  In this paper, we study an unconventional but practically meaningful
reversibility problem of commonly used image filters. We broadly define filters
as operations to smooth images or to produce layers via global or local
algorithms. And we raise the intriguingly problem if they are reservable to the
status before filtering. To answer it, we present a novel strategy to
understand general filter via contraction mappings on a metric space. A very
simple yet effective zero-order algorithm is proposed. It is able to
practically reverse most filters with low computational cost. We present quite
a few experiments in the paper and supplementary file to thoroughly verify its
performance. This method can also be generalized to solve other inverse
problems and enables new applications.
