Bregman Methods for Large-Scale Optimization with Applications in Imaging

Martin Benning () and Erlend Skaldehaug Riis
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Martin Benning: Queen Mary University of London, The School of Mathematical Sciences
Erlend Skaldehaug Riis: The Department of Applied Mathematics and Theoretical Physics

Chapter 3 in Handbook of Mathematical Models and Algorithms in Computer Vision and Imaging, 2023, pp 97-138 from Springer

Abstract: 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.

Keywords: Optimization; 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 (search for similar items in EconPapers)
Date: 2023
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-030-98661-2_62

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DOI: 10.1007/978-3-030-98661-2_62

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