A fast integral equation based method for solving electromagnetic inverse scattering problems with inhomogeneous background
Résumé
A family of difference integral equations, consisting of difference Lippmann-Schwinger integral equation (D-LSIE)
and difference new integral equation (D-NIE), is 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
inhomogeneous background medium, in the frame of the difference integral equation methods, the Green’s function
with homogeneous medium is utilized such that not only fast algorithms (referring to those used in forward
scattering problems, like CG-FFT, FMM) can be adopted but also the burdensome calculation for the numerical
Green’s function for the inhomogeneous background medium is avoided. Especially, to tackle the ISPs with strong
non-linearity, those with large contrast and/or large dimensions, a Low-Pass Filter-Matching (LPFM) regularization
is introduced, which aims to stably match the information from the background medium to the unknown scatterer.
Together with the D-NIE model, the proposed inversion method can efficiently tackle the ISPs with strong non-linearity
while a bounded inhomogeneous medium being present. Against both synthetic and experimental data, several representative
numerical tests illustrate the efficacy of the proposed inversion method.