Key-words : Model-based neural networks, image reconstruction, uncertainty quantification,
Markov Chain Monte Carlo, variational Bayesian methods, proximal algorithms.
Localisation : Laboratoire de Physique de l’ENS Lyon
46 allée d’Italie, 69007 Lyon
Supervisors : Nelly Pustelnik, DR CNRS, ENS Lyon (nelly.pustelnik@ens-lyon.fr)
Barbara Pascal, CR CNRS, Encole Centrale Nantes (barbara.pascal@cnrs.fr)
Laurent Jacques, Prof. UCL et ENS Lyon (laurent.jacques@uclouvain.be)
Context: Image restoration techniques have significantly evolved over the past 10 years with the
rise of neural networks. The proposed topic concerns the so-called model-based neural network
approaches, which are now at the core of most current developments, as they allow for the
combination of theoretical foundations from traditional variational methods with the expressivity
of neural networks.
The two most studied strategies are unfolded neural networks, which aim at mimicking proxi-
mal algorithm iterations to design end-to-end task-specific neural networks, and Plug-and-Play
(PnP), which exploit pretrained denoisers to tackle reconstruction tasks without the need of
further training. While both approaches produce a restored image, they often overlook the quan-
tification of uncertainties on the reconstructed image, which is an essential aspect for assessing
the reliability of the reconstruction.
Quantifying uncertainty is a long-standing subject of research that has been addressed through
a wide variety of methods, ranging from Metropolis Adjusted Langevin Algorithms, Hamiltonian
Monte Carlo, or belief and expectation propagation, to name just a few [1]. While this pro-
blem has been extensively studied in the context of standard variational formulations, leveraging
their Bayesian interpretation, it remains largely underexplored in model-based neural network
approaches (see a contrario [2]).
Subject : During this internship, we aim to revisit standard uncertainty quantification pro-
cedures from the perspective of model-based neural networks. Our approach will focus on two
main directions : first, addressing spatial correlations to reduce the overestimation of uncertainty
regions [3], and second, exploring the potential of multiscale techniques to improve or accelerate
uncertainty estimation. The objective is to investigate both the theoretical aspects and their
practical implementation within the Python library DeepInverse [4].
The developed method will be applied to the spatio-temporal analysis of river dynamics, which
is a key factor in studying and understanding human impacts on floodplains. More specifically,
the objective will be to increase the resolution of Landsat-8/9 images (30m) to the resolution of
Sentinel-2 images (10m) for a detailed analysis of the dynamics (see Figure 1), using the database
and preliminary results developed in [5].
Expected Results
— Develop and compare uncertainty quantification procedures.
— Software prototype in Pytorch.
— Demonstration on an already available satellite image dataset.
Required Skills
— Data science, optimization, image processing, signal processing, neural networks.
— Python, PyTorch, Git.
Références
[1] M. Pereyra, P. Schniter, E. Chouzenoux, J.-C. Pesquet, J.-Y. Tourneret, A.O. Hero, and
S. McLaughlin, A survey of stochastic simulation and optimization methods in signal proces-
sing, IEEE Trans. on Geoscience and Remote Sensing, 61, 2003.
[2] J. Tachella and M. Pereyra, Equivariant bootstrapping for uncertainty quantification in ima-
ging inverse problems, Proc. of Machine Learning Research, 2023.
[3] O. Belhasin, Y. Romano, D. Freedman, E. Rivlin, and M. Elad, Principal uncertainty quan-
tification with spatial correlation for image restoration problems, IEEE Trans. Pattern Anal.
Mach. Intell., 46(5) : 3321–3333, 2023.
[4] Tachella, J., Terris, M., Hurault, S., Wang, A., Chen, D. et al., DeepInverse : A Python
package for solving imaging inverse problems with deep learning, submitted, 2025.
[5] Audisio, P., Belletti, B., and Pustelnik, N., Plug-and-play forward backward algorithm to
restore Landsat images : a preliminary step to uncover the history of surface waters. submitted,
2025.
