A three-dimensional microwave imaging technique combining inverse equivalent current and finite element methods

An approach combining boundary integral and finite element methods for imaging of three-dimensional dielectric objects is presented. Based on the equivalence principle, the problem is decomposed into two parts: a radiation and a cavity problem. While the radiation problem is linear, the latter one is non-linear. A boundary integral formulation is utilized to solve the radiation problem and the cavity problem is solved via a finite element method. Since this part of the problem is nonlinear and ill-posed, a Gauss-Newton approach equipped with a Krylov subspace method is employed to reconstruct the material properties in the sense of regularization. Promising reconstructions are obtained.