# Stochastic Primal-Dual Hybrid Gradient Algorithm with Arbitrary Sampling and Imaging Applications

## TL;DR

This paper introduces a stochastic primal-dual hybrid gradient algorithm with arbitrary sampling, extending previous deterministic methods and demonstrating superior performance in imaging applications.

## Contribution

It presents a novel stochastic extension of the primal-dual hybrid gradient algorithm that handles arbitrary sampling and improves imaging task results.

## Key findings

- Outperforms deterministic variants in imaging tasks
- Handles general convex-concave saddle point problems
- Supports arbitrary sampling of dual variables

## Abstract

We propose a stochastic extension of the primal-dual hybrid gradient algorithm studied by Chambolle and Pock in 2011 to solve saddle point problems that are separable in the dual variable. The analysis is carried out for general convex-concave saddle point problems and problems that are either partially smooth / strongly convex or fully smooth / strongly convex. We perform the analysis for arbitrary samplings of dual variables, and obtain known deterministic results as a special case. Several variants of our stochastic method significantly outperform the deterministic variant on a variety of imaging tasks.