A meshless scheme for reconstructing dielectric objects by integral equation approach

Reconstructing unknown dielectric objects by integral equation approach requires an efficient solution of volume integral equations (VIEs) and the widely-used method of moments (MoM) with the Schaubert-Wilton-Glisson (SWG) basis function may not be appropriate in such a scenario due to the unknown profile of objects in the imaging domain. In this work, we develop a meshless scheme for solving the VIEs of inverse problems. The scheme changes the volume integrals into boundary integrals through the Green-Gauss theorem when the integrands are regularized by excluding a small cube enclosing the observation node in the imaging domain. A numerical example for reconstructing two contacting dielectric spheres is presented to illustrate the inversion approach and good imaging quality can be observed.