Combined Weighted Prediction Error and Minimum Variance Distortionless Response for dereverberation

Considering the dereverberation problem using multichannel processing, two main paradigms exist. The first paradigm utilizes the long-term correlation of the reverberant component for reducing it, e.g. Weighted Prediction Error (WPE) [1]. The second paradigm, treats the reverberation as a diffuse noise field, statically independent of the direct speech component, and aims to reduce it using a superdirective beamformer, e.g. [2]. Here we propose to combine the two paradigms in a two-stages algorithm. The first stage comprises of the WPE method, and the second stage comprises of a Minimum Variance Distortionless Response (MVDR) beamformer for treating the residual reverberant component. We conjecture that the coherence of the reverberant component at the output of the WPE is similar to the coherence of the reverberant component at the microphones which should theoretically correspond to a diffuse noise field. By estimating the coherence from the reverberant components, linearly predicted by the WPE, non-ideal factors such as microphone positions errors, non-equalized frequency responses and acoustic shading are accounted for. The advantageous performance of the proposed method is exemplified in an experiment study using simulations.