Convergence Properties of a Randomized Primal-Dual Algorithm with Applications to Parallel MRI

Eric B. Gutiérrez; Claire Delplancke; Matthias J. Ehrhardt

doi:10.1007/978-3-030-75549-2_21

Convergence Properties of a Randomized Primal-Dual Algorithm with Applications to Parallel MRI

Eric B. Gutiérrez, Claire Delplancke, Matthias J. Ehrhardt

Research output: Chapter or section in a book/report/conference proceeding › Chapter in a published conference proceeding

1 Citation (SciVal)

19 Downloads (Pure)

Abstract

The Stochastic Primal-Dual Hybrid Gradient (SPDHG) was proposed by Chambolle et al. (2018) and is an efficient algorithm to solve some nonsmooth large-scale optimization problems. In this paper we prove its almost sure convergence for convex but not necessarily strongly convex functionals. We also look into its application to parallel Magnetic Resonance Imaging reconstruction in order to test performance of SPDHG. Our numerical results show that for a range of settings SPDHG converges significantly faster than its deterministic counterpart.

Original language	English
Title of host publication	Scale Space and Variational Methods in Computer Vision - 8th International Conference, SSVM 2021, Proceedings
Editors	Abderrahim Elmoataz, Jalal Fadili, Yvain Quéau, Julien Rabin, Loïc Simon
Place of Publication	Germany
Publisher	Springer Science and Business Media Deutschland GmbH
Pages	254-266
Number of pages	13
ISBN (Print)	9783030755485
DOIs	https://doi.org/10.1007/978-3-030-75549-2_21
Publication status	Published - 29 Apr 2021
Event	8th International Conference on Scale Space and Variational Methods in Computer Vision, SSVM 2021 - Virtual, Online Duration: 16 May 2021 → 20 May 2021

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	12679 LNCS
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Conference

Conference	8th International Conference on Scale Space and Variational Methods in Computer Vision, SSVM 2021
City	Virtual, Online
Period	16/05/21 → 20/05/21

Keywords

Convex optimization
Inverse problems
Parallel magnetic resonance imaging
Primal-dual algorithm
Stochastic optimization

ASJC Scopus subject areas

Theoretical Computer Science
Computer Science(all)

Access to Document

10.1007/978-3-030-75549-2_21

2012.01255v1.PDF
This is a post-peer-review, pre-copyedit version of an article published in SSVM 2021: Scale Space and Variational Methods in Computer Vision. The final authenticated version is available online at: https://doi.org/10.1007/978-3-030-75549-2_21
Accepted author manuscript, 196 KB

Cite this

Gutiérrez, E. B., Delplancke, C., & Ehrhardt, M. J. (2021). Convergence Properties of a Randomized Primal-Dual Algorithm with Applications to Parallel MRI. In A. Elmoataz, J. Fadili, Y. Quéau, J. Rabin, & L. Simon (Eds.), Scale Space and Variational Methods in Computer Vision - 8th International Conference, SSVM 2021, Proceedings (pp. 254-266). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 12679 LNCS). Springer Science and Business Media Deutschland GmbH. https://doi.org/10.1007/978-3-030-75549-2_21

Convergence Properties of a Randomized Primal-Dual Algorithm with Applications to Parallel MRI. / Gutiérrez, Eric B.; Delplancke, Claire; Ehrhardt, Matthias J.
Scale Space and Variational Methods in Computer Vision - 8th International Conference, SSVM 2021, Proceedings. ed. / Abderrahim Elmoataz; Jalal Fadili; Yvain Quéau; Julien Rabin; Loïc Simon. Germany: Springer Science and Business Media Deutschland GmbH, 2021. p. 254-266 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 12679 LNCS).

Research output: Chapter or section in a book/report/conference proceeding › Chapter in a published conference proceeding

Gutiérrez, EB, Delplancke, C & Ehrhardt, MJ 2021, Convergence Properties of a Randomized Primal-Dual Algorithm with Applications to Parallel MRI. in A Elmoataz, J Fadili, Y Quéau, J Rabin & L Simon (eds), Scale Space and Variational Methods in Computer Vision - 8th International Conference, SSVM 2021, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 12679 LNCS, Springer Science and Business Media Deutschland GmbH, Germany, pp. 254-266, 8th International Conference on Scale Space and Variational Methods in Computer Vision, SSVM 2021, Virtual, Online, 16/05/21. https://doi.org/10.1007/978-3-030-75549-2_21

Gutiérrez EB, Delplancke C, Ehrhardt MJ. Convergence Properties of a Randomized Primal-Dual Algorithm with Applications to Parallel MRI. In Elmoataz A, Fadili J, Quéau Y, Rabin J, Simon L, editors, Scale Space and Variational Methods in Computer Vision - 8th International Conference, SSVM 2021, Proceedings. Germany: Springer Science and Business Media Deutschland GmbH. 2021. p. 254-266. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). doi: 10.1007/978-3-030-75549-2_21

Gutiérrez, Eric B. ; Delplancke, Claire ; Ehrhardt, Matthias J. / Convergence Properties of a Randomized Primal-Dual Algorithm with Applications to Parallel MRI. Scale Space and Variational Methods in Computer Vision - 8th International Conference, SSVM 2021, Proceedings. editor / Abderrahim Elmoataz ; Jalal Fadili ; Yvain Quéau ; Julien Rabin ; Loïc Simon. Germany : Springer Science and Business Media Deutschland GmbH, 2021. pp. 254-266 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

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abstract = "The Stochastic Primal-Dual Hybrid Gradient (SPDHG) was proposed by Chambolle et al. (2018) and is an efficient algorithm to solve some nonsmooth large-scale optimization problems. In this paper we prove its almost sure convergence for convex but not necessarily strongly convex functionals. We also look into its application to parallel Magnetic Resonance Imaging reconstruction in order to test performance of SPDHG. Our numerical results show that for a range of settings SPDHG converges significantly faster than its deterministic counterpart.",

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Convergence Properties of a Randomized Primal-Dual Algorithm with Applications to Parallel MRI

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