Musical noise suppression using a low-rank and sparse matrix decomposition approach

We address the problem of suppressing musical noise from speech enhanced using a short-time processing algorithm. Enhancement algorithms rely on noise statistics and errors in estimating the statistics lead to residual noise in the enhanced signal. A frequently encountered residual noise type is the so-called musical noise, which is a consequence of spurious peaks occurring at random locations in the time-frequency (t-f) plane. Typically, speech enhancement algorithms operate on a short-time basis and perform attenuation of noisy speech spectral coefficients, effectively leading to a spectrotemporal gain function. We show that in case of speech distorted by musical noise, the spectrotemporal gain function has a distinct signature: the musical noise components are sparse in the t-f domain, whereas the spectrotemporal gain corresponding to the speech region exhibits a low-rank structure. Based on this observation, we propose a low-rank and sparse matrix decomposition of the spectrotemporal gain function. We show that musical noise can be effectively suppressed by reconstructing the speech signal using only the low-rank component. Performance comparison in terms of subjective scores and spectrographic analysis shows that the proposed technique is superior compared with two benchmark techniques. The proposed technique could be used in tandem with any speech enhancement algorithm that gives rise to musical noise.