An Iterative Domain Decomposition Technique Based on Subspace-Based Optimization Method for Solving Highly Nonlinear Inverse Problem

Abstract

Due to the strong nonlinearity, it is always a challenge to reconstruct strong scatterers with high contrasts and/or large dimensions. This article proposes an iterative domain decomposition technique (IDDT) based on the framework of the subspace-based optimization method (SOM) to solve highly nonlinear inverse scattering problems (ISPs). This method takes advantage of the fact that the reduction of unknowns can reduce the nonlinearity of ISPs and different parts of scatterers have different effects on scattered fields. In the inversion procedure, the domain of scatterers (DoS) is obtained by refining the domain of interests (DoI) first. Then, the DoS is divided into two subdomains according to their contributions to scattered fields: the dominant subdomain and the subordinate subdomain. The induced current of the subordinate subdomain is approximated by its deterministic part. Therefore, only the induced current of the dominant subdomain needs to be reconstructed, greatly reducing the dimensions of the solution domain. Then the properties of the entire DoS are retrieved with the properties of the dominant subdomain as initial guesses. This technique can be used repeatedly to improve the reconstruction quality. Compared with the original SOM, this method can reduce the nonlinearity of ISPs and reconstruct stronger scatterers with better reconstruction qualities and less computation loads. The feasibility and efficiency of IDDT-SOM are discussed from the perspective of the relative distribution of induced current by numerical and experimental examples.