Subspace-based inversion methods for solving electromagnetic inverse scattering problems

Abstract

This thesis studies several methods for solving electromagnetic inverse scattering problems, all of which are on the basis of the concept of subspace. The original contributions of this thesis can be cataloged into two folds: Firstly, we not only apply the multiple signal classification (MUSIC) method to locate small anisotropic scatterers, dimensions of which are much less than the wavelength, but also propose a new MUSIC algorithm that improves resolution and in the meanwhile is able to deal with small degenerate scatterers; Secondly, we propose a new series of subspace-based optimization methods (SOM) to solve the inverse scattering problems for extended scatterers, including the nested SOM, twofold SOM, and improved SOM. Based on the concept of subspace, we actually utilize the most stable part of the measured scattered fields, thus, methods proposed in this thesis not only converge fast but also are quite robust against noise. Various numerical simulations have been carried out and validate the proposed algorithms.