Towards Off-the-grid Algorithms for Total Variation Regularized Inverse Problems

Yohann de Castro (1, 2) , Vincent Duval (3, 4) , Romain Petit (4, 3)

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

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

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. 2022. ⟨hal-03406710v2⟩