Stochastic Primal-Dual Three Operator Splitting Algorithm with Extension to Equivariant Regularization-by-Denoising
This work provides an incremental improvement for solving imaging inverse problems by extending existing algorithms to incorporate deep learning priors.
The authors tackled convex three-composite optimization problems by proposing a stochastic primal-dual three-operator splitting algorithm (TOS-SPDHG), achieving an ergodic O(1/K) convergence rate, and extended it to use regularization-by-denoising with deep networks for imaging inverse problems.
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.