A Bayesian Hierarchical Model for Speech Enhancement

This paper addresses the problem of blind adaptive beamforming using a hierarchical Bayesian model. Our probabilistic approach relies on a Gaussian prior for the speech signal and a Gamma hyperprior for the speech precision, combined with a multichannel linear-Gaussian state-space model for the possibly time-varying acoustic channel. Furthermore, we assume a Gamma prior for the ambient noise precision. We present a variational Expectation-Maximization (VEM) algorithm that employs a variant of multi-channel Wiener filter (MCWF) to estimate the sound source and a Kalman smoother to estimate the acoustic channel of the room. It is further shown that the VEM speech estimator can be decomposed into two stages: A multichannel minimum variance distortionless response (MVDR) beamformer and a subsequent single-channel variational postfilter. The proposed algorithm is evaluated in terms of speech quality, for a static scenario with recorded room impulse responses (RIRs). It is shown that a significant improvement is obtained with respect to the noisy signal, and that the proposed algorithm outperforms a baseline algorithm. In terms of channel alignment, a superior channel estimate is demonstrated compared to the causal Kalman filter.