  For voice communication, it is important to extract the speech from its noisy
version without introducing unnaturally artificial noise. By studying the
subband mean-squared error (MSE) of the speech for unsupervised speech
enhancement approaches and revealing its relationship with the existing loss
function for supervised approaches, this paper derives a generalized loss
function, when taking the residual noise control into account, for supervised
approaches. Our generalized loss function contains the well-known MSE loss
function and many other often-used loss functions as special cases. Compared
with traditional loss functions, our generalized loss function is more flexible
to make a good trade-off between speech distortion and noise reduction. This is
because a group of well-studied noise shaping schemes can be introduced to
control residual noise for practical applications. Objective and subjective
test results verify the importance of residual noise control for the supervised
speech enhancement approach.
