Noise robust speech dereverberation with Kalman smoother

A speech dereverberation method is proposed that is robust against background noise. In contrast to conventional methods based on the linear prediction of the given microphone input signal, in which the linear prediction coefficients are not fully optimized when there is background noise, the proposed method optimizes the coefficients by linear prediction of the noiseless reverberant speech signal even when there is background noise. The noiseless reverberant speech signal and the parameters are iteratively updated on the basis of the expectation maximization algorithm. In the expectation step, sufficient statistics of latent variables which include noiseless reverberant speech signal are estimated using the Kalman smoother. Unlike the standard Kalman smoother, which uses a time-invariant covariance matrix as a state-transition covariance matrix, the proposed method utilizes a time-varying covariance matrix, enabling it to meet the time-varying speech characteristics. The parameters are updated so that the Q function is increased in the maximization step. Experimental results show that the proposed method is superior to conventional methods under noisy conditions.