On the implementation of a three-dimensional finite-element contrast source inversion method

The contrast source inversion algorithm coupled to a finite-element method (FEM) has been implemented for three-dimensional (3D) full-vectorial problems. The algorithm solves inverse scattering problems associated with microwave imaging applications. The use of FEM to discretize the Helmholtz differential operator allows the unknown electrical properties of the inverse problem to be distributed on the elements of arbitrary meshes with varying densities. The paper presents an evaluation of the computational complexity of the algorithm and delineates the relevant choices with respect to implementation. The algorithm is validated using multi-frequency experimental datasets collected by the Institut Fresnel of Marseille, France.