Contribution to a conference proceedings/Contribution to a book

FZJ-2017-03726

http://join2-wiki.gsi.de/foswiki/pub/Main/Artwork/join2_logo100x88.png Analytic Existence and Uniqueness Results for PDE-Based Image Reconstruction with the Laplacian

Hoeltgen, L. (Corresponding author) ; Harris, I. ; Breuß, M. ; Kleefeld, A.FZJ*

2017
Springer International Publishing Cham
ISBN: 978-3-319-58770-7 (print), 978-3-319-58771-4 (electronic)

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Please use a persistent id in citations: doi:10.1007/978-3-319-58771-4_6

Abstract: 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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Contributing Institute(s):

1. Jülich Supercomputing Center (JSC)

Research Program(s):

1. 511 - Computational Science and Mathematical Methods (POF3-511) (POF3-511)

Appears in the scientific report 2017

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Database coverage:
Nationallizenz ; SCOPUS

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