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Electrical impedance tomography reconstructions in two and three dimensions: from Calderón to direct methods

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dc.contributor.authorBikowski, Jutta, author
dc.contributor.authorMueller, Jennifer, advisor
dc.date.accessioned2024-03-13T18:50:51Z
dc.date.available2024-03-13T18:50:51Z
dc.date.issued2009
dc.description.abstractElectrical Impedance Tomography (EIT) uses voltage and current measurements from the boundary to reconstruct the electrical conductivity distribution inside an unknown object. In this dissertation two different EIT reconstruction algorithms are investigated. The first was introduced by A. P. Calderón [ Soc. Bras. de Mat., (1980), pp. 65-73]. His method was implemented and successfully applied to both numerical and experimental data in two dimensions, including a phantom that models a cross section of a human chest and data taken from a human chest.
dc.description.abstractThe second algorithm is a non-iterative method that solves the full nonlinear problem and was introduced by A. Nachman [Ann. of Math., 128 (1988), pp 531-576] for three or more dimensions. A version of this method was implemented and applied to spherically symmetric conductivity distributions. It is demonstrated that the texp-approximation to the scattering transform, which worked very well in two dimensions, does not represent an accurate estimate of the actual scattering transform near the origin. Therefore it has limited potential for reconstructions, especially since it is also shown that the scattering transform near the origin has a strong influence on the reconstructions of the conductivity distribution. However, high quality reconstructions can be computed from knowledge of the scattering transform near the origin.
dc.format.mediumborn digital
dc.format.mediumdoctoral dissertations
dc.identifierETDF_Bikowski_2009_3374679.pdf
dc.identifier.urihttps://hdl.handle.net/10217/237584
dc.languageEnglish
dc.language.isoeng
dc.publisherColorado State University. Libraries
dc.relation.ispartof2000-2019
dc.rightsCopyright and other restrictions may apply. User is responsible for compliance with all applicable laws. For information about copyright law, please see https://libguides.colostate.edu/copyright.
dc.rights.licensePer the terms of a contractual agreement, all use of this item is limited to the non-commercial use of Colorado State University and its authorized users.
dc.subjectconductivity problem
dc.subjectEIT reconstruction
dc.subjectelectrical impedance tomography
dc.subjectinverse problem
dc.subjectthree-dimensional
dc.subjectmathematics
dc.subjectbiomedical engineering
dc.titleElectrical impedance tomography reconstructions in two and three dimensions: from Calderón to direct methods
dc.typeText
dcterms.rights.dplaThis Item is protected by copyright and/or related rights (https://rightsstatements.org/vocab/InC/1.0/). You are free to use this Item in any way that is permitted by the copyright and related rights legislation that applies to your use. For other uses you need to obtain permission from the rights-holder(s).
thesis.degree.disciplineMathematics
thesis.degree.grantorColorado State University
thesis.degree.levelDoctoral
thesis.degree.nameDoctor of Philosophy (Ph.D.)

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