An Algebraic Solution Method for Nonlinear Inverse Scattering

By using properly designed synthetic (or “virtual”) experiments and an original approximation of the contrast sources, we are able to recast the inverse scattering problem in an algebraic form (in a subset of points of the imaged domain) and, hence, to solve it by means of closed form formulas. The new approximation relies on the assumption that the contrast sources induced by the different virtual experiments are focused in given points belonging to the scatterer. As such, the method involves a preprocessing step in which the outcome of the original scattering experiments is recombined into the new, virtual, ones capable of enforcing the expected contrast sources behavior. Examples with numerical and experimental data are provided to assess the actual possibility of setting such a virtual experiments framework, and show the effectiveness of the proposed method.