ORIGINAL RESEARCH article
Front. Nucl. Med.
Sec. Physics and Data Analysis
Volume 5 - 2025 | doi: 10.3389/fnume.2025.1641215
This article is part of the Research TopicRapid Image ReconstructionView all articles
Fast PET Reconstruction with Variance Reduction and Prior-Aware Preconditioning
Provisionally accepted
- 1University of Bath, Bath, United Kingdom
- 2University College London, London, United Kingdom
- 3Katholieke Universiteit Leuven, Leuven, Belgium
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We investigate subset-based optimization methods for positron emission tomography (PET) image reconstruction incorporating a regularizing prior. PET reconstruction methods that use a prior, such as the relative difference prior (RDP), are of particular relevance, as they are widely used in clinical practice and have been shown to outperform conventional early-stopped and post-smoothed ordered subsets expectation maximization (OSEM).Our study evaluates these methods on both simulated data and real brain PET scans from the 2024 PET Rapid Image Reconstruction Challenge (PETRIC), where the main objective was to achieve RDP-regularized reconstructions as fast as possible, making it an ideal benchmark. Our key finding is that incorporating the effect of the prior into the preconditioner is crucial for ensuring fast and stable convergence.In extensive simulation experiments, we compare several stochastic algorithms-including Stochastic Gradient Descent (SGD), Stochastic Averaged Gradient Amelioré (SAGA), and Stochastic Variance Reduced Gradient (SVRG)-under various algorithmic design choices and evaluate their performance for varying count levels and regularization strengths. The results show that SVRG and SAGA outperformed SGD, with SVRG demonstrating a slight overall advantage. The insights gained from these simulations directly contributed to the design of our submitted algorithms, which formed the basis of the winning contribution to the PETRIC 2024 challenge.
Keywords: PET, Map, preconditioning, variance reduction, stochastic gradient methods, Regularization methods, image reconstruction
Received: 04 Jun 2025; Accepted: 06 Aug 2025.
Copyright: © 2025 Ehrhardt, Kereta and Schramm. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) or licensor are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.
* Correspondence: Zeljko Kereta, University College London, London, United Kingdom
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