Iterative TV minimization on the graph

• Verfasst von: Niyobuhungiro, Japhet [VerfasserIn]
• Verfasst von: Setterqvist, Eric [VerfasserIn]
• Verfasst von: Åström, Freddie [VerfasserIn]
• Titel: Iterative TV minimization on the graph
• Verf.angabe: Japhet Niyobuhungiro, Eric Setterqvist, Freddie Astroem, George Baravdish
• Jahr: 2019
• Umfang: 28 S.
• Fussnoten: Gesehen am 10.12.2019
• Titel Quelle: Enthalten in: Communications in mathematical sciences
• Ort Quelle: Somerville, Mass. : International Press, 2003
• Jahr Quelle: 2019
• Band/Heft Quelle: 17(2019), 4, Seite 941-968
• ISSN Quelle: 1539-6746
• DOI: doi:10.4310/CMS.2019.v17.n4.a4
• Datenträger: Online-Ressource
• Sprache: eng
• Sach-SW: algorithms
• Sach-SW: bm3d
• Sach-SW: constrained total variation
• Sach-SW: image decomposition
• Sach-SW: Primal-dual
• Sach-SW: ROF model on the graph
• Sach-SW: Split Bregman
• Sach-SW: texture
• Sach-SW: Total variation
• K10plus-PPN: 1684900093

Abstract

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.