Bayesian inference and mathematical imaging - Part 2: Markov chain Monte Carlo | Vidéo | Carmin.tv

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Bayesian inference and mathematical imaging - Part 2: Markov chain Monte Carlo

De Marcelo Pereyra

Apparaît dans la collection : IHP winter school: The mathematics of imaging / Ecole d'hiver IHP : Les mathématiques de l'image

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.

Informations sur la vidéo

Date de captation 09/01/2019
Date de publication 21/01/2019
Institut CIRM
Licence CC BY NC ND
Langue Anglais
Audience Chercheurs, Doctorants
Réalisateur(s) Guillaume Hennenfent
Format MP4

Données de citation

DOI 10.24350/CIRM.V.19486803
Citer cette vidéo Pereyra, Marcelo (09/01/2019). Bayesian inference and mathematical imaging - Part 2: Markov chain Monte Carlo. CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.19486803
URL https://dx.doi.org/10.24350/CIRM.V.19486803

Domaine(s)

Bibliographie

Ay, N., & Amari, S.-I. (2015). A novel approach to canonical divergences within information geometry. Entropy, 17(12), 8111-8129 - https://dx.doi.org/10.3390/e17127866
Cai, X., Pereyra, M., & McEwen, J.D. (2018). Uncertainty quantification for radio interferometric imaging: II. MAP estimation. Monthly Notices of the Royal Astronomical Society, 480(3), 4170-4182 - https://doi.org/10.1093/mnras/sty2015
Chambolle, A., & Pock, T. (2016). An introduction to continuous optimization for imaging. Acta Numerica, 25, 161-319 - https://doi.org/10.1017/S096249291600009X
Deledalle, C.-A., Vaiter, S., Fadili, J., & Peyré, G. (2014). Stein Unbiased GrAdient estimator of the Risk (SUGAR) for multiple parameter selection. SIAM Journal on Imaging Sciences, 7(4), 2448-2487 - https://doi.org/10.1137/140968045
Fernandez-Vidal, A. & Pereyra, M. (2018). Maximum likelihood estimation of regularisation parameters. In 2018 25th IEEE International Conference on Image Processing: Proceedings (pp. 1742-1746) - https://doi.org/10.1109/ICIP.2018.8451795
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

Codes MSC

Document(s)

https://www.cirm-math.fr/ProgWeebly/2019/Renc1993/PresPereyra2.pdf

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