Inverse Scattering via Virtual Experiments and Contrast Source Regularization

In microwave imaging, the linearity of the relationship between the incident and the scattered field offers the possibility of a posteriori recombining the performed scattering experiments and then to cast the underlying inverse problem with respect to the resulting, virtual, ones. The interest of such a circumstance is that properly designed virtual experiments can enforce particular and convenient conditions. In this paper, we present an application of this paradigm to the popular contrast source inversion (CSI) method. In particular, we first design a set of virtual experiments capable to induce contrast sources exhibiting circular symmetries (with respect to some pivot points). Then, we devise an original and effective regularized CSI scheme, in which a penalty term is added to the usual cost functional, in order to account for the symmetry of the auxiliary unknowns. Notably, the approach does not require any a priori assumption on the unknown contrast, as it relies on the particular nature of the virtual contrast sources. Results with single frequency Fresnel experimental data are given to assess the capabilities of the proposed approach.