On Calculating the Inverse of Separation Matrix in Frequency-Domain Blind Source Separation

Abstract

For blind source separation (BSS) of convolutive mixtures, the frequency-domain approach is efficient and practical, because the convolutive mixtures are modeled with instantaneous mixtures at each frequency bin and simple instantaneous independent component analysis (ICA) can be employed to separate the mixtures. However, the permutation and scaling ambiguities of ICA solutions need to be aligned to obtain proper time-domain separated signals. This paper discusses the idea that calculating the inverses of separation matrices obtained by ICA is very important as regards aligning these ambiguities. This paper also shows the relationship between the ICA-based method and the time-frequency masking method for BSS, which becomes clear by calculating the inverses.