Improved time reversal focusing in complex media with inverse filter.

We analyze the problem of improving time‐reversal refocusing in a complex medium through the use of a noninvasive filter. A source at an unknown location emits a pulse, which is recorded by an active set of, possibly distributed, transducers called the focusing array. The goal is to use only the information available at the focusing array to refocus at the source location while minimizing the received energy away from the source. It has been shown that time‐reversal in a random medium exhibits superresolution. However, we investigate further improvement of the resolution by first applying an inverse filter. In general, the construction of such a filter requires invasive measurements on a control array in the vicinity of the source, which we assume are not available. The noninvasive inverse filter utilizes only backscattered signals recorded when the focusing array probes the medium. The result is sharp refocusing at the source comparable to the improvement from use of the invasive filter. Possible applications include communications in complex environments where the goal is to send information to a particular location with low probability of intercept. Temporal compression is also important in communications and we investigate the effect of the inverse filter on this as well.