Inverse 2D obstacle scattering by adaptive iteration

The 2D inverse time harmonic electromagnetic scattering problem of reconstructing the starlike boundary Lambda of an infinitely conducting obstacle from its far field scattering data is considered. An approach that employs weak a priori knowledge by choosing an auxiliary curve Gamma inside the searched boundary Lambda is used. Reconstructions are improved using an iteration scheme to adapt the internal curve Gamma by exploiting information on the reconstruction Lambda of the previous step. The adaptation algorithm yields significant improvements on Lambda, provided a reasonable first reconstruction may be obtained.