Overlapping domain decomposition methods for total variation denoising
(2019) In SIAM Journal on Numerical Analysis 57(3). p.1411-1444- Abstract
Alternating and parallel overlapping domain decomposition methods for the minimization of the total variation are presented. Their derivation is based on the predual formulation of the total variation minimization problem. In particular, the predual total variation minimization problem is decomposed into overlapping domains yielding subdomain problems in the respective dual space. Subsequently these subdomain problems are again dualized, forming a splitting algorithm for the original total variation minimization problem. The convergence of the proposed domain decomposition methods to a solution of the global problem is proved. In contrast to other works, the analysis is carried out in an infinite dimensional setting. Numerical... (More)
Alternating and parallel overlapping domain decomposition methods for the minimization of the total variation are presented. Their derivation is based on the predual formulation of the total variation minimization problem. In particular, the predual total variation minimization problem is decomposed into overlapping domains yielding subdomain problems in the respective dual space. Subsequently these subdomain problems are again dualized, forming a splitting algorithm for the original total variation minimization problem. The convergence of the proposed domain decomposition methods to a solution of the global problem is proved. In contrast to other works, the analysis is carried out in an infinite dimensional setting. Numerical experiments are shown to support the theoretical results and to demonstrate the effectiveness of the algorithms.
(Less)
- author
- Langer, Andreas LU and Gaspoz, Fernando
- publishing date
- 2019
- type
- Contribution to journal
- publication status
- published
- subject
- keywords
- Convergence analysis, Convex optimization, Domain decomposition, Image restoration, Locally weighted total variation, Subspace correction, Total variation minimization
- in
- SIAM Journal on Numerical Analysis
- volume
- 57
- issue
- 3
- pages
- 34 pages
- publisher
- Society for Industrial and Applied Mathematics
- external identifiers
-
- scopus:85069938941
- ISSN
- 0036-1429
- DOI
- 10.1137/18M1173782
- language
- English
- LU publication?
- no
- additional info
- Funding Information: \ast Received by the editors March 5, 2018; accepted for publication (in revised form) March 21, 2019; published electronically June 25, 2019. http://www.siam.org/journals/sinum/57-3/M117378.html Funding: The work of the authors was partially supported by the Ministerium fur Wissenschaft, Forschung und Kunst Baden-Wurttemberg (Az: 7533.-30-10/56/1) through the RISC-project ``Au-tomatische Erkennung von bewegten Objekten in hochauflosenden Bildsequenzen mittels neuer Ge-bietszerlegungsverfahren."" \dagger Institute for Applied Analysis and Numerical Simulation, University of Stuttgart, Pfaffenwaldring 57, 70569 Stuttgart, Germany (andreas.langer@mathematik.uni-stuttgart.de). \ddagger Fakult\a"t fu\"r Mathematik, Technische Universit\a"t Dortmund, Vogelpothsweg 87, 44227 Dortmund, Germany (Fernando.Gaspoz@math.tu-dortmund.de). Publisher Copyright: Copyright © by SIAM. Copyright: Copyright 2019 Elsevier B.V., All rights reserved.
- id
- 88c9003e-2194-43e1-bcd4-1e03ac46503d
- date added to LUP
- 2021-03-15 22:25:18
- date last changed
- 2022-04-27 00:48:36
@article{88c9003e-2194-43e1-bcd4-1e03ac46503d,
abstract = {{<p>Alternating and parallel overlapping domain decomposition methods for the minimization of the total variation are presented. Their derivation is based on the predual formulation of the total variation minimization problem. In particular, the predual total variation minimization problem is decomposed into overlapping domains yielding subdomain problems in the respective dual space. Subsequently these subdomain problems are again dualized, forming a splitting algorithm for the original total variation minimization problem. The convergence of the proposed domain decomposition methods to a solution of the global problem is proved. In contrast to other works, the analysis is carried out in an infinite dimensional setting. Numerical experiments are shown to support the theoretical results and to demonstrate the effectiveness of the algorithms.</p>}},
author = {{Langer, Andreas and Gaspoz, Fernando}},
issn = {{0036-1429}},
keywords = {{Convergence analysis; Convex optimization; Domain decomposition; Image restoration; Locally weighted total variation; Subspace correction; Total variation minimization}},
language = {{eng}},
number = {{3}},
pages = {{1411--1444}},
publisher = {{Society for Industrial and Applied Mathematics}},
series = {{SIAM Journal on Numerical Analysis}},
title = {{Overlapping domain decomposition methods for total variation denoising}},
url = {{http://dx.doi.org/10.1137/18M1173782}},
doi = {{10.1137/18M1173782}},
volume = {{57}},
year = {{2019}},
}