Learning Consistent Discretizations of the Total Variation
Chambolle, Antonin; Pock, Thomas (2021), Learning Consistent Discretizations of the Total Variation, SIAM Journal on Imaging Sciences, 14, 2, p. 778-813. 10.1137/20M1377199
TypeArticle accepté pour publication ou publié
Journal nameSIAM Journal on Imaging Sciences
SIAM - Society for Industrial and Applied Mathematics
MetadataShow full item record
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Institute for Computer Graphics and Vision [Graz] [ICG]
Abstract (EN)In this work, we study a general framework of discrete approximations of the total variation for image reconstruction problems. The framework, for which we can show consistency in the sense of Γ-convergence, unifies and extends several existing discretization schemes. In addition, we propose algorithms for learning discretizations of the total variation in order to achieve the best possible reconstruction quality for particular image reconstruction tasks. Interestingly, the learned discretizations significantly differ between the tasks, illustrating that there is no universal best discretization of the total variation.
Subjects / Keywordstotal variation; image denoising; image inpainting; discretization; finite differences; finite elements; learning; bilevel optimization; primal-dual algorithms
Showing items related by title and author.
Convergence of a Piggyback-style method for the differentiation of solutions of standard saddle-point problems Bogensperger, Lea; Chambolle, Antonin; Pock, Thomas (2022) Document de travail / Working paper
Evolution of characteristic functions of convex sets in the plane by the minimizing total variation flow Alter, François; Caselles, Vincent; Chambolle, Antonin (2005) Article accepté pour publication ou publié