Analytic Existence and Uniqueness Results for PDE-Based Image Reconstruction with the Laplacian
- 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.
Author: | Laurent HoeltgenORCiD, I. Harris, Michael BreußGND, Andreas Kleefeld |
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DOI: | https://doi.org/10.1007/978-3-319-58771-4_6 |
ISBN: | 978-3-319-58770-7 |
Title of the source (English): | Scale Space and Variational Methods in Computer Vision, 6th International Conference on Scale Space and Variational Methods in Computer Vision (SSVM 2017, Kolding, Denmark, June 2017), proceedings |
Publisher: | Springer International Publishing |
Place of publication: | Cham |
Document Type: | Conference Proceeding |
Language: | English |
Year of publication: | 2017 |
Tag: | Partial differential equations Laplace equation Mixed boundary conditions Image reconstruction Image inpainting |
First Page: | 66 |
Last Page: | 79 |
Series ; volume number: | Lecture notes in computer science ; 10302 |
Faculty/Chair: | Fakultät 1 MINT - Mathematik, Informatik, Physik, Elektro- und Informationstechnik / FG Angewandte Mathematik |