Bayesian approach to the anisotropic EIT problem and effect of structural changes on reconstruction algorithm using 2-D D-bar algorithm
Date
2018
Authors
Murthy, Rashmi, author
Mueller, Jennifer L., advisor
Cheney, Margaret, committee member
Pinaud, Oliver, committee member
Buchanan, Kristen, committee member
Journal Title
Journal ISSN
Volume Title
Abstract
Electrical Impedance Tomography (EIT) is a relatively new imaging technique that is non-invasive, low-cost, and non-ionizing with excellent temporal resolution.In EIT, the unknown electrical conductivity in the interior of the medium is determined from the boundary electrical measurements. In this work, we attempt to find a direct reconstruction algorithm to the anisotropic EIT problem based on the well-known Calderón's method. The non-uniqueness of the inverse problem is dealt with assuming that the directions of anisotropy are known. We utilize the quasi-conformal map in the plane to accomplish Calderóns approach. Additionally, we derive a probability distribution for the anisotropic conductivity values using a Bayesian formulation, where the direction of anisotropy is encoded as the prior information. We show that this results in the generalized Tikhonov regularization, where the prior information about the direction of anisotropy is incorporated in the regularization operator. The computations of the anisotropic EIT problem using the Bayesian formulation is conducted on simulated data and the resulting reconstructions for the data are shown. Finally, the work of this thesis is concluded by implementing dynamic changes in boundary of a human data during respiration process successfully in the D-bar algorithm.