English
Bayesian inference and mathematical imaging - Part 2: Markov chain Monte Carlo
Multi angle
Auteurs : Pereyra, Marcelo (Auteur de la Conférence)
CIRM (Editeur )
49N45 - Inverse problems in calculus of variations
62C10 - Bayesian problems; characterization of Bayes procedures
62F15 - Bayesian inference
65C40 - Computational Markov chains (numerical analysis)
65C60 - Computational problems in statistics
65J22 - Inverse problems (numerical methods in abstract spaces)
68U10 - Image processing (computing aspects)
94A08 - Image processing (compression, reconstruction, etc.)
Ressources complémentaires :
https://www.cirm-math.fr/ProgWeebly/2019/Renc1993/PresPereyra2.pdf
CIRM (Editeur )
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Résumé :
This course presents an overview of modern Bayesian strategies for solving imaging inverse problems. We will start by introducing the Bayesian statistical decision theory framework underpinning Bayesian analysis, and then explore efficient numerical methods for performing Bayesian computation in large-scale settings. We will pay special attention to high-dimensional imaging models that are log-concave w.r.t. the unknown image, related to so-called “convex imaging problems”. This will provide an opportunity to establish connections with the convex optimisation and machine learning approaches to imaging, and to discuss some of their relative strengths and drawbacks. Examples of topics covered in the course include: efficient stochastic simulation and optimisation numerical methods that tightly combine proximal convex optimisation with Markov chain Monte Carlo techniques; strategies for estimating unknown model parameters and performing model selection, methods for calculating Bayesian confidence intervals for images and performing uncertainty quantification analyses; and new theory regarding the role of convexity in maximum-a-posteriori and minimum-mean-square-error estimation. The theory, methods, and algorithms are illustrated with a range of mathematical imaging experiments.
Codes MSC : 49N45 - Inverse problems in calculus of variations
62C10 - Bayesian problems; characterization of Bayes procedures
62F15 - Bayesian inference
65C40 - Computational Markov chains (numerical analysis)
65C60 - Computational problems in statistics
65J22 - Inverse problems (numerical methods in abstract spaces)
68U10 - Image processing (computing aspects)
94A08 - Image processing (compression, reconstruction, etc.)
Ressources complémentaires :
https://www.cirm-math.fr/ProgWeebly/2019/Renc1993/PresPereyra2.pdf
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Informations sur la Vidéo
Réalisateur : Hennenfent, GuillaumeLangue : Anglais Date de publication : 21/01/2019 Date de captation : 09/01/2019 Sous collection : Research School arXiv category : Statistics Theory ; Numerical Analysis Domaine : Probability & Statistics ; Control Theory & Optimization ; Numerical Analysis & Scientific Computing Format : MP4 (.mp4) - HD Durée : 01:25:10 Audience : Researchers ; Graduate Students Download : https://videos.cirm-math.fr/2019-01-09_Pereyra_2.mp4 
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Informations sur la Rencontre
Nom de la rencontre : IHP winter school: The mathematics of imaging / Ecole d'hiver IHP : Les mathématiques de l'imageOrganisateurs de la rencontre : Fadili, Jalal ; Melor, Clothilde ; Schönlieb, Carola-Bibiane ; Wirth, Benedikt Dates : 07/01/2019 - 11/01/2019 Année de la rencontre : 2019 URL Congrès : https://conferences.cirm-math.fr/1993.html
Données de citation
DOI : 10.24350/CIRM.V.19486803Citer cette vidéo: Pereyra, Marcelo (2019). Bayesian inference and mathematical imaging - Part 2: Markov chain Monte Carlo. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19486803 URI : http://dx.doi.org/10.24350/CIRM.V.19486803 |
Voir aussi
- [Multi angle] Bayesian inference and mathematical imaging - Part 4: mixture, random fields and hierarchical models / Auteur de la Conférence Pereyra, Marcelo.
- [Multi angle] Bayesian inference and mathematical imaging - Part 1: Bayesian analysis and decision theory / Auteur de la Conférence Pereyra, Marcelo.
- [ Post-edited] Bayesian inference and mathematical imaging - Part 3: probability and convex optimisation / Auteur de la Conférence Pereyra, Marcelo.
Bibliographie
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- Chambolle, A., & Pock, T. (2016). An introduction to continuous optimization for imaging. Acta Numerica, 25, 161-319 - https://doi.org/10.1017/S096249291600009X
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- Green, P.J., Latuszynski, K., Pereyra, M., & Robert, C.P. (2015). Bayesian computation: a summary of the current state, and samples backwards and forwards. Statistics and Computing, 25(4), 835-862 - http://dx.doi.org/10.1007/s11222-015-9574-5
- Pereyra, M. (2016). Maximum-a-posteriori estimation with bayesian confidence regions. SIAM Journal on Imaging Sciences, 10(1), 285–302 - https://doi.org/10.1137/16M1071249
- Pereyra, M. (2016). Revisiting maximum-a-posteriori estimation in log-concave models: from differential geometry to decision theory. 〈arXiv:1612.06149〉 - https://arxiv.org/abs/1612.06149
- Pereyra, M., Bioucas-Dias, J., & Figueiredo, M. (2015). Maximum-a-posteriori estimation with unknown regularisation parameters. In 2015 23rd European Signal Processing Conference (EUSIPCO): Proceedings (pp. 230-234) - https://doi.org/10.1109/EUSIPCO.2015.7362379
- Repetti, A., Pereyra, M., & Wiaux, Y. (2018). Scalable Bayesian uncertainty quantification in imaging inverse problems via convex optimisation.〈arXiv:1803.00889〉 - https://arxiv.org/abs/1803.00889
- Robert, C.P. (2001). The Bayesian Choice. From decision-theoretic foundations to computational implementation. 2nd ed., 1st paperback ed. New York, NY: Springer - http://dx.doi.org/10.1007/0-387-71599-1
- Zhu, L., Zhang, W., Elnatan, D., & Huang, B. (2012). Faster STORM using compressed sensing. Nature Methods, 9(7), 721-723 - https://doi.org/10.1038/nmeth.1978
