Speech dereverberation with convolutive transfer function approximation using map and variational deconvolution approaches

Recordings of a speech signal in an enclosed space are typically corrupted with reverberation. In combination with background noise, these effects may severely degrade the speech quality. In this paper we aim to blindly recover the speech signal from the reverberant and possibly noisy observations, where the signals are represented using the convolutive transfer function model in the STFT domain. The problem of blind speech dereverberation is decomposed into a set of independent blind deconvolution problems that we propose to solve using a maximum a posteriori approach and a variational approach, exploiting the sparsity of the speech signal in the STFT domain. The corresponding optimization problems can be solved using an alternating optimization procedure. Experimental results show that the proposed approach based on variational estimation results in consistent improvements of the instrumentally predicted measures of speech enhancement and dereverberation.