Shape reconstruction via equivalence principles, constrained inverse source problems and sparsity promotion

A new approach for position and shape reconstruction of both penetrable and impenetrable objects from the measurements of the scattered fields is introduced and described. The approach takes advantage of the fact that for perfect electric conductors the induced currents are localized on the boundary, and equivalent sources also placed on the surface of the scatterers can be considered in the case of dielectric targets by virtue of the equivalence theorem. Starting from these considerations, a new inversion approach is formulated in order to retrieve the location and the boundary of unknown objects. Examples with both numerical and experimental data are given to demonstrate and assess the effectiveness of the method.