A Simple Procedure to Design Virtual Experiments for Microwave Inverse Scattering

In a virtual experiment (VE), the data available to solve an inverse scattering problem are linearly combined in order to make the inversion task simpler. This goal is achieved by conditioning contrast sources radiating the scattered fields and exploiting their properties in the inversion procedure, for instance, by devising data-driven approximations or regularization schemes. In this framework, the design of a VE amounts to determine the coefficients ruling the recombination of the available data. In this article, we present a general and simple procedure to design VEs capable of enforcing contrast sources with desired properties. The proposed procedure is computationally straightforward and stable, as it does not require an explicit inversion and regularization process, and just consists in the evaluation of the adjoint solution of an auxiliary problem. The design approach is tested in the case of VE enforcing circularly symmetric contrast sources, and the corresponding inversion procedure is assessed using both simulated and experimental data.