An EM algorithm for joint dual-speaker separation and dereverberation

The scenario of a mixture of two speakers captured by a microphone array in a noisy and reverberant environment is considered. If the problems of source separation and dereverberation are treated separately, performance degradation may result. It is well-known that the performance of blind source separation (BSS) algorithms degrades in the presence of reverberation, unless reverberation effects are properly addressed (leading to the so-called convolutive BSS algorithms). Similarly, the performance of common dereverberation algorithms will severely degrade if an interference signal is also captured by the same microphone array. The aim of the proposed method is to jointly separate and dereverberate the two speech sources, by extending the Kalman expectation-maximization for dereverberation (KEMD) algorithm, previously proposed by the authors. A statistical model is attributed to this scenario, using the convolutive transfer function (CTF) approximation, and the expectation-maximization (EM) scheme is applied to obtain a maximum likelihood (ML) estimate of the parameters. In the expectation step, the separated clean signals are extracted from the observed data by the application of a Kalman Filter, utilizing the parameters that were estimated in the previous iteration. The maximization step updates the parameters estimation according to the E-step output. Simulation results shows that the proposed method improves both the separation of the signals and their overall quality.