A robust and precise method for solving the permutation problem of frequency-domain blind source separation

Blind source separation (BSS) for convolutive mixtures can be solved efficiently in the frequency domain, where independent component analysis (ICA) is performed separately in each frequency bin. However, frequency-domain BSS involves a permutation problem: the permutation ambiguity of ICA in each frequency bin should be aligned so that a separated signal in the time-domain contains frequency components of the same source signal. This paper presents a robust and precise method for solving the permutation problem. It is based on two approaches: direction of arrival (DOA) estimation for sources and the inter-frequency correlation of signal envelopes. We discuss the advantages and disadvantages of the two approaches, and integrate them to exploit their respective advantages. Furthermore, by utilizing the harmonics of signals, we make the new method robust even for low frequencies where DOA estimation is inaccurate. We also present a new closed-form formula for estimating DOAs from a separation matrix obtained by ICA. Experimental results show that our method provided an almost perfect solution to the permutation problem for a case where two sources were mixed in a room whose reverberation time was 300 ms.