Convolutive BSS of short mixtures by ICA recursively regularized across frequencies

This paper proposes a new method of Frequency-Domain Blind Source Separation (FD-BSS), able to separate acoustic sources in challenging conditions. In frequency-domain BSS, the time-domain signals are transformed into time-frequency series and the separation is generally performed by applying Independent Component Analysis (ICA) at each frequency envelope. When short signals are observed and long demixing filters are required, the number of time observations for each frequency is limited and the variance of the ICA estimator increases due to the intrinsic statistical bias. Furthermore, common methods used to solve the permutation problem fail, especially with sources recorded under highly reverberant conditions. We propose a Recursively Regularized implementation of the ICA (RR-ICA) that overcomes the mentioned problem by exploiting two types of deterministic knowledge: 1) continuity of the demixing matrix across frequencies; 2) continuity of the time-activity of the sources. The recursive regularization propagates the statistics of the sources across frequencies reducing the effect of statistical bias and the occurrence of permutations. Experimental results on real-data show that the algorithm can successfully perform a fast separation of short signals (e.g., 0.5-1s), by estimating long demixing filters to deal with highly reverberant environments (e.g., T60 = 700ms).