We consider the problem of simultaneous reduction of acoustic echo,
reverberation and noise. In real scenarios, these distortion sources may occur
simultaneously and reducing them implies combining the corresponding
distortion-specific filters. As these filters interact with each other, they
must be jointly optimized. We propose to model the target and residual signals
after linear echo cancellation and dereverberation using a multichannel
Gaussian modeling framework and to jointly represent their spectra by means of
a neural network. We develop an iterative block-coordinate ascent algorithm to
update all the filters. We evaluate our system on real recordings of acoustic
echo, reverberation and noise acquired with a smart speaker in various
situations. The proposed approach outperforms in terms of overall distortion a
cascade of the individual approaches and a joint reduction approach which does
not rely on a spectral model of the target and residual signals