Optimized weighting for Fourier rebinning of three-dimensional time-of-Flight PET data to non-time-of-flight

Time-of-flight (TOF) PET scanners provide the potential for significantly improved signal-to-noise ratio (SNR) and lesion detectability in clinical PET. Therefore, it is likely that TOF will become the standard for clinical whole body PET in the near future. However, fully 3D TOF PET image reconstruction is a challenging task due to the huge data size. One solution to this problem is to rebin TOF data into a lower dimensional format. We have recently developed Fourier rebinning methods for mapping TOF data into non-TOF formats and achieved substantial SNR advantages over sinograms acquired without TOF information. However, such mappings for rebinning into non-TOF formats are not unique and optimization of rebinning methods has not been widely investigated. In this paper we address the question of optimal rebinning in order to make full use of TOF information and consequently to maximize image quality. We focus on FORET-3D, which rebins 3D TOF data into 3D non-TOF sinogram formats without requiring a Fourier transform in the axial direction. We optimize the weighting for FORET-3D using a uniformly minimum variance unbiased (UMVU) estimator under reasonable approximations. We show that the rebinned data with optimal weights are a sufficient statistic for the unknown image, implying that any information loss due to rebinning is as a result only of the approximations used in developing the optimal weighting. We demonstrate using simulated and real phantom TOF data that the optimal rebinning method achieves significant variance reduction and better contrast recovery compared to other rebinning weightings.