A geometry-independent algorithm for electrical impedance tomography using wavelet-Galerkin discretization and conjugate gradient regularization

Persistent Link:
http://hdl.handle.net/10150/282511
Title:
A geometry-independent algorithm for electrical impedance tomography using wavelet-Galerkin discretization and conjugate gradient regularization
Author:
Friefeld, Andrew Scott, 1967-
Issue Date:
1997
Publisher:
The University of Arizona.
Rights:
Copyright © is held by the author. Digital access to this material is made possible by the University Libraries, University of Arizona. Further transmission, reproduction or presentation (such as public display or performance) of protected items is prohibited except with permission of the author.
Abstract:
Electrical impedance tomography is a rapidly growing discipline with an increasing number of medical and nonmedical applications. Many recent studies indicate that while the technique shows promise, improvements must be made before impedance imaging systems take their place beside more mature imaging technologies in the clinic and in the laboratory. This dissertation is an effort to address two of the shortcomings of currently available impedance tomography systems. First, a new numerical solution to the governing partial differential equation is presented which allows the user a fast, easy means of making geometrical changes. Treating the domain of interest as an input to the problem, recent results from the field of wavelet theory provide a simple means of identifying the boundary as well as giving a method for solving the partial differential equation in a fast, efficient manner. Since the algorithm only requires a pixel representation of the geometry and does not use a grid generation program, it may be of interest in applications where the geometry varies with time or the user may not be familiar with the complexities of typical finite element method grid generation programs. Second, an application of the conjugate gradient method to the problem of regularizing the nonlinear Newton-Raphson conductivity update leads to significant improvement over the popular Levenberg-Marquardt trust region regularization. The use of the conjugate gradient method as a regularization technique allows for convergence of the conductivity reconstruction in far fewer iterations and can perform reconstructions with an initial assumption of uniform conductivity in situations where other methods require either a priori knowledge or internal measurement of voltages.
Type:
text; Dissertation-Reproduction (electronic)
Keywords:
Engineering, Biomedical.; Engineering, Electronics and Electrical.
Degree Name:
Ph.D.
Degree Level:
doctoral
Degree Program:
Graduate College; Electrical and Computer Engineering
Degree Grantor:
University of Arizona
Advisor:
Tharp, Hal

Full metadata record

DC FieldValue Language
dc.language.isoen_USen_US
dc.titleA geometry-independent algorithm for electrical impedance tomography using wavelet-Galerkin discretization and conjugate gradient regularizationen_US
dc.creatorFriefeld, Andrew Scott, 1967-en_US
dc.contributor.authorFriefeld, Andrew Scott, 1967-en_US
dc.date.issued1997en_US
dc.publisherThe University of Arizona.en_US
dc.rightsCopyright © is held by the author. Digital access to this material is made possible by the University Libraries, University of Arizona. Further transmission, reproduction or presentation (such as public display or performance) of protected items is prohibited except with permission of the author.en_US
dc.description.abstractElectrical impedance tomography is a rapidly growing discipline with an increasing number of medical and nonmedical applications. Many recent studies indicate that while the technique shows promise, improvements must be made before impedance imaging systems take their place beside more mature imaging technologies in the clinic and in the laboratory. This dissertation is an effort to address two of the shortcomings of currently available impedance tomography systems. First, a new numerical solution to the governing partial differential equation is presented which allows the user a fast, easy means of making geometrical changes. Treating the domain of interest as an input to the problem, recent results from the field of wavelet theory provide a simple means of identifying the boundary as well as giving a method for solving the partial differential equation in a fast, efficient manner. Since the algorithm only requires a pixel representation of the geometry and does not use a grid generation program, it may be of interest in applications where the geometry varies with time or the user may not be familiar with the complexities of typical finite element method grid generation programs. Second, an application of the conjugate gradient method to the problem of regularizing the nonlinear Newton-Raphson conductivity update leads to significant improvement over the popular Levenberg-Marquardt trust region regularization. The use of the conjugate gradient method as a regularization technique allows for convergence of the conductivity reconstruction in far fewer iterations and can perform reconstructions with an initial assumption of uniform conductivity in situations where other methods require either a priori knowledge or internal measurement of voltages.en_US
dc.typetexten_US
dc.typeDissertation-Reproduction (electronic)en_US
dc.subjectEngineering, Biomedical.en_US
dc.subjectEngineering, Electronics and Electrical.en_US
thesis.degree.namePh.D.en_US
thesis.degree.leveldoctoralen_US
thesis.degree.disciplineGraduate Collegeen_US
thesis.degree.disciplineElectrical and Computer Engineeringen_US
thesis.degree.grantorUniversity of Arizonaen_US
dc.contributor.advisorTharp, Halen_US
dc.identifier.proquest9814400en_US
dc.identifier.bibrecord.b37742383en_US
All Items in UA Campus Repository are protected by copyright, with all rights reserved, unless otherwise indicated.