Multi-Channel late reverberation power spectral density estimation based on nuclear norm minimization

Abstract

Multi-channel methods for estimating the late reverberation power spectral density (PSD) generally assume that the reverberant PSD matrix can be decomposed as the sum of a rank-1 matrix and a scaled diffuse coherence matrix. To account for modeling or estimation errors in the estimated reverberant PSD matrix, in this paper we propose to decompose this matrix as the sum of a low rank (not necessarily rank-1) matrix and a scaled diffuse coherence matrix. Among all pairs of scalars and matrices that yield feasible decompositions, the late reverberation PSD can then be estimated as the scalar associated with the matrix of minimum rank. Since rank minimization is an intractable non-convex optimization problem, we propose to use a convex relaxation approach and estimate the late reverberation PSD based on nuclear norm minimization (NNM). Experimental results show the advantages of using the proposed NNM-based late reverberation PSD estimator in a multichannel Wiener filter for speech dereverberation, significantly outperforming a state-of-the-art maximum likelihood-based PSD estimator and yielding a similar or better performance than a recently proposed eigenvalue decomposition-based PSD estimator.