Variational Bayesian Inference for Multichannel Dereverberation and Noise Reduction

Room reverberation and background noise severely degrade the quality of hands-free speech communication systems. In this work, we address the problem of combined speech dereverberation and noise reduction using a variational Bayesian (VB) inference approach. Our method relies on a multichannel state-space model for the acoustic channels that combines frame-based observation equations in the frequency domain with a first-order Markov model to describe the time-varying nature of the room impulse responses. By modeling the channels and the source signal as latent random variables, we formulate a lower bound on the log-likelihood function of the model parameters given the observed microphone signals and iteratively maximize it using an online expectation-maximization approach. Our derivation yields update equations to jointly estimate the channel and source posterior distributions and the remaining model parameters. An inspection of the resulting VB algorithm for blind equalization and channel identification (VB-BENCH) reveals that the presented framework includes previously proposed methods as special cases. Finally, we evaluate the performance of our approach in terms of speech quality, adaptation times, and speech recognition results to demonstrate its effectiveness for a wide range of reverberation and noise conditions.