  A two-stage lightweight online dereverberation algorithm for hearing devices
is presented in this paper. The approach combines a multi-channel multi-frame
linear filter with a single-channel single-frame post-filter. Both components
rely on power spectral density (PSD) estimates provided by deep neural networks
(DNNs). By deriving new metrics analyzing the dereverberation performance in
various time ranges, we confirm that directly optimizing for a criterion at the
output of the multi-channel linear filtering stage results in a more efficient
dereverberation as compared to placing the criterion at the output of the DNN
to optimize the PSD estimation. More concretely, we show that training this
stage end-to-end helps further remove the reverberation in the range accessible
to the filter, thus increasing the \textit{early-to-moderate} reverberation
ratio. We argue and demonstrate that it can then be well combined with a
post-filtering stage to efficiently suppress the residual late reverberation,
thereby increasing the \textit{early-to-final} reverberation ratio. This
proposed two stage procedure is shown to be both very effective in terms of
dereverberation performance and computational demands, as compared to e.g.
recent state-of-the-art DNN approaches. Furthermore, the proposed two-stage
system can be adapted to the needs of different types of hearing-device users
by controlling the amount of reduction of early reflections.
