Recovering sparse measures from their low frequencies.
Variational approaches to denoising, structure-texture decomposition,... .
Using self-similarities in images to perform restoration.
Towards Off-the-grid Algorithms for Total Variation Regularized Inverse Problems
Yohann De Castro, Vincent Duval, Romain Petit. Journal of Mathematical Imaging and Vision, 2022
An Epigraphical Approach to the Representer Theorem
Vincent Duval. Journal of Convex Analysis, 28 (3), 2021
Sparse analysis for mesoscale convective systems tracking
Jean-Baptiste Courbot, Vincent Duval, Bernard Legras. Signal Processing: Image Communication, 85, 2020
The Sliding Frank-Wolfe Algorithm and its Application to Super-Resolution Microscopy
Q. Denoyelle, V. Duval, G. Peyré, E. Soubies. Inverse Problems, 36 (1), 2019
On Representer Theorems and Convex Regularization
C. Boyer, A. Chambolle, Y. De Castro, V. Duval, F. de Gournay, P. Weiss. SIAM J. on Optimization, 29 (2), 2019
A Characterization of the Non-Degenerate Source Condition in Super-Resolution
Vincent Duval. Information and Inference: A Journal of the IMA, 9 (1), 2019
A Low-Rank Approach to Off-The-Grid Sparse Deconvolution
Paul Catala, Vincent Duval, Gabriel Peyré. SIAM Journal on Imaging Sciences, 12 (3), 2019
Minimal convex extensions and finite difference discretization of the quadratic Monge-Kantorovich problem
Jean-David Benamou, Vincent Duval. European Journal of Applied Mathematics, 30 (6), 2019
Sampling the Fourier transform along radial lines
Charles Dossal, Vincent Duval, Clarice Poon. SIAM J. on Numerical Analysis, 55 (6), 2017
Sparse Spikes Super-resolution on Thin grids II: the Continuous Basis-Pursuit
Vincent Duval, Gabriel Peyré. Inverse Problems, 33 (9), 2017
Sparse Spikes Super-resolution on Thin grids I: the LASSO
Vincent Duval, Gabriel Peyré. Inverse Problems, 33 (5), 2017
Convergence of Entropic Schemes for Optimal Transport and Gradient Flows
Guillaume Carlier, Vincent Duval, Gabriel Peyré, Bernhard Schmitzer. SIAM Journal on Mathematical Analysis, 49 (2), 2017
Geometric properties of solutions to the total variation denoising problem
Antonin Chambolle, Vincent Duval, Gabriel Peyré, Clarice Poon. Inverse Problems, 33 (1), 2016
Support Recovery for Sparse Super-Resolution of Positive Measures
Quentin Denoyelle, Vincent Duval, Gabriel Peyré. J. of Fourier Analysis and Applications, 2016, DOI 10.1007/s00041-016-9502-x
A Gamma-Convergence Result for the Upper Bound Limit Analysis of Plates
Jérémy Bleyer, Guillaume Carlier, Vincent Duval, Jean-Marie Mirebeau, Gabriel Peyré. ESAIM: Mathematical Modelling and Numerical Analysis, 50 (1) January 2016
The original manuscript publication is available at www.esaim-m2an.org
Exact Support Recovery for Sparse Spikes Deconvolution
Vincent Duval, Gabriel Peyré. J. of Foundations of Computational Mathematics, DOI 10.1007/s10208-014-9228-6, pp. 1-41, 2014
Non-local Methods with Shape-Adaptive Patches (NLM-SAP)
Charles-Alban Deledalle, Vincent Duval, Joseph Salmon. J. Math. Imaging Vis., 43 (2), pp. 103-120, 2012
A bias-varance approach for the non-local means
Vincent Duval, Jean-François Aujol, Yann Gousseau. SIAM Journal on Imaging Sciences, 4 (2), pp. 760-788, 2011
Mathematical Modeling of Textures: Application to Color Image Decomposition with a Projected Gradient Algorithm
Vincent Duval, Jean-François Aujol, Luminita Vese. J. Math. Imaging Vis., 37 (3), pp. 232-248, 2010
The TVL1 model: a Geometric Point of View
Vincent Duval, Jean-François Aujol, Yann Gousseau. SIAM Journal on Multiscale Model. Simul., 8 (1), pp. 154-189, 2009
Déconvolution Parcimonieuse sans Grille: une Méthode de Faible Rang
Paul Catala, Vincent Duval, Gabriel Peyré ORASIS, 2017
Sparse Super-resolution from Laplace Measurements
Quentin Denoyelle, Vincent Duval, Gabriel Peyré SPARS, 2017
A Low-Rank Approach to Off-The-Grid Sparse Deconvolution
Paul Catala, Vincent Duval, Gabriel Peyré SPARS, 2017
The Non Degenerate Source Condition: Support Robustness for Discrete and Continuous Sparse Deconvolution
Vincent Duval, Gabriel Peyré IEEE CAMSAP, 2015
Asymptotic of Sparse Support Recovery for Positive Measures
Quentin Denoyelle, Vincent Duval, Gabriel Peyré Journal of Physics: Conference Series, 2015, Volume 657, conference 1
Discrete vs. continuous sparse regularization
Vincent Duval, Gabriel Peyré Proceedings of iTWIST'14
Low noise regimes for l1 regularization : continuous and discrete settings
Vincent Duval, Gabriel Peyré PAMM 14 (1), pp. 943-944, 2014
Anisotropic Non-Local Means with Spatially Adaptive Shapes
Charles-Alban Deledalle, Vincent Duval, Joseph Salmon Scale Space and Variational Methods in Computer Vision, 2011, Springer
Projected Gradient based Color Image Decomposition
Vincent Duval, Jean-François Aujol, Luminita Vese Scale Space and Variational Methods in Computer Vision, 2009, Springer
(Habilitation thesis) Faces and extreme points of convex sets for the resolution of inverse problems
Vincent Duval
A comparative analysis of the TVL1 and the TV-G models
Vincent Duval
HAL preprint, December 2013. This report was written to apply to the Vincent Caselles Student Award.
(PhD thesis) Variational and non-local methods in image processing: a geometric study
Vincent Duval
Advisors: Yann Gousseau, Jean-François Aujol
