Multiscaling Differential Contraction Integral Method for Inverse Scattering Problems with Inhomogeneous Media

Practical applications of microwave imaging often require the solution of inverse scattering problems with inhomogeneous backgrounds. Toward this end, a novel inversion strategy, which combines the multiscaling (MS) regularization scheme and the difference contraction integral equation (DCIE) formulation, is proposed. Such an integrated approach mitigates the nonlinearity 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 Green's function of the inhomogeneous background, and thus, it provides an efficient and effective way to deal with complex scenarios. The performance of the MS-DCIE is assessed by means of numerical and experimental tests in comparison with competitive state-of-the-art inversion strategies as well.