Estimados,
Rogamos dar difusión a la defensa de tesis de doctorado en Ingeniería Eléctrica de la Udelar / Matemática Aplicada de la Universidad de Paris, de Mario González Olmedo.
La defensa tendrá lugar en el salón 701, piso 7 de la Facultad de Ingeniería, el miércoles 15/12 a las 12h. De ser posible, a los efectos de tener un cierto control sobre la cantidad de asistentes debido a medidas sanitarias, solicitamos a aquellos que deseen asistir de forma presencial que escriban a
pmuse@fing.edu.uy.
Se podrá asistir de forma virtual uniéndose a la siguiente sala zoom:
A continuación encontrarán la información relativa a la tesis.
Saludos cordiales,
Andrés Almansa
Pablo Musé
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Title: Bayesian Plug & Play Methods for Inverse Problems in Imaging
Mario González Olmedo
Orientadores
Andrés Almansa, DR, CNRS & Université de Paris
Pablo Musé, Profesor Titular, Universidad de la República
Tribunal
Jean-François Aujol - Professeur des Universités, Université de Bordeaux - Examinador
Pierre Chainais - Professeur des Universités, Ecole Centrale de Lille - Revisor
Julie Delon - Professeur des Universités, Université de Paris - Examinadora
Ricardo Fraiman - Profesor Titular, Universidad de la República - Examinador
Pablo Sprechmann - Research Scientist, Deep Mind - Examinador
Gabriele Steidl - Professor, Technische Universität Berlin - Revisora
Abstract
This thesis deals with Bayesian methods for solving ill-posed inverse problems in imaging with learnt image priors. The first part of this thesis (Chapter 3) concentrates on two particular problems, namely joint denoising and decompression and multi-image super-resolution. After an extensive study of the noise statistics for these problem in the transformed (wavelet or Fourier) domain, we derive two novel algorithms to solve this particular inverse problem. One of them is based on a multi-scale self-similarity prior and can be seen as a transform-domain generalization of the celebrated Non-Local Bayes algorithm to the case of non-Gaussian noise. The second one uses a neural-network denoiser to implicitly encode the image prior, and a splitting scheme to incorporate this prior into an optimization algorithm to find a MAP-like estimator.
The second part of this thesis concentrates on the Variational AutoEncoder (VAE) model and some of its variants that show its capabilities to explicitly capture the probability distribution of high-dimensional datasets such as images. Based on these VAE models, we propose two ways to incorporate them as priors for general inverse problems in imaging:
• The first one (Chapter 4) computes a joint (space-latent) MAP estimator named Joint Posterior Maximization using an Autoencoding Prior (JPMAP). We show theoretical and experimental evidence that the proposed objective function satisfies a weak bi convexity property which is sufficient to guarantee that our optimization scheme converges to a stationary point. Experimental results also show the higher quality of the solutions obtained by our JPMAP approach with respect to other non-convex MAP approaches which more often get stuck in spurious local optima.
• The second one (Chapter 5) develops a Gibbs-like posterior sampling algorithm for the exploration of posterior distributions of inverse problems using multiple chains and a VAE as image prior. We show how to use those samples to obtain MMSE estimates and their corresponding uncertainty.
Keywords: Inverse problems, Bayesian statistics, image processing, optimization
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Pablo Musé, PhD
Full Professor of Signal Processing
Universidad de la República
Uruguay
+598 27110974
iie.fing.edu.uy/~pmuse/