  A promising approach for multi-microphone speech separation involves two deep
neural networks (DNN), where the predicted target speech from the first DNN is
used to compute signal statistics for time-invariant minimum variance
distortionless response (MVDR) beamforming, and the MVDR result is then used as
extra features for the second DNN to predict target speech. Previous studies
suggested that the MVDR result can provide complementary information for the
second DNN to better predict target speech. However, on fixed-geometry arrays,
both DNNs can take in, for example, the real and imaginary (RI) components of
the multi-channel mixture as features to leverage the spatial and spectral
information for enhancement. It is not explained clearly why the linear MVDR
result can be complementary and why it is still needed, considering that the
DNNs and the beamformer use the same input, and the DNNs perform non-linear
filtering and could render the linear filtering of MVDR unnecessary. Similarly,
in monaural cases, one can replace the MVDR beamformer with a monaural weighted
prediction error (WPE) filter. Although the linear WPE filter and the DNNs use
the same mixture RI components as input, the WPE result is found to
significantly improve the second DNN. This study provides a novel explanation
from the perspective of the low-distortion nature of such algorithms, and finds
that they can consistently improve phase estimation. Equipped with this
understanding, we investigate several low-distortion target estimation
algorithms including several beamformers, WPE, forward convolutive prediction,
and their combinations, and use their results as extra features to train the
second network to achieve better enhancement. Evaluation results on single- and
multi-microphone speech dereverberation and enhancement tasks indicate the
effectiveness of the proposed approach, and the validity of the proposed view.
