2-D D-bar conductivity reconstructions on non-circular domains

Abstract

We study the 2-D Electrical Impedance Tomography problem, which is the problem of finding the conductivity inside a domain from knowledge of the Dirichlet-to-Neumann map. The focus of this dissertation is to improve the numerical implementation of the D-bar method. The D-bar method is a direct (non-iterative) method that solves the full nonlinear problem with no data fitting. The major contribution of this dissertation is the improvement in the calculation of the scattering transform. The scattering transform is an intermediate function, not directly measurable in experiments, that plays an important role in the conductivity reconstructions. The main focus of this work is to incorporate accurate domain modeling in the algorithm, such as the boundary of a cross-section of a human chest. We show good improvement from previous implementations, and provide a thorough study showing the effects of modeling assumptions and errors in data on conductivity reconstructions.