Solving the Permutation and Circularity Problems of Frequency-Domain Blind Source Separation

Blind source separation (BSS) for convolutive mixtures can be performed efficiently in the frequency domain, where independent component analysis (ICA) is applied separately in each frequency bin. However, frequencydomain BSS involves two major problems that must be solved. The first is the permutation problem: the permutation ambiguity of ICA should be aligned so that a separated signal in the time-domain contains the frequency components of the same source signal. The second problem is the circularity problem: the frequency responses obtained separately by ICA should be constrained so that the corresponding time-domain filter does not rely on the circularity effect of discrete frequency representation. This paper discusses these two problems and presents our methods for solving them. The effectiveness of the BSS method is shown by experimental results for the separation of up to four sources in a reverberant environment.