A mathematical model for electrical impedance process tomography

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dc.contributor Aalto-yliopisto fi
dc.contributor Aalto University en
dc.contributor.author Pikkarainen, Hanna Katriina
dc.date.accessioned 2012-02-17T06:58:30Z
dc.date.available 2012-02-17T06:58:30Z
dc.date.issued 2005-05-13
dc.identifier.isbn 951-22-7672-0
dc.identifier.issn 0784-3143
dc.identifier.uri https://aaltodoc.aalto.fi/handle/123456789/2563
dc.description.abstract We consider the process tomography problem of the following kind: based on electromagnetic measurements on the surface of a pipe, describe the concentration distribution of a given substance in a fluid moving in the pipeline. We view the problem as a state estimation problem. The concentration distribution is treated as a stochastic process satisfying a stochastic differential equation. This is referred to as the state evolution equation. The measurements are described in terms of an observation equation containing the measurement noise. The time evolution is modelled by a stochastic convection-diffusion equation. The measurement situation is represented by the most realistic model for electrical impedance tomography, the complete electrode model. In this thesis, we give the mathematical formulation of the state evolution and observation equations and then we derive the discrete infinite dimensional state estimation system. Since our motive is to monitor the flow in the pipeline in real time, we are dealing with a filtering problem in which the estimator is based on the current history of the measurement process. For computational reasons we present a discretized state estimation system where the discretization error is taken into account. The discretized filtering problem is solved by the Bayesian filtering method. en
dc.format.extent 172
dc.format.mimetype application/pdf
dc.language.iso en en
dc.publisher Helsinki University of Technology en
dc.publisher Teknillinen korkeakoulu fi
dc.relation.ispartofseries Research reports / Helsinki University of Technology, Institute of Mathematics. A en
dc.relation.ispartofseries 486 en
dc.subject.other Medical sciences en
dc.subject.other Physics en
dc.title A mathematical model for electrical impedance process tomography en
dc.type G4 Monografiaväitöskirja fi
dc.description.version reviewed en
dc.contributor.department Department of Engineering Physics and Mathematics en
dc.contributor.department Teknillisen fysiikan ja matematiikan osasto fi
dc.subject.keyword statistical inversion theory en
dc.subject.keyword nonstationary inverse problem en
dc.subject.keyword state estimation en
dc.subject.keyword Bayesian filtering en
dc.subject.keyword process tomography en
dc.subject.keyword electrical impedance tomography en
dc.subject.keyword complete electrode model en
dc.identifier.urn urn:nbn:fi:tkk-005178
dc.type.dcmitype text en
dc.type.ontasot Väitöskirja (monografia) fi
dc.type.ontasot Doctoral dissertation (monograph) en
dc.contributor.lab Institute of Mathematics en
dc.contributor.lab Matematiikan laitos fi

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