Non-iterative exact inverse scattering using simultaneous orthogonal matching pursuit (S-OMP)

Even though recently proposed time-reversal MUSIC approach for inverse scattering problem is non-iterative and exact, the approach breaks down when there are more targets than sensors. The main contribution of this paper is a novel non-iterative exact inverse scattering algorithm that still guarantees the exact recovery of the extended targets under a very relaxed constraint on the number of source and receivers, where the conventional time-reversal MUSIC fails. Such breakthrough was possible from the observation that the induced currents on the unknown targets assume the same sparse support, which can be recovered accurately using the simultaneous orthogonal matching pursuit developed for multiple measurement vector problems. Simulation results demonstrate that perfect reconstruction can be quickly obtained from a very limited number of samples.