New tools and series for forward and inverse scattering problems in lossy media

A convenient rewriting of the pertinent integral equation is exploited to introduce a new model for two-dimensional electromagnetic scattering by dielectric objects in lossy media. Exploiting this latter, a new series expansion is introduced to solve the forward problem accurately and effectively. The first term of such a series coincides, in particular situations, with the well-known extended Born approximation. Theoretical tools and results are given on the range of applicability and rate of convergence of the series, which favorably compares with the traditional Born one. These tools allow noticing that the new model exhibits a lower "degree of nonlinearity" with respect to parameters embedding dielectric characteristics as compared to the traditional model, thus suggesting its exploitation in the solution of the inverse problem. Numerical examples assessing effectiveness and convenience of the proposed models, tools and inversion methods are presented.