Inverse parameter and shape problem for an isotropic scatterer with two conductivity coefficients

arXiv (Cornell University)

Abstract

In this paper, we consider the direct and inverse problem for isotropic scatterers with two conductive boundary conditions. First, we show the uniqueness for recovering the coefficients from the known far-field data at a fixed incident direction for multiple frequencies. Then, we address the inverse shape problem for recovering the scatterer for the measured far-field data at a fixed frequency. Furthermore, we examine the direct sampling method for recovering the scatterer by studying the factorization for the far-field operator. The direct sampling method is stable with respect to noisy data and valid in two dimensions for partial aperture data. The theoretical results are verified with numerical examples to analyze the performance by the direct sampling method.

Authors 3

1. Rafael Ceja Ayala

   Forschungszentrum Jülich · Jülich Supercomputing Centre

   Affiliation as printed

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

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