  We investigate the effectiveness of convolutive prediction, a novel
formulation of linear prediction for speech dereverberation, for speaker
separation in reverberant conditions. The key idea is to first use a deep
neural network (DNN) to estimate the direct-path signal of each speaker, and
then identify delayed and decayed copies of the estimated direct-path signal.
Such copies are likely due to reverberation, and can be directly removed for
dereverberation or used as extra features for another DNN to perform better
dereverberation and separation. To identify such copies, we solve a linear
regression problem per frequency efficiently in the time-frequency (T-F) domain
to estimate the underlying room impulse response (RIR). In the multi-channel
extension, we perform minimum variance distortionless response (MVDR)
beamforming on the outputs of convolutive prediction. The beamforming and
dereverberation results are used as extra features for a second DNN to perform
better separation and dereverberation. State-of-the-art results are obtained on
the SMS-WSJ corpus.
