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

TL;DR

This work addresses the computational bottlenecks in variational tomography by introducing ProxSkip-VR, which combines data-splitting-based variance-reduced gradients with random proximal skipping. The approach yields two complementary cost reductions: cheaper gradient evaluations via subsets of measurements and reduced proximal computations via probabilistic skipping of the regulariser step. Empirical results on TV tomography with real data and PnP-BM3D on simulated data demonstrate substantial speed-ups (typically 5× to over 20×) without compromising reconstruction quality. The findings support broader adoption of ProxSkip-VR in large-scale inverse problems and open avenues for accelerator-enhanced schemes and extensions to other imaging modalities.

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.

Figures (5)

• Figure 1: Left: FBP reconstruction of the post–partial oxidation of methane reaction Matras2021 and high-accuracy reference (TV-regularised) solution, computed with $2\times 10^{5}$ PDHG iterations using diagonal preconditioning ChambollePock_2011_Diagonal. Right: Example of data splitting ($N=5$) using staggered indexing for the projection angles: $b_k=\{k,\,k+5,\,k+10,\,\ldots\}$ for $k=0,\ldots,4$.
• Figure 2: CPU time for TV proximal (10/100 iterations), BM3D, deterministic/stochastic gradients, and full stochastic gradients for different $N$.
• Figure 3: ProxSVRG vs ProxSVRGSkip comparison in terms of data passes (left) and time (right). Top: fixed number of subsets $N$ and varying probabilities $p$. Bottom: Fixed probability $p$ and varying number of subsets N.
• Figure 4: Convergence (relative error vs. CPU time) for TV tomography reconstruction with 10 (top) and 100 (bottom) inner iterations. Only methods reaching the target accuracy $10^{-5}$ within our computational budget are shown.
• Figure 5: PnP–BM3D tomographic reconstruction on simulated foam data (3-minute budget). Top: ground truth, FBP, and reconstructions from all algorithms. Middle: PSNR (left) and SSIM (right) versus wall-clock time. The number of subsets is $N=50$ with $p=0.05$ and $\#$BM3D denotes the number of calls for the BM3D denoiser.