Two-dimensional inverse scattering problems of small and extended scatterers

Abstract

This thesis studies two-dimensional inverse scattering problems of small scatterers, extended scatterers, and anisotropic scatterers. For small scatterers, the impact of the choice of test source and signal subspace on the performance of multiple signal classification (MUSIC) is studied. A non-iterative two-step least squares based method is proposed for retrieving the polarization tensors of small scatterers. For extended scatterers, a new multipole based linear sampling method (MLSM) is proposed, which uses a radiation model for linear sampling method and a physical regularization scheme. MLSM is used to generate an initial guess for subspace based optimization method (SOM), a fast and robust method for the reconstruction of extended scatterers. Further, SOM is extended for the vectorial inverse scattering problem. For anisotropic scatterers, a modified MUSIC algorithm is proposed, which computes the optimal test direction at each point non-iteratively. The application of SOM is extended for the reconstruction of extended anisotropic scatterers.