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000830149 0247_ $$2ISSN$$a1611-3349
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000830149 037__ $$aFZJ-2017-03726
000830149 041__ $$aEnglish
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000830149 1001_ $$0P:(DE-HGF)0$$aHoeltgen, Laurent$$b0$$eCorresponding author
000830149 1112_ $$a6th International Conference on Scale Space and Variational Methods in Computer Vision$$cKolding$$d2017-06-04 - 2017-06-08$$gSSVM 2017$$wDänemark
000830149 245__ $$aAnalytic Existence and Uniqueness Results for PDE-Based Image Reconstruction with the Laplacian
000830149 260__ $$aCham$$bSpringer International Publishing$$c2017
000830149 29510 $$aScale Space and Variational Methods in Computer Vision / Lauze, François (Editor)   ; Cham : Springer International Publishing, 2017, Chapter 6 ; ISSN: 0302-9743=1611-3349 ; ISBN: 978-3-319-58770-7=978-3-319-58771-4 
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000830149 4900_ $$aLecture Notes in Computer Science$$v10302
000830149 520__ $$aPartial differential equations are well suited for dealing with image reconstruction tasks such as inpainting. One of the most successful mathematical frameworks for image reconstruction relies on variations of the Laplace equation with different boundary conditions. In this work we analyse these formulations and discuss the existence and uniqueness of solutions of corresponding boundary value problems, as well as their regularity from an analytic point of view. Our work not only sheds light on useful aspects of the well posedness of several standard problem formulations in image reconstruction but also aggregates them in a common framework. In addition, the performed analysis guides us to specify two new formulations of the classic image reconstruction problem that may give rise to new developments in image reconstruction.
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000830149 7001_ $$0P:(DE-HGF)0$$aHarris, Isaac$$b1
000830149 7001_ $$0P:(DE-HGF)0$$aBreuß, Michael$$b2
000830149 7001_ $$0P:(DE-Juel1)169421$$aKleefeld, Andreas$$b3$$ufzj
000830149 773__ $$a10.1007/978-3-319-58771-4_6
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