A novel speech enhancement method based on constrained low-rank and sparse matrix decomposition

In this paper, we present a novel speech enhancement method based on the principle of constrained low-rank and sparse matrix decomposition (CLSMD). According to the proposed method, noise signal can be assumed as a low-rank component because noise spectra within different time frames are usually highly correlated with each other; while the speech signal is regarded as a sparse component since it is relatively sparse in time frequency domain. Based on these assumptions, we develop an alternative projection algorithm to separate the speech and noise magnitude spectra by imposing rank and sparsity constraints, with which the enhanced time-domain speech can be constructed from sparse matrix by inverse discrete Fourier transform and overlap-add-synthesis. The proposed method is significantly different from existing speech enhancement methods. It can estimate enhanced speech in a straightforward manner, and does not need a voice activity detector to find noise-only excerpts for noise estimation. Moreover, it can obtain better performance in low SNR conditions, and does not need to know the exact distribution of noise signal. Experimental results show the new method can perform better than conventional methods in many types of strong noise conditions, in terms of yielding less residual noise and lower speech distortion. (C) 2014 Elsevier B.V. All rights reserved.