A direct D-bar reconstruction algorithm for complex admittivities in W2,∞(Ω) for the 2-D EIT problem
Date
2012
Authors
Hamilton, Sarah Jane, author
Mueller, Jennifer L., advisor
Duchateau, Paul, committee member
Tavener, Simon, committee member
Lear, Kevin, committee member
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Abstract
Electrical Impedance Tomography (EIT) is a fairly new, portable, relatively inexpensive, imaging system that requires no ionizing radiation. Electrodes are placed at the surface of a body and low frequency, low amplitude current is applied on the electrodes, and the resulting voltage value on each electrode is measured. By applying a basis of current patterns, one can obtain sufficient information to recover the complex admittivity distribution of the region in the plane of the electrodes. In 2000, Elisa Francini presented a nearly constructive proof that was the first approach using D-bar methods to solve the full nonlinear problem for twice-differentiable conductivities and permittivities. In this thesis the necessary formulas to turn her proof into a direct D-bar reconstruction algorithm that solves the full nonlinear admittivity problem in 2-D are described. Reconstructions for simulated Finite Element data for circular and non-circular domains are presented.
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Subject
Calderon problem
inverse problems
inverse conductivity problem
D-bar