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

• Vincent Duval (PI),

• Yohann De Castro,

• Emmanuel Soubies,

• Jean-Baptiste Courbot

• Romain Petit (PhD student)

• Robert Tovey (postdoc)

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

Publications

1. 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

2. An Epigraphical Approach to the Representer Theorem

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

Preprints

• "FISTA" in Banach spaces with adaptive discretisations

  Antonin Chambolle, Robert Tovey HAL preprint

• Towards off-the-grid algorithms for total variation regularized inverse problems (long version)

  Romain Petit, Yohann De Castro, Vincent Duval. HAL preprint

Software and reproducible research

• The Sliding Frank-Wolfe for TV regularization (Python code)