A constrained sequential EM algorithm for speech enhancement

Speech enhancement is a fundamental problem, the goal of which is to estimate clean speech st, given a noise-contaminated signal st+nt, where nt is white or colored noise. This task can be viewed as a probabilistic inference problem which involves estimating the posterior distribution of hidden clean speech, given a noisy observation. Kalman filter is a representative method but is restricted to Gaussian distributions only. We consider the generalized auto-regressive (GAR) model in order to capture the non-Gaussian characteristics of speech. Then we present a constrained sequential EM algorithm where Rao-Blackwellized particle filters (RBPFs) are used in the E-step and model parameters are updated in a sequential manner in the M-step under positivity constraints for noise variance parameters. Numerical experiments confirm the high performance of our proposed method, compared to Kalman filter-based methods, in the task of sequential speech enhancement.