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ITERATIVE TV MINIMIZATION ON THE GRAPH
Univ Rwanda, Rwanda.
Univ Vienna, Austria.
Heidelberg Univ, Germany.
Linköping University, Department of Science and Technology, Physics, Electronics and Mathematics. Linköping University, Faculty of Science & Engineering.
2019 (English)In: Communications in Mathematical Sciences, ISSN 1539-6746, E-ISSN 1945-0796, Vol. 17, no 4, p. 941-968Article in journal (Refereed) Published
Abstract [en]

We define the space of functions of bounded variation (BV) on the graph. Using the notion of divergence of flows on graphs, we show that the unit ball of the dual space to BV in the graph setting can be described as the image of the unit ball of the space l(infinity) by the divergence operator. Based on this result, we propose a new iterative algorithm to find the exact minimizer for the total variation (TV) denoising problem on the graph. The proposed algorithm is provable convergent and its performance on image denoising examples is compared with the Split Bregman and Primal-Dual algorithms as benchmarks for iterative methods and with BM3D as a benchmark for other state-of-the-art denoising methods. The experimental results show highly competitive empirical convergence rate and visual quality for the proposed algorithm.

Place, publisher, year, edition, pages
INT PRESS BOSTON, INC , 2019. Vol. 17, no 4, p. 941-968
Keywords [en]
Total variation; ROF model on the graph; Split Bregman; Primal-dual; BM3D
National Category
Computational Mathematics
Identifiers
URN: urn:nbn:se:liu:diva-162089DOI: 10.4310/CMS.2019.v17.n4.a4ISI: 000493314300004OAI: oai:DiVA.org:liu-162089DiVA, id: diva2:1371318
Note

Funding Agencies|The World Academy of Sciences (TWAS), RGA [17 RG/MATHS/AF/AC_I-FR3240297744]; Austrian Science Fund (FWF)Austrian Science Fund (FWF) [S117]

Available from: 2019-11-19 Created: 2019-11-19 Last updated: 2019-11-19

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CiteExportLink to record
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Citation style
  • apa
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Language
  • de-DE
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Output format
  • html
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