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Source Localization of Reaction-Diffusion Models for Brain Tumors
Linköping University, Department of Science and Technology. Linköping University, Faculty of Science & Engineering.
Linköping University, Department of Science and Technology, Communications and Transport Systems. Linköping University, Faculty of Science & Engineering.
Heidelberg University, Germany.
Linköping University, Department of Science and Technology, Communications and Transport Systems. Linköping University, Faculty of Science & Engineering. Aston University, England.
2016 (English)In: PATTERN RECOGNITION, GCPR 2016, Springer Publishing Company, 2016, Vol. 9796, 414-425 p.Conference paper, Published paper (Refereed)
Abstract [en]

We propose a mathematically well-founded approach for locating the source (initial state) of density functions evolved within a nonlinear reaction-diffusion model. The reconstruction of the initial source is an ill-posed inverse problem since the solution is highly unstable with respect to measurement noise. To address this instability problem, we introduce a regularization procedure based on the nonlinear Landweber method for the stable determination of the source location. This amounts to solving a sequence of well-posed forward reaction-diffusion problems. The developed framework is general, and as a special instance we consider the problem of source localization of brain tumors. We show numerically that the source of the initial densities of tumor cells are reconstructed well on both imaging data consisting of simple and complex geometric structures.

Place, publisher, year, edition, pages
Springer Publishing Company, 2016. Vol. 9796, 414-425 p.
Series
Lecture Notes in Computer Science, ISSN 0302-9743 (print), 1611-3349 (online)
National Category
Computational Mathematics
Identifiers
URN: urn:nbn:se:liu:diva-133404DOI: 10.1007/978-3-319-45886-1_34ISI: 000389019900034ISBN: 978-3-319-45886-1 (electronic)ISBN: 978-3-319-45885-4 (print)OAI: oai:DiVA.org:liu-133404DiVA: diva2:1059992
Conference
38th German Conference on Pattern Recognition (GCPR)
Available from: 2016-12-27 Created: 2016-12-22 Last updated: 2017-01-19

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Jaroudi, RymBaravdish, GeorgeJohansson, Thomas
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CiteExportLink to record
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Citation style
  • apa
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