Bayesian approach to the anisotropic EIT problem and effect of structural changes on reconstruction algorithm using 2-D D-bar algorithm
| dc.contributor.author | Murthy, Rashmi, author | |
| dc.contributor.author | Mueller, Jennifer L., advisor | |
| dc.contributor.author | Cheney, Margaret, committee member | |
| dc.contributor.author | Pinaud, Oliver, committee member | |
| dc.contributor.author | Buchanan, Kristen, committee member | |
| dc.date.accessioned | 2018-09-10T20:05:44Z | |
| dc.date.available | 2019-09-06T20:05:05Z | |
| dc.date.issued | 2018 | |
| dc.description.abstract | Electrical Impedance Tomography (EIT) is a relatively new imaging technique that is non-invasive, low-cost, and non-ionizing with excellent temporal resolution.In EIT, the unknown electrical conductivity in the interior of the medium is determined from the boundary electrical measurements. In this work, we attempt to find a direct reconstruction algorithm to the anisotropic EIT problem based on the well-known Calderón's method. The non-uniqueness of the inverse problem is dealt with assuming that the directions of anisotropy are known. We utilize the quasi-conformal map in the plane to accomplish Calderóns approach. Additionally, we derive a probability distribution for the anisotropic conductivity values using a Bayesian formulation, where the direction of anisotropy is encoded as the prior information. We show that this results in the generalized Tikhonov regularization, where the prior information about the direction of anisotropy is incorporated in the regularization operator. The computations of the anisotropic EIT problem using the Bayesian formulation is conducted on simulated data and the resulting reconstructions for the data are shown. Finally, the work of this thesis is concluded by implementing dynamic changes in boundary of a human data during respiration process successfully in the D-bar algorithm. | |
| dc.format.medium | born digital | |
| dc.format.medium | doctoral dissertations | |
| dc.identifier | Murthy_colostate_0053A_15071.pdf | |
| dc.identifier.uri | https://hdl.handle.net/10217/191473 | |
| dc.language | English | |
| dc.language.iso | eng | |
| dc.publisher | Colorado State University. Libraries | |
| dc.relation.ispartof | 2000-2019 | |
| dc.rights | Copyright 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.title | Bayesian approach to the anisotropic EIT problem and effect of structural changes on reconstruction algorithm using 2-D D-bar algorithm | |
| dc.type | Text | |
| dcterms.embargo.expires | 2019-09-06 | |
| dcterms.embargo.terms | 2019-09-06 | |
| dcterms.rights.dpla | This 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.discipline | Mathematics | |
| thesis.degree.grantor | Colorado State University | |
| thesis.degree.level | Doctoral | |
| thesis.degree.name | Doctor of Philosophy (Ph.D.) |
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