Research Internship in optimization, machine learning, and inverse problems

Assignment
Assignments:
Under the supervision of Nelly Pustelnik, Elisa Riccietti and Ségolène Martin the recruited intern will develop and study multilevel plug-and-play algorithms based on flow matching for large-scale image restoration. The work will involve algorithm design, numerical experiments, and the investigation of convergence properties. For more details see the descriptions
here
.
For a better knowledge of the proposed research subject:
The following publications provide background on the proposed research topic:
N. Laurent, J. Tachella, E. Riccietti, and N. Pustelnik.
Multilevel Plug-and-Play Image Restoration
. IEEE Transactions on Computational Imaging, 12, 445–456, 2026.
S. Martin, A. Gagneux, P. Hagemann, and G. Steidl.
PnP-Flow: Plug-and-Play Image Restoration with Flow Matching
. International Conference on Learning Representations, 2025.
G. Lauga, E. Riccietti, N. Pustelnik, and P. Gonçalves.
IML FISTA: A Multilevel Framework for Inexact and Inertial Forward-Backward. Application to Image Restoration
. SIAM Journal on Imaging Sciences, 17(3), 1347–1376, 2024.
Collaboration:
The intern will work closely with the supervisors and interact with researchers in optimization, inverse problems, and generative modeling at ENS de Lyon.
Responsibilities:
The intern will be responsible for implementing and evaluating the proposed algorithms, analyzing numerical results, and contributing to the theoretical study. They will be encouraged to take initiatives in exploring algorithmic improvements.
Steering/Management:
The intern will organize and report on their research progress through regular meetings with the supervisors. No management responsibilities are expected.
Main activities
Main activities (5 maximum):
Review the literature on plug-and-play methods, flow matching, and multilevel optimization algorithms.
Develop and implement multilevel plug-and-play algorithms incorporating flow-matching-based denoisers, and study it numerically.
Conduct numerical experiments on image restoration tasks and compare the proposed methods with existing approaches.
Skills
Technical skills and level required:
Strong background in applied mathematics, optimization, and machine learning. Good Python programming skills (PyTorch). Knowledge of inverse problems is appreciated.
Languages:
English or French
Relational skills:
Autonomy, scientific curiosity, teamwork, and analytical thinking.
Other valued skills:
Interest in generative models, numerical experiments, and theoretical analysis.