On single-channel noise reduction with rank-deficient noise correlation matrix

The widely studied subspace and linear filtering methods for noise reduction require the noise correlation matrix to be invertible. In certain application scenarios, however, this matrix is either rank deficient or very ill conditioned, so this requirement cannot be fulfilled. In this paper, we investigate possible solutions to this important problem based on subspace techniques for single-channel time-domain noise reduction. The eigenvalue decomposition is applied to both the speech and noise correlation matrices to separate the null and nonnull subspaces. Then, a set of optimal and suboptimal filters are derived from the nullspace of the noise signal. Through simulations, we observe that the proposed filters are able to significantly reduce noise without introducing much distortion to the desired signal. In comparison with the conventional Wiener approach, the developed filters perform significantly better in improving both the signal-to-noise ratio (SNR) and the perceptual evaluation of speech quality (PESQ) score when the noise correlation matrix is rank deficient.