An approximation method for electrical impedance tomography

Electrical impedance tomography is an imaging method with applications to geophysics and medical imaging. A new approximation is presented based on Nachman's 2-dimensional construction for closed domains. It improves upon existing approximations by extending the range of application from resolving 2 times the surface conductivity to imaging perfect conductors and insulators. With perfect knowledge of boundary data, this approximation exactly resolves a single conductive disc embedded in a homogenous domain. The problem, however, is ill-posed, and imaging performance degrades quickly as the distance from the boundary increases. The key to the approximation lies in (a) approximating Fadeev's Green's function (b) pre-processing measured voltages based on a boundary-integral equation (c) solving a linearized inverse problem (d) solving a d-bar equation, and (e) scaling the resulting image based on analytical results for a disc. In the development of the approximation, a new formula for Fadeev's Green's function is presented in terms of the Exponential Integral function. Also, new comparisons are made between reconstructions with and without solving the d-bar equation, showing that the added computational expense of solving the d-bar equation is not justified for radial problems. There is no discernible improvement in image quality. As a result, the approximation converts the inverse conductivity problem into a novel one-step linear problem with pre-conditioning of boundary data and scaling of the resulting image. Several extensions to this work are possible. The approximation is implemented for a circular domain with unit conductivity near the boundary, and extensions to other domains, bounded and unbounded should be possible, with non-constant conductivity near the boundary requiring further approximation. Ultimately, further research is required to ascertain whether it is possible to extend these techniques to imaging problems in three dimensions.

Name thesis:degree_name

Master of Applied Science - MASc

Level thesis:degree_level

master's

Discipline thesis:degree_discipline

Electrical and Computer Engineering

Grantor dc:publisher

University of British Columbia

Year dc:date

2008

Author dc:creator

• Pereira, Paulo J. S.

Statement dc:rights

• Attribution-NonCommercial-NoDerivatives 4.0 International

Licence

• http://creativecommons.org/licenses/by-nc-nd/4.0/

Language dc:language

eng

Handle dc:identifier

http://hdl.handle.net/2429/1536

OAI identifier oai:identifier

oai:circle.library.ubc.ca:2429/1536