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

• Published in: IEEE transactions on speech and audio processing Vol. 12; no. 5; pp. 530 - 538
• Main Authors: Sawada, H., Mukai, R., Araki, S., Makino, S.
• Format: Journal Article
• Language: English
• Published: IEEE 01.09.2004
• Subjects: Blind source separation; Blinds; Direction of arrival estimation; Discrete Fourier transforms; Exact solutions; Finite impulse response filter; Frequency domain analysis; Frequency estimation; Independent component analysis; Low frequencies; Mathematical analysis; Permutations; Reverberation time; Robustness; Separation; Source separation; Speech; Time domain analysis
• ISSN: 1063-6676; 1558-2353
• DOI: 10.1109/TSA.2004.832994

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 interfrequency 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.