Not yet reviewed by Pith; the record is open.

Practical applications of microwave imaging often require the solution of inverse scattering problems with inhomogeneous backgrounds. Towards this end, a novel inversion strategy, which combines the multi-scaling (MS) regularization scheme and the Difference Contraction Integral Equation (DCIE) formulation, is proposed. Such an integrated approach mitigates the non-linearity and the ill-posedness of the problem to obtain reliable high-resolution reconstructions of the unknown scattering profiles. The arising algorithmic implementation, denoted as MS-DCIE, does not require the computation of the Green's function of the inhomogeneous background, thus it provides an efficient and effective way to deal with complex scenarios. The performance of the MS-DCIE are assessed by means of numerical and experimental tests, in comparison with competitive state-of-the-art inversion strategies, as well.