Split, Skip and Play: Variance-Reduced ProxSkip for Tomography Reconstruction is Extremely Fast

TL;DR

This paper introduces a novel variance-reduced, randomized skipping method for tomographic reconstruction that significantly accelerates convergence, achieving 5 to 20 times faster results than traditional approaches.

Contribution

It is the first to combine randomized skipping with variance reduction in subset-based optimization for large-scale tomographic problems.

Findings

Achieved 5x to 20x speed-ups in reconstruction times.

Demonstrated effectiveness on synthetic and real data.

Provided a foundation for broader adoption in inverse problems.

Abstract

Many modern iterative solvers for large-scale tomographic reconstruction incur two major computational costs per iteration: expensive forward/adjoint projections to update the data fidelity term and costly proximal computations for the regulariser, often done via inner iterations. This paper studies for the first time the application of methods that couple randomised skipping of the proximal with variance-reduced subset-based optimisation of data-fit term, to simultaneously reduce both costs in challenging tomographic reconstruction tasks. We provide a series of experiments using both synthetic and real data, demonstrating striking speed-ups of the order 5x--20x compared to the non-skipped counterparts which have been so far the standard approach for efficiently solving these problems. Our work lays the groundwork for broader adoption of these methods in inverse problems.