Accurate Iterative Inverse Scattering Methods Based on Finite-Difference Frequency-Domain Inversion

Abstract

Two accurate finite-difference frequency-domain (FDFD)-based iterative inverse methods, referred to as FDFD-based iterative method (FIM) and distorted FDFD-based iterative method (DFIM), are proposed for electromagnetic inverse scattering. They can be considered as FDFD-based versions of BIM and DBIM and inherit the advantage of the traditional direct FDFD inversion method, i.e., there is no need for Green’s function of complex background, especially for the inhomogeneous medium. The difference is that full-wave consideration is implemented in the proposed methods to build an iterative framework. Then, the scattered field and object parameter profile are updated in each iteration. Using the high-order components in iteration formulation, both the methods are able to reconstruct high-contrast objects and provide accurate reconstruction results. Compared with other full-wave methods based on differential equation, the two methods also have a distinct characteristic that the inversion accuracy is not limited by extra constraints. The difference between the two proposed methods is whether the background coefficient matrix is updated. Generally, DFIM has faster convergence than FIM due to the updated background coefficient matrix in the iterations. To demonstrate the effectiveness of both the methods, several typical 2-D experiments are conducted. The results show that the proposed methods could achieve good accuracy and high imaging quality.