Direct sampling method via Landweber iteration for an absorbing scatterer with a conductive boundary

arXiv (Cornell University)

Abstract

In this paper, we consider the inverse shape problem of recovering isotropic scatterers with a conductive boundary condition. Here, we assume that the measured far-field data is known at a fixed wave number. Motivated by recent work, we study a new direct sampling indicator based on the Landweber iteration and the factorization method. Therefore, we prove the connection between these reconstruction methods. The method studied here falls under the category of qualitative reconstruction methods where an imaging function is used to recover the absorbing scatterer. We prove stability of our new imaging function as well as derive a discrepancy principle for recovering the regularization parameter. The theoretical results are verified with numerical examples to show how the reconstruction performs by the new Landweber direct sampling method.

Authors 3

1. Rafael Ceja Ayala

   Purdue University West Lafayette

   Affiliation as printed

   Department of Mathematics , Purdue University , West Lafayette , IN 47907

2. Isaac Harris Aachen Faculty of Medical Engineering and Technomathematics

   FH Aachen · Purdue University West Lafayette

   Affiliation as printed

   Department of Mathematics , Purdue University , West Lafayette , IN 47907

   University of Applied Sciences Aachen , Faculty of Medical Engineering and Technomathematics , Heinrich-Mußmann-Str. 1 , 52428 Jülich , Germany

3. Andreas Kleefeld

   Forschungszentrum Jülich · Jülich Supercomputing Centre

   Affiliation as printed

   Forschungszentrum Jülich GmbH , Jülich Supercomputing Centre , Wilhelm-Johnen-Straße , 52425 Jülich , Germany