While the sparse spikes recovery problem in the continuous setting has drawn a lot of attention in recent years, a major challenge is to extend the "continuous domain" solvers to the recovery of more compex images, e.g. made of curves or simple geometric shapes.
The team consists of
Vincent Duval (PI),
Below is an example for cartoon image reconstruction using the total gradient variation.
Towards Off-the-grid Algorithms for Total Variation Regularized Inverse Problems.
Romain Petit, Yohann De Castro, Vincent Duval. Proceedings of the Scale Space and Variational Methods (SSVM) 2021 conference
An Epigraphical Approach to the Representer Theorem
Vincent Duval. Journal of Convex Analysis, 28 (3), 2021