Exploring Electrical Impedance Tomography Techniques for Breast Cancer Detection in Three Dimensions

Electrical Impedance Tomography (EIT) is an imaging modality whose reconstruction problem is severely ill-posed; large changes in the interior conductivity can present as small changes in the data. Due to this ill-posedness, reconstructed images generally have low spatial resolution. However, EIT remains a promising area of study for many medical imaging applications, including breast imaging. In this dissertation, a proof of concept study is discussed in Project 1: "Machine Learning for Breast Cancer Detection" wherein machine learning techniques are used to classify breast tumors as malignant or benign from simulated EIT voltage data. Promising results in terms of accuracy and generalizability suggest that this is an avenue worthy of future exploration. This document also explores a fast and robust class of reconstruction algorithms using Complex Geometrical Optics (CGOs) and one such method, denoted the t^B method, is implemented for the first time on electrode data and compared to existing CGO-based methods. This is the basis for Project 2: "The t^B Complex Geometrical Optics Algorithm for Absolute Imaging in 3D." In this work, the t^B method was not found to produce significant improvements over existing CGO-based algorithms, though increasing the number of electrodes resulted in increased spatial resolution across all of the CGO-based methods. Finally, Project 3: "Improving Full- and Partial-Boundary 3D CGO-based Reconstructions with a priori information'' explores the use of application-specific a priori information to improve the inherently smooth reconstructions from CGO-based methods. Reconstructions largely improved in terms of spatial resolution and target localization when informed with a prior. These methods may prove particularly useful for medical imaging applications where priors could represent healthy EIT scans.