Analysis of theMulti-Channel Source Separation and Dereverberation Problem

Abstract:
In this contribution we address the problem of Least- Squares (LS) optimal FIR inverse-filtering of an acoustic convolutive mixing system, specified by acoustic impulse responses (AIRs). The optimal FIR-filters result from the LS-solution of a block-Toeplitz matrix equation. As a function of the number of sources and sensors and the AIR length, lower bounds for the required FIR-filter lengths are derived where perfect separation and deconvolution, i.e., the inversion of the convolutive mixing system is possible. For settings where these bounds are not met, the filters can be optimized to focus either on separation, dereverberation or uncorrelated noise suppression, or to yield a balanced result. Results are shown for real recordings and measured AIRs.