particularly challenging as the observations are the mixtures of latent components as well as their delayed versions. CBSS is usually solved in frequency domain since convolutive mixtures in time domain is just instantaneous mixtures in frequency domain, which allows to recover source frequency components independently of each frequency bin by running ordinary BSS, and then concatenate them to form the Fourier transformation of source signals. Because BSS has inherent permutation ambiguity, this category of CBSS methods suffers from a common drawback: it is very difficult to choose the frequency components belonging to a specific source as they are estimated from different frequency bins using BSS. This paper presents a tensor framework that can completely eliminate the permutation ambiguity. By combining each frequency bin with an anchor frequency bin that is chosen arbitrarily in advance, we establish a new virtual BSS model where the corresponding correlation matrices comply with a block tensor decomposition (BTD) model. The essential uniqueness of BTD and the sparse structure of coupled mixing parameters allow the estimation of the mixing matrices free of permutation ambiguity. Extensive simulation results confirmed that the proposed algorithm could achieve higher separation accuracy compared with the state-of-the-art methods.