Séminaire Image : « Convergent Plug-and-Play methods to solve inverse problems », Nicolas Papadakis

Nous aurons le plaisir d’écouter Nicolas Papadakis, Institut de Mathématiques de Bordeaux.
Il donnera un séminaire IMAGE le jeudi 18 septembre à 14h00 en salle de séminaire F-200.

Titre : « Convergent Plug-and-Play methods to solve inverse problems »

Résumé :
In image sciences, Plug-and-Play methods constitute a class of iterative algorithms for solving inverse problems where regularization is performed by an off-the-shelf denoiser. Although Plug-and-Play methods can lead to tremendous visual performance for various image problems, most existing convergence guarantees are based on unrealistic (or suboptimal) hypotheses on the denoiser, or limited to strongly convex data terms. In this talk, we discuss a type of Plug-and-Play method for which the denoiser is realized as a gradient descent step on a nonconvex functional parameterized by a deep neural network. Exploiting convergence results for proximal gradient descent algorithms in the non-convex setting, we show that the proposed Plug-and-Play algorithm is a convergent iterative scheme that targets stationary points of an explicit global functional. Besides, experiments show that it is possible to learn such a deep denoiser while not compromising the performance in comparison to other state-of-the-art deep denoisers used in Plug-and-Play schemes. The deep proximal gradient algorithms are applied to various ill-posed inverse problems, e.g. deblurring, super-resolution and inpainting. For all these applications, numerical results empirically confirm the convergence results. Experiments also show that these algorithms reach state-of-the-art performance, both quantitatively and qualitatively.