104 citations · 265 across the 17 of their papers we have counts for
21 papers
A variational method for curve extraction with curvature-dependent energies
Majid Arthaud, Antonin Chambolle, Vincent Duval
We introduce a variational approach for extracting curves between a list of possible endpoints, based on the discretization of an energy and Smirnov's decomposition theorem for vec…
The Total Variation-Wasserstein Problem
Antonin Chambolle, Vincent Duval, Joao Miguel Machado
In this work we analyze the Total Variation-Wasserstein minimization problem. We propose an alternative form of deriving optimality conditions from the approach of Calier\&Poon'18,…
Exact recovery of the support of piecewise constant images via total variation regularization
Yohann De Castro, Vincent Duval, Romain Petit
This work is concerned with the recovery of piecewise constant images from noisy linear measurements. We study the noise robustness of a variational reconstruction method, which is…
One-dimensional approximation of measures in Wasserstein distances
Antonin Chambolle, Vincent Duval, Joao Miguel Machado
We propose a variational approach to approximate measures with measures uniformly distributed over a 1 dimentional set. The problem consists in minimizing a Wasserstein distance as…
Dynamical Programming for off-the-grid dynamic Inverse Problems
Vincent Duval, Robert Tovey
In this work we consider algorithms for reconstructing time-varying data into a finite sum of discrete trajectories, alternatively, an off-the-grid sparse-spikes decomposition whic…
Towards Off-the-grid Algorithms for Total Variation Regularized Inverse Problems
Yohann de Castro, Vincent Duval, Romain Petit
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…