Real time inverse filter focusing through iterative time reversal

In order to achieve an optimal focusing through heterogeneous media we need to build the inverse filter of the propagation operator. Time reversal is an easy and robust way to achieve such an inverse filter in nondissipative media. However, as soon as losses appear in the medium, time reversal is not equivalent to the inverse filter anymore. Consequently, it does not produce the optimal focusing and beam degradations may appear. In such cases, we showed in previous works that the optimal focusing can be recovered by using the so-called spatiotemporal inverse filter technique. This process requires the presence of a complete set of receivers inside the medium. It allows one to reach the optimal focusing even in extreme situations such as ultrasonic focusing through human skull or audible sound focusing in strongly reverberant rooms. But, this technique is time consuming and implied fastidious numerical calculations. In this paper we propose a new way to process this inverse filter focusing technique in real time and without any calculation. The new process is based on iterative time reversal process. Contrary to the classical inverse filter technique, this iteration does not require any computation and achieves the inverse filter in an experimental way using wave propagation instead of computational power. The convergence from time reversal to inverse filter during the iterative process is theoretically explained. Finally, the feasibility of this iterative technique is experimentally demonstrated for ultrasound applications.