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@INBOOK{Hoeltgen:830149,
      author       = {Hoeltgen, Laurent and Harris, Isaac and Breuß, Michael and
                      Kleefeld, Andreas},
      title        = {{A}nalytic {E}xistence and {U}niqueness {R}esults for
                      {PDE}-{B}ased {I}mage {R}econstruction with the {L}aplacian},
      volume       = {10302},
      address      = {Cham},
      publisher    = {Springer International Publishing},
      reportid     = {FZJ-2017-03726},
      isbn         = {978-3-319-58770-7 (print)},
      series       = {Lecture Notes in Computer Science},
      pages        = {66 - 79},
      year         = {2017},
      comment      = {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},
      booktitle     = {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},
      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.},
      month         = {Jun},
      date          = {2017-06-04},
      organization  = {6th International Conference on Scale
                       Space and Variational Methods in
                       Computer Vision, Kolding (Dänemark), 4
                       Jun 2017 - 8 Jun 2017},
      cin          = {JSC},
      ddc          = {004},
      cid          = {I:(DE-Juel1)JSC-20090406},
      pnm          = {511 - Computational Science and Mathematical Methods
                      (POF3-511)},
      pid          = {G:(DE-HGF)POF3-511},
      typ          = {PUB:(DE-HGF)8 / PUB:(DE-HGF)7},
      UT           = {WOS:000432210900006},
      doi          = {10.1007/978-3-319-58771-4_6},
      url          = {https://juser.fz-juelich.de/record/830149},
}