Single channel speech enhancement using Bayesian NMF with recursive temporal updates of prior distributions

We present a speech enhancement algorithm which is based on a Bayesian Nonnegative Matrix Factorization (NMF). Both Minimum Mean Square Error (MMSE) and Maximum a-Posteriori (MAP) estimates of the magnitude of the clean speech DFT coefficients are derived. To exploit the temporal continuity of the speech and noise signals, a proper prior distribution is introduced by widening the posterior distribution of the NMF coefficients at the previous time frames. To do so, a recursive temporal update scheme is proposed to obtain the mean value of the prior distribution; also, the uncertainty of the prior information is governed by the shape parameter of the distribution which is learnt automatically based on the nonstationarity of the signals. Simulations show a considerable improvement compared to the maximum likelihood NMF based speech enhancement algorithm for different input SNRs.