High-Order Regularized Regression in Electrical Impedance Tomography
We present a novel approach for the inverse problem in electrical impedance tomography based on regularized quadratic regression. Our contribution introduces a new formulation for the forward model in the form of a nonlinear integral transform, which maps changes in the electrical properties of a do...
| Main Authors: | , , |
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| Other Authors: | |
| Format: | Article |
| Language: | en_US |
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Society for Industrial and Applied Mathematics
2013
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| Online Access: | http://hdl.handle.net/1721.1/77895 |
| _version_ | 1826211267371597824 |
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| author | Polydorides, Nick Adhasi, Alireza Miller, Eric L. |
| author2 | MIT Energy Initiative |
| author_facet | MIT Energy Initiative Polydorides, Nick Adhasi, Alireza Miller, Eric L. |
| author_sort | Polydorides, Nick |
| collection | MIT |
| description | We present a novel approach for the inverse problem in electrical impedance tomography based on regularized quadratic regression. Our contribution introduces a new formulation for the forward model in the form of a nonlinear integral transform, which maps changes in the electrical properties of a domain to their respective variations in boundary data. Using perturbation theory the transform is approximated to yield a high-order misfit function which is then used to derive a regularized inverse problem. In particular, we consider the nonlinear problem to second-order accuracy; hence our approximation method improves upon the local linearization of the forward mapping. The inverse problem is approached using Newton's iterative algorithm, and results from simulated experiments are presented. With a moderate increase in computational complexity, the method yields superior results compared to those of regularized linear regression and can be implemented to address the nonlinear inverse problem. |
| first_indexed | 2024-09-23T15:03:14Z |
| format | Article |
| id | mit-1721.1/77895 |
| institution | Massachusetts Institute of Technology |
| language | en_US |
| last_indexed | 2024-09-23T15:03:14Z |
| publishDate | 2013 |
| publisher | Society for Industrial and Applied Mathematics |
| record_format | dspace |
| spelling | mit-1721.1/778952022-09-29T12:19:42Z High-Order Regularized Regression in Electrical Impedance Tomography Polydorides, Nick Adhasi, Alireza Miller, Eric L. MIT Energy Initiative Polydorides, Nick We present a novel approach for the inverse problem in electrical impedance tomography based on regularized quadratic regression. Our contribution introduces a new formulation for the forward model in the form of a nonlinear integral transform, which maps changes in the electrical properties of a domain to their respective variations in boundary data. Using perturbation theory the transform is approximated to yield a high-order misfit function which is then used to derive a regularized inverse problem. In particular, we consider the nonlinear problem to second-order accuracy; hence our approximation method improves upon the local linearization of the forward mapping. The inverse problem is approached using Newton's iterative algorithm, and results from simulated experiments are presented. With a moderate increase in computational complexity, the method yields superior results compared to those of regularized linear regression and can be implemented to address the nonlinear inverse problem. Research Promotion Foundation (Cyprus) Massachusetts Institute of Technology. Laboratory for Energy and the Environment (Cyprus Institute Program for Energy, Environment and Water Resources (CEEW)) 2013-03-13T19:37:22Z 2013-03-13T19:37:22Z 2012-08 2012-05 Article http://purl.org/eprint/type/JournalArticle 1936-4954 http://hdl.handle.net/1721.1/77895 Polydorides, Nick, Alireza Aghasi, and Eric L. Miller. “High-Order Regularized Regression in Electrical Impedance Tomography.” SIAM Journal on Imaging Sciences 5.3 (2012): 912–943. CrossRef. Web. © 2012, Society for Industrial and Applied Mathematics. en_US http://dx.doi.org/10.1137/11084724x SIAM Journal on Imaging Sciences Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use. application/pdf Society for Industrial and Applied Mathematics SIAM |
| spellingShingle | Polydorides, Nick Adhasi, Alireza Miller, Eric L. High-Order Regularized Regression in Electrical Impedance Tomography |
| title | High-Order Regularized Regression in Electrical Impedance Tomography |
| title_full | High-Order Regularized Regression in Electrical Impedance Tomography |
| title_fullStr | High-Order Regularized Regression in Electrical Impedance Tomography |
| title_full_unstemmed | High-Order Regularized Regression in Electrical Impedance Tomography |
| title_short | High-Order Regularized Regression in Electrical Impedance Tomography |
| title_sort | high order regularized regression in electrical impedance tomography |
| url | http://hdl.handle.net/1721.1/77895 |
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