  In this paper, a new inversion model for 2D microwave imaging is introduced
by means of a convenient rewriting of the usual Lippmann Schwinger integral
scattering equation. Such model is derived by decomposing the Greens function
and the corresponding internal radiation operator in two different
contributions. In fact, one of them can be easily computed from the collected
scattered data. In 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 performances are
tested by comparing the proposed model with the usual one based on the
Lippman-Schwinger equation in both cases of linearly approximated and full
non-linear frameworks. Both numerical and experimental data are considered.
