Inverse source and compressive sensing for qualitative reconstruction

A new linear approach for support reconstruction of both penetrable and impenetrable objects from the measurements of the scattered fields is introduced and described. The approach takes advantage from the fact that for both high conductivity and dielectric scatterers, induced and `equivalent' currents can be considered localized on the boundary. Starting from these considerations, an ad hoc compressive sensing inspired inversion approach is formulated to localize and retrieve the shape of the unknown objects without a priori assumptions on them.