Fast Convergence Algorithm for State-Space Model Based Speech Dereverberation by Multi-Channel Non-Negative Matrix Factorization

A multi-channel speech dereverberation technique based on a state-space model whose convergence speed is faster than the conventional method is proposed. The proposed method can skip a time-consuming Kalman smoother step, which is utilized in the conventional parameter optimization method based on the expectation-maximization (EM) algorithm. Instead, the proposed method optimizes parameters with an auxiliary function approach similarly to multi-channel non-negative matrix factorization. The proposed cost function is derived as an approximation of the log-likelihood function of the original state-space model under the assumption that a part of the sufficient statistics of latent state vectors are fixed at the parameter optimization step. The sufficient statistics of the state-space model can be estimated in the Kalman filter part without the Kalman smoother. In the proposed method, the Kalman filter and minimization of the approximated cost function are iteratively performed. Experimental results show that the proposed method can increase the original likelihood function faster than the conventional method. Speech dereverberation experiments under noisy environments show that the proposed method can reduce reverberation effectively.