Stochastic Primal-Dual Three Operator Splitting Algorithm with Extension to Equivariant Regularization-by-Denoising
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Abstract (arXiv)
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.
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References · 10
- 2016Beyond a Gaussian Denoiser: Residual Learning of Deep CNN for Image Denoisingcited by 1,352
- 2014SAGA: A Fast Incremental Gradient Method With Support for Non-Strongly Convex Composite Objectivescited by 401
- 2016The Little Engine that Could: Regularization by Denoising (RED)cited by 303
- 2016Katyusha: The First Direct Acceleration of Stochastic Gradient Methodscited by 134
- 2014A Proximal Stochastic Gradient Method with Progressive Variance Reductioncited by 78
- 2015A Three-Operator Splitting Scheme and its Optimization Applicationscited by 34
- 2017Stochastic Primal-Dual Hybrid Gradient Algorithm with Arbitrary Sampling and Imaging Applicationscited by 29
- 2013Accelerated, Parallel and Proximal Coordinate Descentcited by 25
- 2015Mini-Batch Semi-Stochastic Gradient Descent in the Proximal Settingcited by 10
- 2019The Practicality of Stochastic Optimization in Imaging Inverse Problemscited by 9
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