On causal algorithms for speech enhancement

Kalman filtering is a powerful technique for the estimation of a signal observed in noise that can be used to enhance speech observed in the presence of acoustic background noise. In a speech communication system, the speech signal is typically buffered for a period of 10-40 ms and, therefore, the use of either a causal or a noncausal filter is possible. We show that the causal Kalman algorithm is in conflict with the basic properties of human perception and address the problem of improving its perceptual quality. We discuss two approaches to improve perceptual performance. The first is based on a new method that combines the causal Kalman algorithm with pre- and postfiltering to introduce perceptual shaping of the residual noise. The second is based on the conventional Kalman smoother. We show that a short lag removes the conflict resulting from the causality constraint and we quantify the minimum lag required for this purpose. The results of our objective and subjective evaluations confirm that both approaches significantly outperform the conventional causal implementation. Of the two approaches, the Kalman smoother performs better if the signal statistics are precisely known, if this is not the case the perceptually weighted Kalman filter performs better.