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Discretization and Bayesian modeling in inverse problems and imaging

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dc.contributor Aalto-yliopisto fi
dc.contributor Aalto University en
dc.contributor.author Helin, Tapio
dc.date.accessioned 2012-08-24T07:47:03Z
dc.date.available 2012-08-24T07:47:03Z
dc.date.issued 2010
dc.identifier.isbn 978-952-60-3041-8 (electronic)
dc.identifier.isbn 978-952-60-3040-1 (printed) #8195;
dc.identifier.issn 1797-5867
dc.identifier.uri https://aaltodoc.aalto.fi/handle/123456789/4747
dc.description.abstract In this thesis the Bayesian modeling and discretization are studied in inverse problems related to imaging. The treatise consists of four articles which focus on the phenomena that appear when more detailed data or a priori information become available. Novel Bayesian methods for solving ill-posed signal processing problems in edge-preserving manner are introduced and analysed. Furthermore, modeling photographs in image processing problems is studied and a novel model is presented. en
dc.format.extent Verkkokirja (271 KB, 29 s.)
dc.format.mimetype application/pdf
dc.language.iso en en
dc.publisher Aalto-yliopiston teknillinen korkeakoulu en
dc.relation.ispartofseries Research reports. Helsinki University of Technology, Institute of Mathematics, A, 584 en
dc.relation.haspart [Publication 1]: Tapio Helin. 2009. On infinite-dimensional hierarchical probability models in statistical inverse problems. Inverse Problems and Imaging, volume 3, number 4, pages 567-597. en
dc.relation.haspart [Publication 2]: Tapio Helin and Matti Lassas. 2007. Bayesian signal restoration and Mumford-Shah functional. Proceedings in Applied Mathematics and Mechanics, volume 7, number 1, Special Issue: Sixth International Congress on Industrial Applied Mathematics (ICIAM07) and GAMM Annual Meeting, pages 2080013-2080014. en
dc.relation.haspart [Publication 3]: Tapio Helin and Matti Lassas. 2009. Hierarchical models in statistical inverse problems and the Mumford–Shah functional. arXiv:0908.3396v2 [math.ST]. en
dc.relation.haspart [Publication 4]: Tapio Helin, Matti Lassas, and Samuli Siltanen. 2010. Infinite photography: new mathematical model for high-resolution images. Journal of Mathematical Imaging and Vision, volume 36, number 2, pages 140-158. en
dc.subject.other Mathematics
dc.title Discretization and Bayesian modeling in inverse problems and imaging en
dc.type G5 Artikkeliväitöskirja fi
dc.contributor.school Aalto-yliopiston teknillinen korkeakoulu fi
dc.contributor.department Matematiikan ja systeemianalyysin laitos fi
dc.contributor.department Department of Mathematics and Systems Analysis en
dc.subject.keyword inverse problems en
dc.subject.keyword Mumford-Shah functional en
dc.subject.keyword Bayesian inversion en
dc.subject.keyword hierarchical modeling en
dc.subject.keyword discretization invariance en
dc.subject.keyword image model en
dc.subject.keyword Borel measure en
dc.subject.keyword metric space en
dc.identifier.urn URN:ISBN:978-952-60-3041-8
dc.type.dcmitype text en
dc.type.ontasot Väitöskirja (artikkeli) fi
dc.type.ontasot Doctoral dissertation (article-based) en
dc.contributor.supervisor Nevanlinna, Olavi, Prof.
local.aalto.digifolder Aalto_67851
local.aalto.digiauth ask

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