Hauptseite > Publikationsdatenbank > Analytic Existence and Uniqueness Results for PDE-Based Image Reconstruction with the Laplacian > print

001     830149
005     20210129230431.0
020 _ _ |a 978-3-319-58770-7 (print)
020 _ _ |a 978-3-319-58771-4 (electronic)
024 7 _ |a 10.1007/978-3-319-58771-4_6
|2 doi
024 7 _ |a 0302-9743
|2 ISSN
024 7 _ |a 1611-3349
|2 ISSN
024 7 _ |a WOS:000432210900006
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037 _ _ |a FZJ-2017-03726
041 _ _ |a English
082 _ _ |a 004
100 1 _ |a Hoeltgen, Laurent
|0 P:(DE-HGF)0
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|e Corresponding author
111 2 _ |a 6th International Conference on Scale Space and Variational Methods in Computer Vision
|g SSVM 2017
|c Kolding
|d 2017-06-04 - 2017-06-08
|w Dänemark
245 _ _ |a Analytic Existence and Uniqueness Results for PDE-Based Image Reconstruction with the Laplacian
260 _ _ |a Cham
|c 2017
|b Springer International Publishing
295 1 0 |a Scale 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
300 _ _ |a 66 - 79
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490 0 _ |a Lecture Notes in Computer Science
|v 10302
520 _ _ |a Partial 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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700 1 _ |a Harris, Isaac
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700 1 _ |a Breuß, Michael
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700 1 _ |a Kleefeld, Andreas
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773 _ _ |a 10.1007/978-3-319-58771-4_6
909 C O |o oai:juser.fz-juelich.de:830149
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914 1 _ |y 2017
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