Inverse medium problem for a singular contrast

Abstract

We consider an inverse medium problem in two- and three-dimensional cases. Namely, we investigate the problem of reconstruction of unknown compactly supported refractive index (contrast) from L2 with a fixed positive wave number. The proof is based on the new estimates for the Green-Faddeev function in L∞ space. The main goal of this work is to prove a uniqueness result in the two- and three-dimensional cases and to discuss some possible constructive methods for solving the problem. Finally, we present some numerical examples to demonstrate the results in two dimensions.We consider an inverse medium problem in two- and three-dimensional cases. Namely, we investigate the problem of reconstruction of unknown compactly supported refractive index (contrast) from L2 with a fixed positive wave number. The proof is based on the new estimates for the Green-Faddeev function in L∞ space. The main goal of this work is to prove a uniqueness result in the two- and three-dimensional cases and to discuss some possible constructive methods for solving the problem. Finally, we present some numerical examples to demonstrate the results in two dimensions.