[Todos CMAT] Fwd: Defensa de tesis de doctorado (Ing. Eléctrica Udelar / Matemática Aplicada, U. de Paris) de Mario González Olmedo, viernes 15/12, 12h

[roma]

----- Mensaje reenviado de Pablo Musé <pmuse en fing.edu.uy> -----
  Fecha: Fri, 10 Dec 2021 18:04:25 -0300
     De: Pablo Musé <pmuse en fing.edu.uy>
Asunto: Defensa de tesis de doctorado (Ing. Eléctrica Udelar /  
Matemática Aplicada, U. de Paris) de Mario González Olmedo, viernes  
15/12, 12h

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 en fing.edu.uy  
<mailto:pmuse en fing.edu.uy>.

Se podrá asistir de forma virtual uniéndose a la siguiente sala zoom:

https://salavirtual-udelar.zoom.us/j/81746848850?pwd=bExhMzBVSUJXdk9TenY3bkt6Z3Vjdz09  
<https://salavirtual-udelar.zoom.us/j/81746848850?pwd=bExhMzBVSUJXdk9TenY3bkt6Z3Vjdz09>
ID de reunión: 817 4684 8850
Código de acceso: 04v13p+4*p

A continuación encontrarán la información relativa a la tesis.

Saludos cordiales,

Andrés Almansa
Pablo Musé



———————————————————————————————————————————


Title: Bayesian Plug & Play Methods for Inverse Problems in Imaging

Mario González

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

----------------------------------------------
Pablo Musé, PhD
Full Professor of Signal Processing
Universidad de la República
Uruguay
+598 27110974
iie.fing.edu.uy/~pmuse/

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