Séminaire Images Optimisation et Probabilités

Responsable : Luis Fredes et Camille Male

Le 25 avril 2024 à 11:00

Salle de conférénces

Maud Biquard ISAE-SUPAERO and CNES

Variational Bayes image restoration with (compressive) autoencoders

Regularization of inverse problems is of paramount importance in computational imaging. The ability of neural networks to learn efficient image representations has been recently exploited to design powerful data-driven regularizers. While state-of-the-art plug-and-play methods rely on an implicit regularization provided by neural denoisers, alternative Bayesian approaches consider Maximum A Posteriori (MAP) estimation in the latent space of a generative model, thus with an explicit regularization. However, state-of-the-art deep generative models require a huge amount of training data compared to denoisers. Besides, their complexity hampers the optimization involved in latent MAP derivation. In this work, we first propose to use compressive autoencoders instead. These networks, which can be seen as variational autoencoders with a flexible latent prior, are smaller and easier to train than state-of-the-art generative models. As a second contribution, we introduce the Variational Bayes Latent Estimation (VBLE) algorithm, which performs latent estimation within the framework of variational inference. Thanks to a simple yet efficient parameterization of the variational posterior, VBLE allows for fast and easy (approximate) posterior sampling. Experimental results on image datasets BSD and FFHQ demonstrate that VBLE reaches similar performance than state-of-the-art plug-and-play methods, while being able to quantify uncertainties faster than other existing posterior sampling techniques.

Le 2 mai 2024 à 11:00

Séminaire Images Optimisation et Probabilités

Salle de conférences

Jérôme Bolte Université de Toulouse 1

Nonsmooth differentiation of algorithms and solution maps

The recent surge in algorithmic differentiation through the massive use of TensorFlow and PyTorch "autodiff" has democratized "computerized differentiation" for a broad spectrum of applications and solvers. Motivated by the challenges of nonsmoothness (such as thresholding, constraints, and ReLU) and the need to adjust parameters in various contexts directly via these solvers, we have devised tools for nonsmooth differentiation compatible with autodiff. We have in particular developed a nonsmooth implicit function calculus, aiming to provide robust guarantees for prevalent differentiation practices. We will discuss applications of these findings through the differentiation of algorithms and equations.

Le 16 mai 2024 à 11:00

Séminaire Images Optimisation et Probabilités

Salle de conférénces

Bruno Galerne Université d'Orleans

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Le 23 mai 2024 à 11:00

Séminaire Images Optimisation et Probabilités

Salle de conférénce

Stephane Dartois À préciser

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Les anciens séminaires

Séminaire Images Optimisation et Probabilités

Institut de Mathématiques de Bordeaux UMR 5251