Time reversal for classical waves in random media

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.