SYMMETRIC UPWIND SCHEME FOR DISCRETE WEIGHTED TOTAL VARIATION

Sonia Tabti 1 Julien Rabin 1 Abderrahim Elmoataz 1
1 Equipe Image - Laboratoire GREYC - UMR6072
GREYC - Groupe de Recherche en Informatique, Image, Automatique et Instrumentation de Caen
Abstract : This paper is devoted to the study of the discrete formulations of the weighted Total Variation (TV) based on upwind schemes that have been proposed for imaging problems in a local setting by Chambolle and al. in 2011 and in a non-local setting for graphs and point-clouds by Elmoataz et al. in 2008. We focus on two new symmetric formulations based on the euclidean and infinite norms respectively and propose a dedicated optimization algorithm to solve convex problems based on such TV penalties. We demonstrate the theoretical and practical interest of such formulations for image processing tasks.
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Sonia Tabti, Julien Rabin, Abderrahim Elmoataz. SYMMETRIC UPWIND SCHEME FOR DISCRETE WEIGHTED TOTAL VARIATION. 2018 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), Apr 2018, calgary, Canada. ⟨10.1109/ICASSP.2018.8461736⟩. ⟨hal-01629413⟩

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