Stochastic Primal-Dual Hybrid Gradient Algorithm with Arbitrary Sampling and Imaging Applications
This work addresses computational efficiency in imaging applications, representing an incremental improvement over existing deterministic methods.
The authors tackled the problem of solving saddle point problems in imaging by proposing a stochastic extension of the primal-dual hybrid gradient algorithm, which significantly outperformed deterministic variants on various imaging tasks.
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.