Inverse scattering through Compressive sensing and synthetic experiments

The potentialities of Compressive sensing (CS) in inverse scattering problems are considerable, because of the intrinsic nature of the targets that one has to reconstruct in actual applications. However, the CS theory is well established only for linear recovery problems, whereas inverse scattering problems are nonlinear. Hence, an actual exploitation of CS in inverse scattering based applications is a still open issue. As a step in this direction, in this paper we introduce a solution procedure based on the joint exploitation of CS and a recently introduced inversion approach that, by means of proper preprocessing techniques, allows a linearization of the problem, which holds true for a set of cases largely exceeding the validity range of the Born approximation.