  We introduce the concept of quasi-inverse of quantum and classical channels,
prove general properties of these inverses and determine them for a large class
of channels acting in an arbitrary finite dimension. Therefore we extend the
previous results of [1] to arbitrary dimensional channels and to the classical
domain. We demonstrate how application of the proposed scheme can increase on
the average the fidelity between a given random pure state and its image
transformed by the quantum channel followed by its quasi-inversion.
