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

^*Corresponding author for this work

Mathematics

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

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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
Subtitle of host publication	10th International Conference, SSVM 2025, Dartington, UK, May 18–22, 2025, Proceedings, Part II
Editors	Tatiana A. Bubba, Romina Gaburro, Silvia Gazzola, Kostas Papafitsoros, Marcelo Pereyra, Carola-Bibiane Schönlieb
Publisher	Springer
Pages	30-41
Number of pages	11
Edition	1
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 - Dartington, United Kingdom Duration: 18 May 2025 → 22 May 2025 Conference number: 10 https://ecmiindmath.org/event/10th-international-conference-on-scale-space-and-variational-methods-in-computer-vision-ssvm/

Publication series

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

Conference

Conference	10th International Conference on Scale Space and Variational Methods in Computer Vision
Abbreviated title	SSVM 2025
Country/Territory	United Kingdom
City	Dartington
Period	18/05/25 → 22/05/25
Internet address	https://ecmiindmath.org/event/10th-international-conference-on-scale-space-and-variational-methods-in-computer-vision-ssvm/

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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, Dartington, UK, May 18–22, 2025, Proceedings, Part II (1 ed., pp. 30-41). (Lecture Notes in Computer Science; Vol. 15668). Springer. https://doi.org/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, Dartington, UK, May 18–22, 2025, Proceedings, Part II. editor / Tatiana A. Bubba ; Romina Gaburro ; Silvia Gazzola ; Kostas Papafitsoros ; Marcelo Pereyra ; Carola-Bibiane Schönlieb. 1. ed. Springer, 2025. pp. 30-41 (Lecture Notes in Computer Science).

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title = "Stochastic Primal-Dual Three Operator Splitting Algorithm with Extension to Equivariant Regularization-by-Denoising",

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.",

author = "Junqi Tang and Ehrhardt, {Matthias J.} and Carola-Bibiane Sch{\"o}nlieb",

year = "2025",

month = may,

day = "17",

doi = "10.1007/978-3-031-92369-2_3",

language = "English",

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editor = "Bubba, {Tatiana A.} and Romina Gaburro and Silvia Gazzola and Kostas Papafitsoros and Marcelo Pereyra and Carola-Bibiane Sch{\"o}nlieb",

booktitle = "Scale Space and Variational Methods in Computer Vision",

edition = "1",

note = "10th International Conference on Scale Space and Variational Methods in Computer Vision, SSVM 2025 ; Conference date: 18-05-2025 Through 22-05-2025",

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Tang, J, Ehrhardt, MJ & Schönlieb, C-B 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, Dartington, UK, May 18–22, 2025, Proceedings, Part II. 1 edn, Lecture Notes in Computer Science, vol. 15668, Springer, pp. 30-41, 10th International Conference on Scale Space and Variational Methods in Computer Vision, Dartington, United Kingdom, 18/05/25. 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, Dartington, UK, May 18–22, 2025, Proceedings, Part II. ed. / Tatiana A. Bubba; Romina Gaburro; Silvia Gazzola; Kostas Papafitsoros; Marcelo Pereyra; Carola-Bibiane Schönlieb. 1. ed. Springer, 2025. p. 30-41 (Lecture Notes in Computer Science; Vol. 15668).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

TY - GEN

T1 - Stochastic Primal-Dual Three Operator Splitting Algorithm with Extension to Equivariant Regularization-by-Denoising

AU - Tang, Junqi

AU - Ehrhardt, Matthias J.

AU - Schönlieb, Carola-Bibiane

N1 - Conference code: 10

PY - 2025/5/17

Y1 - 2025/5/17

N2 - 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.

AB - 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.

U2 - 10.1007/978-3-031-92369-2_3

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

M3 - Conference contribution

SN - 9783031923685

T3 - Lecture Notes in Computer Science

SP - 30

EP - 41

BT - Scale Space and Variational Methods in Computer Vision

A2 - Bubba, Tatiana A.

A2 - Gaburro, Romina

A2 - Gazzola, Silvia

A2 - Papafitsoros, Kostas

A2 - Pereyra, Marcelo

A2 - Schönlieb, Carola-Bibiane

PB - Springer

T2 - 10th International Conference on Scale Space and Variational Methods in Computer Vision

Y2 - 18 May 2025 through 22 May 2025

ER -

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, Dartington, UK, May 18–22, 2025, Proceedings, Part II. 1 ed. Springer. 2025. p. 30-41. (Lecture Notes in Computer Science). doi: 10.1007/978-3-031-92369-2_3

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

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