Delay and predict equalization for blind speech dereverberation

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 linear prediction will both equalize the reverberation filter and whiten the source. We exploit the channel spatial diversity, and the speech signal non-stationarity to estimate the source correlation structure, which can hence be used to determine a source whitening filter. Multichannel linear prediction is then applied to the sensor signals filtered by the source whitening filter, to obtain source dereverberation. Particular attention is paid to the alignment of the received signals on the various microphones. This leads to an increase in the prediction performance, and allows the use of shorter predictor. The proposed approach represents hence a paradigm shift from the delay-and-sum beamformer to the delay-and-predict equalizer.