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

TL;DR

This paper introduces a stochastic primal-dual three-operator splitting algorithm for convex optimization, extending SPDHG, with convergence guarantees and applications in imaging inverse problems using deep denoising priors.

Contribution

It presents a novel stochastic three-operator splitting algorithm extending SPDHG, with convergence analysis and integration of deep denoising priors via RED.

Findings

Achieves ergodic $O(1/K)$ convergence rate.

Effective in imaging inverse problems.

Leverages pretrained deep denoising networks as priors.

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 priors.