Blind source separation : detecting unknown sources number in covariance domain

Convolutive blind source separation (BSS) refers the scenario that sources are recorded by multiple sensors in a reverberant environment, which can be depicted as a convolutive mixing model. A big task in convolutive BSS is to identify the number of the source before the sources are separated from mixtures. In this paper, it shows that this problem can be categorized as the detection of columns (hidden hyperlines) of the mixing matrix in frequency domain. Motivated by the observation that only one source is active, or locally dominant in the covariance domain, the hyperlines are first estimated by searching the optimal projection direction based on the locally Second Order of Statistics (SOSs) of mixtures. After the estimated hyperlines are estimated, a density-based clustering method is then proposed to evaluate the true number of hyperlines in terms of sorted scores, which is calculated from a product of the local density and the intracluster distance of hyperlines. Such scores are further utilized to automatically search the optimal estimate sources number by a gap-based detection method. Finally, the number with the highest proportion from a selected frequency bins is guaranteed as the estimated number of sources. The experiment results show that the proposed method achieves a stable performance in various of under-determined cases.