Accelerated time-of-flight (TOF) PET image reconstruction using TOF bin subsetization and TOF weighting matrix pre-computation

Time-of-flight (TOF) positron emission tomography (PET) technology has recently regained popularity in clinical PET studies for improving image quality and lesion detectability. Using TOF information, the spatial location of annihilation events is confined to a number of image voxels along each line of response, thereby the cross-dependencies of image voxels are reduced, which in turns results in improved signal-to-noise ratio and convergence rate. In this work, we propose a novel approach to further improve the convergence of the expectation maximization (EM)-based TOF PET image reconstruction algorithm through subsetization of emission data over TOF bins as well as azimuthal bins. Given the prevalence of TOF PET, we elaborated the practical and efficient implementation of TOF PET image reconstruction through the pre-computation of TOF weighting coefficients while exploiting the same in-plane and axial symmetries used in pre-computation of geometric system matrix. In the proposed subsetization approach, TOF PET data were partitioned into a number of interleaved TOF subsets, with the aim of reducing the spatial coupling of TOF bins and therefore to improve the convergence of the standard maximum likelihood expectation maximization (MLEM) and ordered subsets EM (OSEM) algorithms. The comparison of on-the-fly and pre-computed TOF projections showed that the pre-computation of the TOF weighting coefficients can considerably reduce the computation time of TOF PET image reconstruction. The convergence rate and bias-variance performance of the proposed TOF subsetization scheme were evaluated using simulated, experimental phantom and clinical studies. Simulations demonstrated that as the number of TOF subsets is increased, the convergence rate of MLEM and OSEM algorithms is improved. It was also found that for the same computation time, the proposed subsetization gives rise to further convergence. The bias-variance analysis of the experimental NEMA phantom and a clinical FDG-PET study also revealed that for the same noise level, a higher contrast recovery can be obtained by increasing the number of TOF subsets. It can be concluded that the proposed TOF weighting matrix pre-computation and subsetization approaches enable to further accelerate and improve the convergence properties of OSEM and MLEM algorithms, thus opening new avenues for accelerated TOF PET image reconstruction.