Computational Methods for Microwave Medical Imaging

Medical imaging methods have become increasingly important in diagnosing diseases and assisting therapeutic treatment. In particular, early detection of breast cancer is considered as a critical factor in reducing the mortality rate of women. Within the various alternative breast imaging modalities being investigated to improve breast cancer detection, microwave imaging is attractive due to the high dielectric property contrast between the cancerous and the normal tissue and has received significant interest over the last decade. The investigation into two-dimensional microwave imaging at the Thayer School of Engineering, Dartmouth College, began in the early 1990’s where the first clinical microwave imaging system was brought online at the Dartmouth-Hitchcock Medical Center (DHMC) in 1999. Although the two dimensional microwave imaging has shown great promise, the image quality is essentially compromised by the various approximations associated with operating in 2D. In this thesis, we focus on the theoretical aspects of the nonlinear tomographic image reconstruction problem with particular emphasis on developing efficient numerical algorithms for 3D microwave imaging. An incremental approach was devised to assess this progress. The concept of the dual-mesh was generalized and served as an organizing theme from which the computational efficiency of various forward field modelling methods were investigated. These methods included the 2D finite element coupled with boundary element methods and the 2D FDTD method with its exiii iv Abstract tension to 3D space. Significant effort was spent on optimizing the 3D forward model in order to reconstruct images efficiently. Additional reconstruction techniques such as the adjoint method, the nodal adjoint approximation as well as a multiple-frequency dispersion reconstruction algorithm were developed to enhance both the speed and quality of the recovered images. An in-depth analysis of the Jacobian matrix was performed in the context of investigating various important factors including the resolution limit and the impact of system parameters on image quality. Additionally, a mathematical theory encompassing the properties of the phase unwrapping integral and its use with respect to our log-magnitude/phase form (LMPF) imaging algorithm was developed and discussed with particular attention to microwave scattering nulls.