Symmetric Upwind Scheme for Discrete Weighted Total Variation

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 in [1] and in a non-local setting for graphs and point-clouds in [2]. We focus on two new symmetric formulations based on the $\ell^{2}$ and $\ell^{\infty}$ 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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