A convergent overlapping domain decomposition method for total variation minimization
(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.
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/aed47741-5770-480e-8463-980ccd38ad42
- author
- Fornasier, Massimo ; Langer, Andreas LU and Schönlieb, Carola Bibiane
- publishing date
- 2010
- 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}}, }