Mehmet Nejat Tek

Least Squares Regularization Techniques for Contactless Electrical Conductivity Imaging

Date: Tuesday, August 3rd

Abstract:

Contactless electrical conductivity imaging (CECI) is designed to collect magnetic field measurements of induced currents in biological subjects. Although this data acquisition scheme evades surface electrodes, and electrode related limitations of the electrical impedance tomography (EIT), CECI still suffers from diminishing measurement strength caused by increasing depth. In this study, a numerical model is designed to simulate the physics of the CECI problem with finite element method (FEM). Then, the numerical model is used to express the image reconstruction problem in the least squares form. The image reconstruction problem is solved with regularized least squares algorithms, such as Tikhonov regularization, Moore-Penrose truncated inversion, regularization under variance uniformization, and bounded data uncertainties. A novel variant of the bounded data uncertainties is proposed to provide column weighted or block weighted regularization to the solutions. The performances of the algorithms are analyzed on two simulated phantoms, and results are presented in a comparative form. Finally, experimental data is used to reconstruct images of physical phantoms. It is found that the novel BDU variant provides superior image quality among the aforementioned algorithms, and it is a promising tool for similar applications, such as electrical impedance tomography, and eddy current imaging.

Committee:
Prof. Bahram Shafai (ECE), advisor
Prof. Steve McKnight (ECE)
Prof. Vinay Ingle (ECE)
Prof. Dana Brooks (ECE)