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ROF model on the graph
Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, The Institute of Technology. Department of Mathematics, School of pure and applied sciences, College of Science and Technology, University of Rwanda, P.O. Box 117 Butare, Rwanda.ORCID iD: 0000-0002-8188-7672
Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, The Institute of Technology.
2014 (English)Report (Other academic)
Abstract [en]

In this paper we consider an analogue of the well-known in image processing, Rudin-Osher-Fatemi (ROF) denoising model on a general finite directed and connected graph. We consider the space BV on the graph and show that the unit ball of its dual space can be described as the image of the unit ball of the space ℓinfinity on the graph by a divergence operator. Based on this result, we propose a new fast algorithm to find the exact minimizer for the ROF model. Finally we prove convergence of the algorithm and illustrate its performance on some image denoising test examples.

Place, publisher, year, edition, pages
Linköping University Electronic Press, 2014. , 25 p.
Series
LiTH-MAT-R, ISSN 0348-2960 ; 2014:06
Keyword [en]
ROF model, Directed graph, L–functional, Image processing, Dual BV, Regularization.
National Category
Mathematics
Identifiers
URN: urn:nbn:se:liu:diva-106920ISRN: LiTH-MAT-R--2014/06--SEOAI: oai:DiVA.org:liu-106920DiVA: diva2:719719
Available from: 2014-05-26 Created: 2014-05-26 Last updated: 2014-05-27

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ROF model on the graph(3755 kB)203 downloads
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Niyobuhungiro, JaphetSetterqvist, Eric

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CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • harvard1
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • oxford
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf