"Time-Reversal Super-Resolution in the Regime of Parabolic Approximation"

Jean-Pierre Fouque
Department of Mathematics
North Carolina State University

Abstract

In this third talk I will show the spatial effect of time-reversal: super-resolution or aperture enhancement. This is done in the regime where the fluctuations are small and high frequencies so that the backscattered wave can be neglected. In the white noise regime this leads to a random Schrodinger equation, an example of stochastic partial differential equation. The multi-pathing effect is contained is the spatial correlation of the noise which creates an effective or enhanced aperture. This scaling is relevant in the domain of wireless communications. my web page, as well as an article in pdf by Mathias Fink in Scientific American (November 1999).