A Meshless Method of Solving Inverse Scattering Problems for Imaging Dielectric Objects

To image dielectric objects by integral equation approach, the forward scattering integral equation (FSIE) and the inverse scattering integral equation (ISIE) are alternatively solved in an iterative scheme. For solving the FSIE, we propose a meshless method that changes volume integrals into boundary integrals based on the Green-Gauss theorem. The meshless method uses a set of discrete points without connection to describe the integral domain, yielding much convenience of discretizing imaging domain. In addition, the transformation of volume integrals into boundary integrals can greatly simplify the numerical solution of FSIE and allow an initial guess of larger imaging domain to reduce the possibility of reselecting the imaging domain. The transformation requires an exclusion of small cube from the imaging domain to regularize singular integrands, and we present an effective technique to evaluate subtracted hypersingular integrals. For solving the ISIE, we use the Gauss-Newton minimization approach with a multiplicative regularization method to facilitate the regularization and enhance the convergence of solutions. Numerical examples for imaging typical dielectric objects in sensing atmosphere and space are presented to illustrate the approach, and good results have been obtained.