Narrow Results

The authors prove the uniqueness in the inverse acoustic scattering problem within convex polygonal domains by a single incident direction in the sound-soft case and the sound-hard case, and by two incident directions in the case of the impedance boundary condition. The proof is based on analytic continuation on a straight line.

The goal of this paper is to present recent progress on several aspects of an inverse medium problem. A recursive linearization method for solving the nonlinear inverse problem is introduced. Convergence of the method is studied. We address issues on regularity and stability for the scattering map which maps the scatterer to the scattered field. Preliminary computational results are also presented.