Discretization and Bayesian modeling in inverse problems and imaging

Helin, Tapio

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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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