Inverse 3D acoustic and electromagnetic obstacle scattering by iterative adaptation

Abstract

The inverse three-dimensional time-harmonic scattering problem of reconstructing the starlike and smooth boundary Λ of an impenetrable obstacle from its far field scattering data, for both, the acoustic and electromagnetic case, is considered. An approach, based on a method proposed by Kirsch and Kress [2], that employs weak a priori knowledge by choosing an auxiliary curve gG inside the searched boundary Λ is used. Initial reconstructions are improved using an iteration scheme to adapt the internal surface Γ by exploiting information on the reconstruction Λ of the previous step. The adaptation algorithm yields significant improvements on Λ, provided a reasonable first reconstruction may be obtained.