ANR CIPRESSI - Continuous Image Processing: models and algorithms

The CIPRESSI Project (ANR-19-CE48-0017-01) is an ANR JCJC project. It aims at developing innovative discretisation methods for optimisation problems which arise in inverse problems. While many problems in signal or image processing can be formulated in a continuous domain, most resolution methods introduce a grid for the computations, which tends to induces visual artifacts (such as blur and anisotropy) and a high computational burden. Our goal with CIPRESSI is to design models and algorithms which are as close as possible to the original continuous problem.

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

Below is an example for cartoon image reconstruction using the total gradient variation.

The Sliding Frank-Wolfe for total (gradient) regularization


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

  2. Romain Petit, Yohann De Castro, Vincent Duval. Proceedings of the Scale Space and Variational Methods (SSVM) 2021 conference

  3. An Epigraphical Approach to the Representer Theorem

    Vincent Duval. Journal of Convex Analysis, 28 (3), 2021


Software and reproducible research