  This paper addresses the problem of multichannel online dereverberation. The
proposed method is carried out in the short-time Fourier transform (STFT)
domain, and for each frequency band independently. In the STFT domain, the
time-domain room impulse response is approximately represented by the
convolutive transfer function (CTF). The multichannel CTFs are adaptively
identified based on the cross-relation method, and using the recursive least
square criterion. Instead of the complex-valued CTF convolution model, we use a
nonnegative convolution model between the STFT magnitude of the source signal
and the CTF magnitude, which is just a coarse approximation of the former
model, but is shown to be more robust against the CTF perturbations. Based on
this nonnegative model, we propose an online STFT magnitude inverse filtering
method. The inverse filters of the CTF magnitude are formulated based on the
multiple-input/output inverse theorem (MINT), and adaptively estimated based on
the gradient descent criterion. Finally, the inverse filtering is applied to
the STFT magnitude of the microphone signals, obtaining an estimate of the STFT
magnitude of the source signal. Experiments regarding both speech enhancement
and automatic speech recognition are conducted, which demonstrate that the
proposed method can effectively suppress reverberation, even for the difficult
case of a moving speaker.
