Stochastic Primal-Dual Three Operator Splitting Algorithm with Extension to Equivariant Regularization-by-Denoising
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arXiv
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| Format: | Preprint |
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2022
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| _version_ | 1866913736418131968 |
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| author | Tang, Junqi Ehrhardt, Matthias Schönlieb, Carola-Bibiane |
| author_facet | Tang, Junqi Ehrhardt, Matthias Schönlieb, Carola-Bibiane |
| contents | 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 priors. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2208_01631 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Stochastic Primal-Dual Three Operator Splitting Algorithm with Extension to Equivariant Regularization-by-Denoising Tang, Junqi Ehrhardt, Matthias Schönlieb, Carola-Bibiane Optimization and Control Machine Learning Image and Video Processing 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 priors. |
| title | Stochastic Primal-Dual Three Operator Splitting Algorithm with Extension to Equivariant Regularization-by-Denoising |
| topic | Optimization and Control Machine Learning Image and Video Processing |
| url | https://arxiv.org/abs/2208.01631 |