A preconditioned linear sampling method in inverse acoustic obstacle scattering

摘要

The problem of determining the shape of an obstacle from far-field measurements is considered. It is well known that Kirsch's (F*F)(1/4)-metbod has been widely used for shape reconstructions obtained via the singular system of the ill conditioned discretized far-field operator F. In this work we present a preconditioned version of this method. In particular, the singular system of an appropriate preconditioner constructed via the Algebraic Multigrid Method (AMG) is used for the reconstructions since it exploits stable eigenvalues, in contrast to the ones of the disretized far field operator.