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.

翻译：本文提出了一种随机原始-对偶三算子分裂算法（TOS-SPDHG），用于求解一类凸性三复合优化问题。该方案是SPDHG算法[Chambolle et al. 2018]向三算子分裂的直接扩展。我们给出了理论收敛性分析，证明了遍历意义下的$O(1/K)$收敛速率，并通过成像逆问题验证了算法的有效性。此外，我们进一步提出了TOS-SPDHG-RED与TOS-SPDHG-eRED算法，它们利用去噪正则化（RED）框架，将预训练的深度去噪网络作为先验信息进行集成。