Date of Award

12-2018

Document Type

Thesis

Degree Name

Master of Science (MS)

Department

Mathematical Sciences

Committee Member

Dr. Taufiquar Khan, Committee Chair

Committee Member

Dr. Shitao Liu

Committee Member

Dr. Jeong Yoon

Abstract

Electrical impedance tomography ("EIT") has many significant applications, ranging from geophysical and medical imaging, to the military, to industrial fields. Due to the relevance of EIT in fields of critical importance to society, further development of EIT is vital. The instability of image reconstruction and the highly nonlinear behavior of the image reconstruction problem, make the problem particularly difficult, are referred to as ill-posed inverse problem. Specifically, development of a comprehensive set of techniques to solve the EIT problem is necessary, due to both its ill-posed, nonlinear nature, and its scope. In this thesis, several approaches to the inversion of the EIT problem are presented, as well as a comparison with the inversion software EIDORS (Electrical Impedance Tomography and Diffuse Optical Tomography Reconstruction Software). In this thesis, the advantages and disadvantages of EIT as compared to other imaging techniques is discussed. Then the theory of EIT, including the governing equations, the forward problem, and methods for solving the inverse problem are presented. Next, the reconstruction software EIDORS is presented, in which artificial data is created, and the reconstruction algorithms are implemented. The effect of noise on the simulated data is investigated. Lastly, experimental data is implemented, and the results are discussed. We considered absolute conductivities in reconstruction, which was a gap in previous work, and have thus resolved this missing element of the work. The experimental data was successfully reconstructed with two different absolute reconstruction algorithms. Additionally, the optimal injection patterns were evaluated for accuracy and practical application. Lastly, we observed that the reconstruction algorithms were extremely sensitive to the regularization parameter, implying that the parameter selection method is of paramount importance. In this thesis, we have considered smoothness constraints such as TV regularization and L_2 regularization which leads to reasonable reconstruction using experimental data and leads the way for future comparison to sparsity and statistical approaches to solve the EIT inverse problem.

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