Convolutive blind source separation by efficient blind deconvolution and minimal filter distortion

Convolutive blind source separation (BSS) usually encounters two difficulties-the filter indeterminacy in the recovered sources and the relatively high computational load. In this paper we propose an efficient method to convolutive BSS, by dealing with these two issues. It consists of two stages, namely, multichannel blind deconvolution (MBD) and learning the post-filters with the minimum filter distortion (MFD) principle. We present a computationally efficient approach to MBD in the first stage: a vector autoregression (VAR) model is first fitted to the data, admitting a closed-form solution and giving temporally independent errors; traditional independent component analysis (ICA) is then applied to these errors to produce the MBD results. In the second stage, the least linear reconstruction error (LLRE) constraint of the separation system, which was previously used to regularize the solutions to nonlinear ICA, enforces a MFD principle of the estimated mixing system for convolutive BSS. One can then easily learn the post-filters to preserve the temporal structure of the sources. We show that with this principle, each recovered source is approximately the principal component of the contributions of this source to all observations. Experimental results on both synthetic data and real room recordings show the good performance of this method.