A Bayesian Hierarchical Model for Speech Dereverberation

In this paper, the problem of speech dereverberation in a noiseless scenario is addressed in a hierarchical Bayesian framework. Our probabilistic approach relies on a Gaussian model for the early speech signal combined with a multichannel Gaussian model for the relative early transfer function (RETF). The late reverberation is modelled as a Gaussian additive interference, and the speech and reverberation precisions are modelled with Gamma distribution. We derive a variational Expectation-Maximization (VEM) algorithm which uses a variant of the multichannel Wiener filter (MCWF) to infer the early speech component while suppressing the late reverberation. The proposed algorithm was evaluated using real room impulse responses (RIRs) recorded in our acoustic lab with a reverberation time set to 0.36 s and 0.61 s. It is shown that a significant improvement is obtained with respect to the reverberant signal, and that the proposed algorithm outperforms a baseline algorithm. In terms of channel alignment, a superior channel estimate is demonstrated.