A Fast Integral Equation-Based Method for Solving Electromagnetic Inverse Scattering Problems With Inhomogeneous Background

A family of difference integral equations (IEs), consisting of difference Lippmann-Schwinger IE and difference new IE (D-NIE), are proposed to solve the electromagnetic inverse scattering problems (ISPs) with inhomogeneous background medium bounded in a finite domain. Without resorting to Green's function for an inhomogeneous background medium, in the frame of the difference IE methods, Green's function with a homogeneous medium is utilized such that not only fast algorithms (referring to those used in forward scattering problems, such as conjugate-gradient fast Fourier transform and fast multipole method) can be adopted but also the burdensome calculation of the numerical Green's function for the inhomogeneous background medium is avoided. Especially, to tackle the ISPs with a strong nonlinearity, those with large contrast and/or large dimensions, a low-pass filter-matching regularization is introduced, which aims to stably match the information from the background medium to the unknown scatterers. Together with the D-NIE model, the proposed inversion method can efficiently tackle the ISPs with strong nonlinearity while a bounded inhomogeneous medium is present. Against both synthetic and experimental data, several representative numerical tests illustrate the efficacy of the proposed inversion method.