Shape reconstruction through sparsity promotion and properly correlated inverse source problems

By taking advantage from the fact that for high conductivity and dielectric scatterers, induced and 'equivalent'currents can be considered localized on the boundary, a new strategy for support reconstruction of both penetrable and impenetrable objects from the measurements of the scattered fields is introduced and described. In particular, an ad hoc sparsity promoting inversion approach is formulated to localize and retrieve the shape of the unknown objects.