On Determining the Separability of Sources for Second-order Statistics Based Blind Source Separation

The separability conditions imposed on mixing matrices and sources, which form the basis for blind source separation, are usually supposed to be satisfied when an algorithm is proposed or used. However, in practice, we only have the observations at hand, and if an algorithm fails to separate sources in a given scenario, it is especially interesting to know why this could happen. In this paper, we propose a method to determine, on the basis of the observed mixture statistics, whether the conditions for SOS-based BSS are satisfied. The proposed method not only tells us when separation should be possible, given the correlation matrices at hand, but also guides us toward selecting a suitable set of correlation matrices to be jointly diagonalized. Further, only when we know the basic characteristics of the sources well such as speech signals, can we recognize if the sources have been separated or partly separated, so we discussed how can we tell if the sources have been separated completely or not by the separated signals themselves.