CEREMADE
Duval Vincent
INRIA Senior Researcher
Biography
Vincent Duval is an INRIA researcher in the MOKAPLAN team. After completing his engineering studies in applied mathematics at Ecole polytechnique and Télécom ParisTech, he obtained a PhD degree in 20011 at Télécom ParisTech for his thesis on denoising methods in imaging. Then, he worked for almost two years at the ANSSI as an engineer. In 2013, he joined Gabriel Peyré's team for a postdoc in CEREMADE. In 2014, he obtained a position as an INRIA researcher (détaché du corps des Mines) in the MOKAPLAN team. He obtained the "habilitation à diriger des recherches" in 2022. His research interests include variational problems in the space of measures, with applications in image processing or physics.
Publications
Articles
Duval V., Tovey R. (2024), Dynamical Programming for off-the-grid dynamic Inverse Problems, Control, Optimisation and Calculus of Variations, vol. 30, n°7 
De Castro Y., Duval V., Petit R. (2022), Towards Off-the-Grid Algorithms for Total Variation Regularized Inverse Problems, Journal of Mathematical Imaging and Vision, p. 25
Duval V. (2021), An Epigraphical Approach to the Representer Theorem, Journal of Convex Analysis, vol. 28, n°3, p. 819-836
Courbot J-B., Duval V., Legras B. (2020), Sparse analysis for mesoscale convective systems tracking, Signal Processing: Image Communication, vol. 85, p. 115854
Boyer C., Chambolle A., De Castro Y., Duval V., de Gournay F., Weiss P. (2019), On Representer Theorems and Convex Regularization, SIAM Journal on Optimization, vol. 29, n°2, p. 1260–1281
Denoyelle Q., Duval V., Peyré G., Soubies E. (2019), The Sliding Frank-Wolfe Algorithm and its Application to Super-Resolution Microscopy, Inverse Problems, vol. 36, n°1, p. 014001
Catala P., Duval V., Peyré G. (2019), A Low-Rank Approach to Off-the-Grid Sparse Superresolution, SIAM Journal on Imaging Sciences, vol. 12, n°3, p. 1464-1500
Duval V. (2019), A characterization of the Non-Degenerate Source Condition in super-resolution, Information and Inference, p. 1-31
Duval V., Benamou J-D. (2018), Minimal convex extensions and finite difference discretisation of the quadratic Monge–Kantorovich problem, European Journal of Applied Mathematics, p. 1-38
Dossal C., Duval V., Poon C. (2017), Sampling the Fourier transform along radial lines, SIAM Journal on Numerical Analysis, vol. 55, n°6, p. 2540-2564
Carlier G., Duval V., Peyré G., Schmitzer B. (2017), Convergence of Entropic Schemes for Optimal Transport and Gradient Flows, SIAM Journal on Mathematical Analysis, vol. 49, n°2, p. 1385-1418
Duval V., Peyré G. (2017), Sparse Spikes Super-resolution on Thin Grids II: the Continuous Basis Pursuit, Inverse Problems, vol. 33, n°9
Duval V., Peyré G. (2017), Sparse Regularization on Thin Grids I: the LASSO, Inverse Problems, vol. 33, n°5
Catala P., Duval V., Peyré G. (2017), A Low-Rank Approach to Off-The-Grid Sparse Deconvolution, Journal of Physics. Conference Series, vol. 904, n°conférence 1
Chambolle A., Duval V., Peyré G., Poon C. (2016), Geometric properties of solutions to the total variation denoising problem, Inverse Problems, vol. 33, n°1
Bleyer J., Carlier G., Duval V., Mirebeau J-M., Peyré G. (2016), A Γ-Convergence Result for the Upper Bound Limit Analysis of Plates, ESAIM: Mathematical Modelling and Numerical Analysis, vol. 50, n°1, p. 215-235
Denoyelle Q., Duval V., Peyré G. (2016), Support Recovery for Sparse Super-Resolution of Positive Measures, Journal of Fourier Analysis and Applications, vol. 23, n°5, p. 1153–1194
Duval V., Peyré G. (2015), Exact Support Recovery for Sparse Spikes Deconvolution, Foundations of Computational Mathematics, vol. 15, n°5, p. 1315-1355
Duval V., Peyré G. (2014), Low noise regimes for ℓ regularization : continuous and discrete settings, Proceedings in Applied Mathematics and Mechanics, vol. 14, n°1, p. 943–944
Communications avec actes
Chambolle A., Duval V., Machado J. (2023), The Total Variation-Wasserstein Problem, in Nielsen, F., Barbaresco, F. (eds), Berlin Heidelberg, Springer International Publishing, 610-619 p.
De Castro Y., Duval V., Petit R. (2021), Towards Off-the-grid Algorithms for Total Variation Regularized Inverse Problems, in Abderrahim Elmoataz, Jalal Fadili, Yvain Quéau, Julien Rabin, Loïc Simon, Scale Space and Variational Methods in Computer Vision, Proceedings of SSVM 2021, 553-564 p.
Denoyelle Q., Duval V., Peyré G., Soubies E. (2019), The Sliding Frank-Wolfe Algorithm for the BLASSO, in , Toulouse, Proceedings of the Workshop on Signal Processing with Adaptative Sparse Structured Representations -, 2 p.
Chambolle A., Duval V., Peyré G., Poon C. (2016), Total Variation Denoising and Support Localization of the Gradient, in , Cachan, Journal of Physics. Conference Series
Denoyelle Q., Duval V., Peyré G. (2015), Asymptotic of Sparse Support Recovery for Positive Measures, in , Journal of physics: Conference series
Duval V., Peyré G. (2015), The Non Degenerate Source Condition: Support Robustness for Discrete and Continuous Sparse Deconvolution, in , IEEE International Workshop on Computational Advances in Multi-Sensor Adaptive Processing, Dec 2015, Cancun, Mexico, Cancun, IEEE - Institute of Electrical and Electronics Engineers
Prépublications / Cahiers de recherche
Castro Y., Duval V., Petit R. (2023), Exact recovery of the support of piecewise constant images via total variation regularization, Paris, Cahier de recherche CEREMADE, Université Paris Dauphine-PSL, 43 p.
Chambolle A., Duval V., Machado J. (2023), 1D approximation of measures in Wasserstein spaces, Paris, Cahier de recherche CEREMADE, Université Paris Dauphine-PSL, 38 p.
Tovey R., Duval V. (2022), Dynamical Programming for off-the-grid dynamic Inverse Problems, Paris, Cahier de recherche CEREMADE, Université Paris Dauphine-PSL, 43 p.
Duval V., Peyré G. (2015), Sparse Spikes Deconvolution on Thin Grids, Paris, Université Paris-Dauphine, 56 p.
Rapports
Duval V. (2014), A comparative analysis of the TVL1 and the TV-G models, Université Paris-Dauphine, 26 p.