Bayesian inference and mathematical imaging - Part 3: probability and convex optimisation | Vidéo | Carmin.tv

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Chapters

Bayesian inference and mathematical imaging - Part 3: probability and convex optimisation

By Marcelo Pereyra

Appears in collections : IHP winter school: The mathematics of imaging / Ecole d'hiver IHP : Les mathématiques de l'image, Ecoles de recherche

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.

Information about the video

Date of recording 10/01/2019
Date of publication 21/01/2019
Institution CIRM
Licence CC BY NC ND
Language English
Director(s) Guillaume Hennenfent
Format MP4

Citation data

DOI 10.24350/CIRM.V.19486103
Cite this video Pereyra, Marcelo (10/01/2019). Bayesian inference and mathematical imaging - Part 3: probability and convex optimisation. CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.19486103
URL https://dx.doi.org/10.24350/CIRM.V.19486103

Domain(s)

Bibliography

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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
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MSC codes

Document(s)

https://www.cirm-math.fr/ProgWeebly/2019/Renc1993/PresPereyra3.pdf

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