Alpha-stable low-rank plus residual decomposition for speech enhancement

In this study, we propose a novel probabilistic model for separating clean speech signals from noisy mixtures by decomposing the mixture spectrograms into a structured speech part and a more flexible residual part. The main novelty in our model is that it uses a family of heavy-tailed distributions, so called the α-stable distributions, for modeling the residual signal. We develop an expectation-maximization algorithm for parameter estimation and a Monte Carlo scheme for posterior estimation of the clean speech. Our experiments show that the proposed method outperforms relevant factorization-based algorithms by a significant margin.