An expectation-maximization algorithm for multichannel adaptive speech dereverberation in the frequency-domain

This paper presents an online dereverberation algorithm that is derived within the maximum-likelihood expectation-maximization (ML-EM) framework. We formulate an overlap-save observation model for the multichannel blind problem in the DFT-domain. The modeling of acoustic channel impulse responses as random variables with a first-order Markov property facilitates the ensuing algorithm to cope with time-varying conditions. We then show that the ML-EM learning rules for the multichannel state-space model at hand take the form of a recursive posterior estimator for the channels, followed by an equalization stage for recovering the speech signal subject to an expectation with respect to the estimated channel posterior. Our derivation thus results in an iterative ML algorithm for blind equalization and channel identification (ML-BENCH) which comprises two distinct and coupled subsystems. The dereverberation performance of the proposed system is evaluated by considering spectrograms and instrumental quality measures.