  The task of compression of data -- as stated by the source coding theorem --
is one of the cornerstones of information theory. Data compression usually
exploits statistical redundancies in the data according to its prior
distribution. Motivated by situations where one does not have access to the
statistics of data, but has some information about a transformation that is
going to be applied to it, we propose a novel method for data compression
called reverse compression. It is defined in such a way that works for both
classical and quantum information processes, and furthermore relies exclusively
on the channel to be used: all input data leading to indistinguishable outputs
is compressed to the same state, regardless of their prior distribution.
Moreover, this process can be characterized as a higher order operation within
the type of preprocessing. We also consider as an example the application of
the method to the classical and quantum erasure channel. The examples suggest
that noiseless reverse compression can take place only in trivial cases,
although meaningful instances of noisy reverse compression can exist.
