Fast PET reconstruction with variance reduction and prior-aware preconditioning

We investigated 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 because they are widely used in clinical practice and have been shown to outperform conventional early-stopped and post-smoothed ordered subset expectation maximization. Our study evaluated these methods using 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 compared 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 evaluated their performance for varying count levels and regularization strengths. The results showed 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.