An Effective Rewriting of the Inverse Scattering Equations via Green's Function Decomposition

In this article, a new inversion model for 2-D microwave imaging is introduced by means of a convenient rewriting of the usual Lippmann-Schwinger integral scattering equation. Such a model is derived by decomposing Green's function and the corresponding internal radiation operator in two different contributions, one of them easily computed from the collected scattered data. In the case of lossless backgrounds, the resulting model turns out to be more convenient than the traditional one, as it exhibits a lower degree of nonlinearity with respect to parameters embedding the unknown dielectric characteristics. This interesting property suggests its exploitation in the solution of the inverse scattering problem. The achievable performance is tested by comparing the proposed model with the one based on the usual Lippman-Schwinger equation in both cases of linearly approximated and full nonlinear frameworks. Both numerical and experimental data are considered.