Blind dereverberation of quasi-periodic sources based on multichannel linear prediction

In this paper, we consider the blind multichannel dereverberation problem for a single source. The multichannel reverberation impulse response is assumed to be stationary enough to allow estimation of the correlations it induces from the received signals. It is well-known that a single-input multi-output (SIMO) filter can be equalized blindly by applying multichannel linear prediction (LP) to its output when the input is white. When the input is colored, the multichannel LP will both equalize the reverberation filter and whiten the source. We exploit the observation that a multichannel reverberation filter tends to become allpass as the number of channels and/or the reverberation delay spread increases. As a result, the sum of the channel output correlations approximates the source correlation structure which can hence be used to determine a source whitening filter. Multichannel LP is then applied to the sensor signals filtered by the source whitenening filter, to obtain source dereverberation. It is important to emphasize that non-stationarity of the source is irrelevant as long as the source correlations are estimated with the same temporal averaging as for the multichannel linear prediction.