Time reversal and Lanczos iterations

We describe a new time-reversal algorithm capable of focusing on multiple scatterers in a relatively small number of iterations. We recognize that the traditional time-reversal method is based on utilizing power iterations to determine the dominant eigenpairs of the time-reversal operator. The convergence properties of these iterations are known to be sub-optimal. Motivated by this we propose and describe a new time-reversal method based on Lanczos iterations. We consider a simplified scatterer identification problem and compare the performance of the Lanczos and power iterations based methods. We conclude that for the same number of transmitted and received signals, the Lanczos iterations based approach is substantially more accurate.