  The majority of deep neural network (DNN) based speech enhancement algorithms
rely on the mean-square error (MSE) criterion of short-time spectral amplitudes
(STSA), which has no apparent link to human perception, e.g. speech
intelligibility. Short-Time Objective Intelligibility (STOI), a popular
state-of-the-art speech intelligibility estimator, on the other hand, relies on
linear correlation of speech temporal envelopes. This raises the question if a
DNN training criterion based on envelope linear correlation (ELC) can lead to
improved speech intelligibility performance of DNN based speech enhancement
algorithms compared to algorithms based on the STSA-MSE criterion. In this
paper we derive that, under certain general conditions, the STSA-MSE and ELC
criteria are practically equivalent, and we provide empirical data to support
our theoretical results. Furthermore, our experimental findings suggest that
the standard STSA minimum-MSE estimator is near optimal, if the objective is to
enhance noisy speech in a manner which is optimal with respect to the STOI
speech intelligibility estimator.
