Time reversal, imaging and communications in random media.

G.C. Papanicolaou

Department of Mathematics
Stanford University
Stanford CA 94305 USA

I will present an exposition of the mathematical problems that arise in using arrays of transducers for imaging and communications in random media. The key to understanding their performance capabilities is the phenomenon of statistically stable super-resolution in time reversal, which I will explain carefully. Signals that are recorded, time reversed and re-emitted by the array into the medium tend to focus on their source location with much tighter resolution when there is multipathing because of random inhomogeneities. I will explain how this super-resolution enters into array imaging and communications when there is multipathing.