Generalized linearization techniques in electrical impedance tomography

dc.contributorAalto-yliopistofi
dc.contributorAalto Universityen
dc.contributor.authorHyvönen, Nuuttien_US
dc.contributor.authorMustonen, Laurien_US
dc.contributor.departmentDepartment of Mathematics and Systems Analysisen
dc.contributor.groupauthorNumerical Analysisen
dc.date.accessioned2020-01-17T13:27:58Z
dc.date.available2020-01-17T13:27:58Z
dc.date.issued2018-09en_US
dc.description.abstractElectrical impedance tomography aims at reconstructing the interior electrical conductivity from surface measurements of currents and voltages. As the current–voltage pairs depend nonlinearly on the conductivity, impedance tomography leads to a nonlinear inverse problem. Often, the forward problem is linearized with respect to the conductivity and the resulting linear inverse problem is regarded as a subproblem in an iterative algorithm or as a simple reconstruction method as such. In this paper, we compare this basic linearization approach to linearizations with respect to the resistivity or the logarithm of the conductivity. It is numerically demonstrated that the conductivity linearization often results in compromised accuracy in both forward and inverse computations. Inspired by these observations, we present and analyze a new linearization technique which is based on the logarithm of the Neumann-to-Dirichlet operator. The method is directly applicable to discrete settings, including the complete electrode model. We also consider Fréchet derivatives of the logarithmic operators. Numerical examples indicate that the proposed method is an accurate way of linearizing the problem of electrical impedance tomography.en
dc.description.versionPeer revieweden
dc.format.extent26
dc.format.extent95-120
dc.format.mimetypeapplication/pdfen_US
dc.identifier.citationHyvönen, N & Mustonen, L 2018, ' Generalized linearization techniques in electrical impedance tomography ', Numerische Mathematik, vol. 140, no. 1, pp. 95-120 . https://doi.org/10.1007/s00211-018-0959-1en
dc.identifier.doi10.1007/s00211-018-0959-1en_US
dc.identifier.issn0029-599X
dc.identifier.issn0945-3245
dc.identifier.otherPURE UUID: 5fe801c7-d913-445f-aa7b-4f164097fe6een_US
dc.identifier.otherPURE ITEMURL: https://research.aalto.fi/en/publications/5fe801c7-d913-445f-aa7b-4f164097fe6een_US
dc.identifier.otherPURE LINK: http://www.scopus.com/inward/record.url?scp=85044214004&partnerID=8YFLogxKen_US
dc.identifier.otherPURE FILEURL: https://research.aalto.fi/files/40175796/SCI_HyvonenMustonen_Generalized_Linarization.NumMath_2018.pdfen_US
dc.identifier.urihttps://aaltodoc.aalto.fi/handle/123456789/42517
dc.identifier.urnURN:NBN:fi:aalto-202001171632
dc.language.isoenen
dc.publisherSPRINGER HEIDELBERG
dc.relation.ispartofseriesNumerische Mathematiken
dc.relation.ispartofseriesVolume 140, issue 1en
dc.rightsopenAccessen
dc.titleGeneralized linearization techniques in electrical impedance tomographyen
dc.typeA1 Alkuperäisartikkeli tieteellisessä aikakauslehdessäfi
dc.type.versionacceptedVersion

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