Stochastic Primal-Dual Three Operator Splitting Algorithm with Extension to Equivariant Regularization-by-Denoising

Junqi Tang; Matthias J. Ehrhardt; Carola Bibiane Schönlieb

doi:10.1007/978-3-031-92369-2_3

Stochastic Primal-Dual Three Operator Splitting Algorithm with Extension to Equivariant Regularization-by-Denoising

Junqi Tang, Matthias J. Ehrhardt, Carola Bibiane Schönlieb

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

Abstract

In this work we propose a stochastic primal-dual three-operator splitting algorithm (TOS-SPDHG) for solving a class of convex three-composite optimization problems. Our proposed scheme is a direct three-operator splitting extension of the SPDHG algorithm [Chambolle et al. 2018]. We provide theoretical convergence analysis showing ergodic O(1/K) convergence rate, and demonstrate the effectiveness of our approach in imaging inverse problems. Moreover, we further propose TOS-SPDHG-RED and TOS-SPDHG-eRED which utilizes the regularization-by-denoising (RED) framework to leverage pretrained deep denoising networks as image priors for improved reconstruction.

Original language	English
Title of host publication	Scale Space and Variational Methods in Computer Vision - 10th International Conference, SSVM 2025, Proceedings
Editors	Tatiana A. Bubba, Romina Gaburro, Silvia Gazzola, Kostas Papafitsoros, Marcelo Pereyra, Carola-Bibiane Schönlieb
Place of Publication	Cham, Switzerland
Publisher	Springer
Pages	30-41
Number of pages	12
ISBN (Electronic)	9783031923692
ISBN (Print)	9783031923685
DOIs	https://doi.org/10.1007/978-3-031-92369-2_3
Publication status	Published - 17 May 2025
Event	10th International Conference on Scale Space and Variational Methods in Computer Vision, SSVM 2025 - Dartington, UK United Kingdom Duration: 18 May 2025 → 22 May 2025

Publication series

Name	Lecture Notes in Computer Science
Volume	15668 LNCS
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Conference

Conference	10th International Conference on Scale Space and Variational Methods in Computer Vision, SSVM 2025
Country/Territory	UK United Kingdom
City	Dartington
Period	18/05/25 → 22/05/25

Keywords

Primal-Dual Algorithms
Regularization-by-Denoising
Stochastic Optimization

ASJC Scopus subject areas

Theoretical Computer Science
General Computer Science

Access to Document

10.1007/978-3-031-92369-2_3

https://arxiv.org/abs/2208.01631

Cite this

Tang, J., Ehrhardt, M. J., & Schönlieb, C. B. (2025). Stochastic Primal-Dual Three Operator Splitting Algorithm with Extension to Equivariant Regularization-by-Denoising. In T. A. Bubba, R. Gaburro, S. Gazzola, K. Papafitsoros, M. Pereyra, & C.-B. Schönlieb (Eds.), Scale Space and Variational Methods in Computer Vision - 10th International Conference, SSVM 2025, Proceedings (pp. 30-41). (Lecture Notes in Computer Science; Vol. 15668 LNCS). Springer. https://doi.org/10.1007/978-3-031-92369-2_3

Stochastic Primal-Dual Three Operator Splitting Algorithm with Extension to Equivariant Regularization-by-Denoising. / Tang, Junqi; Ehrhardt, Matthias J.; Schönlieb, Carola Bibiane.
Scale Space and Variational Methods in Computer Vision - 10th International Conference, SSVM 2025, Proceedings. ed. / Tatiana A. Bubba; Romina Gaburro; Silvia Gazzola; Kostas Papafitsoros; Marcelo Pereyra; Carola-Bibiane Schönlieb. Cham, Switzerland: Springer, 2025. p. 30-41 (Lecture Notes in Computer Science; Vol. 15668 LNCS).

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

Tang, J, Ehrhardt, MJ & Schönlieb, CB 2025, Stochastic Primal-Dual Three Operator Splitting Algorithm with Extension to Equivariant Regularization-by-Denoising. in TA Bubba, R Gaburro, S Gazzola, K Papafitsoros, M Pereyra & C-B Schönlieb (eds), Scale Space and Variational Methods in Computer Vision - 10th International Conference, SSVM 2025, Proceedings. Lecture Notes in Computer Science, vol. 15668 LNCS, Springer, Cham, Switzerland, pp. 30-41, 10th International Conference on Scale Space and Variational Methods in Computer Vision, SSVM 2025, Dartington, UK United Kingdom, 18/05/25. https://doi.org/10.1007/978-3-031-92369-2_3

Tang J, Ehrhardt MJ, Schönlieb CB. Stochastic Primal-Dual Three Operator Splitting Algorithm with Extension to Equivariant Regularization-by-Denoising. In Bubba TA, Gaburro R, Gazzola S, Papafitsoros K, Pereyra M, Schönlieb CB, editors, Scale Space and Variational Methods in Computer Vision - 10th International Conference, SSVM 2025, Proceedings. Cham, Switzerland: Springer. 2025. p. 30-41. (Lecture Notes in Computer Science). Epub 2025 May 17. doi: 10.1007/978-3-031-92369-2_3

Tang, Junqi ; Ehrhardt, Matthias J. ; Schönlieb, Carola Bibiane. / Stochastic Primal-Dual Three Operator Splitting Algorithm with Extension to Equivariant Regularization-by-Denoising. Scale Space and Variational Methods in Computer Vision - 10th International Conference, SSVM 2025, Proceedings. editor / Tatiana A. Bubba ; Romina Gaburro ; Silvia Gazzola ; Kostas Papafitsoros ; Marcelo Pereyra ; Carola-Bibiane Schönlieb. Cham, Switzerland : Springer, 2025. pp. 30-41 (Lecture Notes in Computer Science).

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