  We propose a mathematical theory for the refocusing properties observed in
time-reversal experiments, where classical waves propagate through a medium,
are recorded in time, then time-reversed and sent back into the medium. The
salient feature of such experiments is that the refocusing quality of the
time-reversed reemitted signals is greatly enhanced when the underlying medium
is heterogeneous. Based on the Wigner transform formalism, we show that random
media indeed greatly improve refocusing. We analyze two different types of
random media, where in the limit of high frequencies, the Wigner transform
satisfies a random Liouville equation or a linear transport equation.
