Why do we regularise in every iteration for imaging inverse problems?

TL;DR

This paper investigates the application of the ProxSkip algorithm, originally for federated learning, to imaging inverse problems, demonstrating it can accelerate computations without sacrificing reconstruction quality.

Contribution

It introduces the novel PDHGSkip algorithm and evaluates ProxSkip's effectiveness in various imaging inverse problems, showing significant computational speedups.

Findings

ProxSkip reduces computational time in imaging inverse problems.

PDHGSkip is a new variant tailored for these problems.

Methods maintain high-quality reconstructions despite acceleration.

Abstract

Regularisation is commonly used in iterative methods for solving imaging inverse problems. Many algorithms involve the evaluation of the proximal operator of the regularisation term in every iteration, leading to a significant computational overhead since such evaluation can be costly. In this context, the ProxSkip algorithm, recently proposed for federated learning purposes, emerges as an solution. It randomly skips regularisation steps, reducing the computational time of an iterative algorithm without affecting its convergence. Here we explore for the first time the efficacy of ProxSkip to a variety of imaging inverse problems and we also propose a novel PDHGSkip version. Extensive numerical results highlight the potential of these methods to accelerate computations while maintaining high-quality reconstructions.