# A mathematical model for electrical impedance process tomography

 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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