TY  - CHAP
AU  - Hoeltgen, Laurent
AU  - Harris, Isaac
AU  - Breuß, Michael
AU  - Kleefeld, Andreas
TI  - Analytic Existence and Uniqueness Results for PDE-Based Image Reconstruction with the Laplacian
VL  - 10302
CY  - Cham
PB  - Springer International Publishing
M1  - FZJ-2017-03726
SN  - 978-3-319-58770-7 (print)
T2  - Lecture Notes in Computer Science
SP  - 66 - 79
PY  - 2017
AB  - 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.
T2  - 6th International Conference on Scale Space and Variational Methods in Computer Vision
CY  - 4 Jun 2017 - 8 Jun 2017, Kolding (Dänemark)
Y2  - 4 Jun 2017 - 8 Jun 2017
M2  - Kolding, Dänemark
LB  - PUB:(DE-HGF)8 ; PUB:(DE-HGF)7
UR  - <Go to ISI:>//WOS:000432210900006
DO  - DOI:10.1007/978-3-319-58771-4_6
UR  - https://juser.fz-juelich.de/record/830149
ER  -