Electrical impedance tomography reconstructions in two and three dimensions: from Calderón to direct methods - Bikowski, Jutta, author; Mueller, Jennifer, advisor (Colorado State University. Libraries, 2009)
Electrical Impedance Tomography (EIT) uses voltage and current measurements from the boundary to reconstruct the electrical conductivity distribution inside an unknown object. In this dissertation two different EIT reconstruction algorithms are investigated. The first was introduced by A. P. Calderón [ Soc. Bras. de Mat., (1980), pp. 65-73]. His method was implemented and successfully applied to both numerical and experimental data in two dimensions, including a phantom that models a cross section of a human chest and data taken from a human chest.

The second algorithm is a non-iterative method that solves the full nonlinear problem and was introduced by A. Nachman [Ann. of Math., 128 (1988), pp 531-576] for three or more dimensions. A version of this method was implemented and applied to spherically symmetric conductivity distributions. It is demonstrated that the texp-approximation to the scattering transform, which worked very well in two dimensions, does not represent an accurate estimate of the actual scattering transform near the origin. Therefore it has limited potential for reconstructions, especially since it is also shown that the scattering transform near the origin has a strong influence on the reconstructions of the conductivity distribution. However, high quality reconstructions can be computed from knowledge of the scattering transform near the origin.
Keywords: conductivity problem; EIT reconstruction; electrical impedance tomography; inverse problem; three-dimensional; mathematics; biomedical engineering