A finite element boundary element domain decomposition inverse scattering technique

Abstract

A three dimensional inverse scattering technique exploiting the equivalence principle is presented. Based on a domain decomposition approach, the inverse scattering problem is divided into two parts by introducing equivalent currents on a surface surrounding the domain of interest. While the first part is a linear inverse source problem, the second part is a nonlinear inverse boundary value problem. A boundary integral method accelerated by the Multilevel Fast Multipole Method is used in order to obtain equivalent surface currents. Once the equivalent surface currents are reconstructed, the inverse problem is reduced to a cavity problem with inhomogeneous boundary condition. As this part is nonlinear, the Gauss-Newton method equipped with a Krylov subspace regularization technique is employed to reconstruct material properties in the domain of interest. In order to see the effectiveness of the proposed technique, it has been tested against real datasets.