Fast PET Reconstruction with Variance Reduction and Prior-Aware Preconditioning

TL;DR

This paper introduces a variance reduction technique with prior-aware preconditioning for faster, more stable PET image reconstruction, demonstrating superior performance of SVRG and SAGA algorithms over SGD in simulations and real data.

Contribution

It proposes a novel preconditioning approach that incorporates prior effects, improving convergence speed and stability in subset-based PET reconstruction algorithms.

Findings

SVRG and SAGA outperform SGD in convergence speed.

Incorporating prior effects into preconditioning is crucial.

The proposed methods won the PETRIC 2024 challenge.

Abstract

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 Amelior\'e (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.