Benning, Martin;
Riis, Erlend Skaldehaug;
(2021)
Bregman Methods for Large-Scale Optimisation with Applications in Imaging.
In: Chen, Ke and Schönlieb, Carola-Bibiane and Tai, Xue-Cheng and Younce, Laurent, (eds.)
Handbook of Mathematical Models and Algorithms in Computer Vision and Imaging.
(pp. 1-42).
Springer Cham: Cham, Switzerland.
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Abstract
In this chapter we review recent developments in the research of Bregman methods, with particular focus on their potential use for large-scale applications. We give an overview on several families of Bregman algorithms and discuss modifications such as accelerated Bregman methods, incremental and stochastic variants, and coordinate descent-type methods. We conclude this chapter with numerical examples in image and video decomposition, image denoising, and dimensionality reduction with auto-encoders.
| Type: | Book chapter |
|---|---|
| Title: | Bregman Methods for Large-Scale Optimisation with Applications in Imaging |
| ISBN-13: | 9783030030094 |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.1007/978-3-030-03009-4_62-1 |
| Publisher version: | https://doi.org/10.1007/978-3-030-03009-4_62-1 |
| Language: | English |
| Additional information: | This version is the author-accepted manuscript. For information on re-use, please refer to the publisher’s terms and conditions. |
| Keywords: | Optimisatio, Bregman proximal methods, Bregman iterations, Inverse problems, Nesterov acceleration, Mirror descent, Kaczmarz method, Coordinate descent, Itoh-Abe method, Alternating direction method of multipliers, Primal-dual hybrid gradient, Robust principal components analysis, Deep learning, Image denoising |
| UCL classification: | UCL UCL > Provost and Vice Provost Offices > UCL BEAMS UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Engineering Science UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Engineering Science > Dept of Computer Science |
| URI: | https://discovery.ucl.ac.uk/id/eprint/10189902 |
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