Discretization and Bayesian modeling in inverse problems and imaging

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Volume Title
Aalto-yliopiston teknillinen korkeakoulu | Doctoral thesis (article-based)
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Date
2010
Major/Subject
Mcode
Degree programme
Language
en
Pages
Verkkokirja (271 KB, 29 s.)
Series
Research reports. Helsinki University of Technology, Institute of Mathematics, A, 584
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.
Description
Supervising professor
Nevanlinna, Olavi, Prof.
Keywords
inverse problems, Mumford-Shah functional, Bayesian inversion, hierarchical modeling, discretization invariance, image model, Borel measure, metric space
Other note
Parts
  • [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.
  • [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.
  • [Publication 3]: Tapio Helin and Matti Lassas. 2009. Hierarchical models in statistical inverse problems and the Mumford–Shah functional. arXiv:0908.3396v2 [math.ST].
  • [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.
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