Enhanced multilevel linear sampling methods for inverse scattering problems

We develop two enhanced techniques for the multilevel linear sampling method (MLSM) proposed in [32] for inverse scattering problems. Under some practical situations, the MLSM suffers certain undesirable "breakage cells" problem. We propose to avoid the curse of "breakage cells" by incorporating "expanding" and "searching" techniques. The new techniques are shown to significantly improve the robustness of the MLSM, and meanwhile they possess the same optimal computational complexity as the MLSM. Numerical experiments are presented to illustrate the promising features of the enhanced MLSMs.