Crouzeix-Raviart approximation of the total variation on simplicial meshes

Antonin Chambolle (1) , Thomas Pock (2)

1 CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique
2 ICG - Institute for Computer Graphics and Vision [Graz]

We propose an adaptive implementation of a Crouzeix-Raviart based discretization of the total variation, which has the property of approximating from below the total variation, with metrication errors only depending on the local curvature, rather than on the orientation as is usual for other approaches.

Mots clés: Image processing; nonconforming P1 finite elements (Crouzeix-Raviart); total variation; nonconforming P1 (Crouzeix-Raviart) finite elements

Domaines: Analyse numérique [math.NA]

Antonin Chambolle, Thomas Pock. Crouzeix-Raviart approximation of the total variation on simplicial meshes. Journal of Mathematical Imaging and Vision, 2020, 62 (6-7), pp.872--899. ⟨10.1007/s10851-019-00939-3⟩. ⟨hal-01787012v3⟩