Source Reconstruction From Wideband and Band-Limited Responses by FDTD Time Reversal and Regularized Least Squares

Time-reversal (TR) methods have been applied to reconstruct electromagnetic sources. Electromagnetic signals emitted by unknown sources are received at preselected output locations in a loss-free ergodic cavity, reversed in time, and then reinjected back into the output locations; the peak values of the resulting fields in the cavity indicate in most cases the original source locations. In this paper, we summarize the theoretical foundations of computational TR in terms of the finite-difference time-domain model and derive a condition for reconstructing multiple sources without the need to know the Green's functions and to identify the field peaks. We then develop a method to apply this new approach to practical problems. Furthermore, we develop a method to reconstruct sources effectively from band-limited field responses. Thus, practical applications of the TR method become feasible. Numerical experiments are provided to verify the theoretical analyses and effectiveness of the proposed methods.