Towards off-the-grid algorithms for total variation regularized inverse problems

Yohann de Castro (1) , Vincent Duval (2, 3) , Romain Petit (2, 3)

1 ICJ - Institut Camille Jordan
2 CEREMADE - CEntre de REcherches en MAthématiques de la DEcision
3 MOKAPLAN - Méthodes numériques pour le problème de Monge-Kantorovich et Applications en sciences sociales

We introduce an algorithm to solve linear inverse problems regularized with the total (gradient) variation in a gridless manner. Contrary to most existing methods, that produce an approximate solution which is piecewise constant on a fixed mesh, our approach exploits the structure of the solutions and consists in iteratively constructing a linear combination of indicator functions of simple polygons.

Mots clés: Off-the-grid imaging; Inverse problems; Total variation

Domaines: Analyse numérique [math.NA]; Optimisation et contrôle [math.OC]; Traitement du signal et de l'image [eess.SP]

Yohann de Castro, Vincent Duval, Romain Petit. Towards off-the-grid algorithms for total variation regularized inverse problems. 8th International Conference on Scale Space and Variational Methods in Computer Vision (SSVM 2021), May 2021, Online event, France. pp.553-564, ⟨10.1007/978-3-030-75549-2_44⟩. ⟨hal-03196916v1⟩