Reconstruction of Dielectric Objects Based on Meshless Discretization of Imaging Domain

Abstract

Reconstruction of dielectric objects by integral equation approach requires to alternatively solve the forward scattering integral equation (FSIE) and inverse scattering integral equation (ISIE) in the frame of Born iterative method (BIM) or distorted BIM (DBIM). Solving the FSIE is very tedious because an intensive calculation of volume integrals over imaging domain is required. In this work, we use a novel meshless scheme to simplify the calculation of volume integrals in the solution of FSIE so that the reconstruction can be accelerated. The meshless scheme changes the volume integrals into boundary integrals through the Green-Gauss theorem after the integrands are regularized in the imaging domain and the volumetric discretization of the imaging domain is not necessary. The ISIE is solved by the Gauss-Newton minimization approach (GNMA) with the multiplicative regularization method (MRM). A typical numerical example is presented to demonstrate the inversion approach and good results have been obtained.