Electrical impedance tomography with Calderón's method in two and three dimensions
Date
2020
Authors
Shin, Kwancheol, author
Mueller, Jennifer L., advisor
Cheney, Margaret, committee member
Pinaud, Olivier, committee member
Hussam, Mahmoud, committee member
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Abstract
Electrical impedance tomography (EIT) is a non-invasive imaging technique in which electrical measurements on the electrodes attached to the boundary of a subject are used to reconstruct the electrical properties of the subject. That is, voltage data arising from currents applied on the boundary are used to reconstruct the conductivity distribution in the interior. Calderón's method is a direct linearized reconstruction method for the inverse conductivity problem with the attributes that it can provide absolute images with no need for forward modeling, reconstructions can be computed in real-time, and both conductivity and permittivity can be reconstructed. In this three-paper dissertation, first, an explicit relationship between Calderón's method and the D-bar method is provided, facilitating a "higher-order" Calderón's method in which a correction term is included, derived from the relationship to the D-bar method. Furthermore, a method of including a spatial prior is provided. These advances are demonstrated on tank data collected with the ACE1 EIT system. On the other hand, it has been demonstrated that various EIT reconstruction algorithms are very sensitive to the measurement and incorrect modeling of the boundary shape. Calderón's method has been implemented with correct boundary shape, but the exact location of the electrodes are disregarded as they are assumed to be spaced uniformly in angle. In the second body of work, Calderón's method is implemented with a new expansion technique which enables the use of the correct location of the electrodes as well as the shape of the boundary resulting in improved absolute images. We test our new algorithm with experimental data collected with the ACE1 EIT system. Finally, the first implementation of Calderón's method on a 3-D cylindrical domain with data collected on a portion of the boundary is provided. The effectiveness of the method to localize inhomogeneities in the plane of the electrodes and in the z-direction is demonstrated on simulated and experimental data.
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Subject
electrical impedance tomography
medical imaging
Calderón's method
PDEs
inverse problems