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A convergent overlapping domain decomposition method for total variation minimization

Fornasier, Massimo ; Langer, Andreas LU and Schönlieb, Carola Bibiane (2010) In Numerische Mathematik 116(4). p.645-685
Abstract

In this paper we are concerned with the analysis of convergent sequential and parallel overlapping domain decomposition methods for the minimization of functionals formed by a discrepancy term with respect to the data and a total variation constraint. To our knowledge, this is the first successful attempt of addressing such a strategy for the nonlinear, nonadditive, and nonsmooth problem of total variation minimization. We provide several numerical experiments, showing the successful application of the algorithm for the restoration of 1D signals and 2D images in interpolation/inpainting problems, respectively, and in a compressed sensing problem, for recovering piecewise constant medical-type images from partial Fourier ensembles.

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author
; and
publishing date
type
Contribution to journal
publication status
published
subject
in
Numerische Mathematik
volume
116
issue
4
pages
41 pages
publisher
Springer
external identifiers
  • scopus:77957164123
ISSN
0029-599X
DOI
10.1007/s00211-010-0314-7
language
English
LU publication?
no
additional info
Copyright: Copyright 2010 Elsevier B.V., All rights reserved.
id
aed47741-5770-480e-8463-980ccd38ad42
date added to LUP
2021-03-15 22:37:08
date last changed
2022-04-27 01:09:37
@article{aed47741-5770-480e-8463-980ccd38ad42,
  abstract     = {{<p>In this paper we are concerned with the analysis of convergent sequential and parallel overlapping domain decomposition methods for the minimization of functionals formed by a discrepancy term with respect to the data and a total variation constraint. To our knowledge, this is the first successful attempt of addressing such a strategy for the nonlinear, nonadditive, and nonsmooth problem of total variation minimization. We provide several numerical experiments, showing the successful application of the algorithm for the restoration of 1D signals and 2D images in interpolation/inpainting problems, respectively, and in a compressed sensing problem, for recovering piecewise constant medical-type images from partial Fourier ensembles.</p>}},
  author       = {{Fornasier, Massimo and Langer, Andreas and Schönlieb, Carola Bibiane}},
  issn         = {{0029-599X}},
  language     = {{eng}},
  number       = {{4}},
  pages        = {{645--685}},
  publisher    = {{Springer}},
  series       = {{Numerische Mathematik}},
  title        = {{A convergent overlapping domain decomposition method for total variation minimization}},
  url          = {{http://dx.doi.org/10.1007/s00211-010-0314-7}},
  doi          = {{10.1007/s00211-010-0314-7}},
  volume       = {{116}},
  year         = {{2010}},
}