摘要： Fully 3D time-of-flight (TOF) PET scanners offer the potential of substantially improved image quality in clinical PET imaging. The main challenges of 3D TOF PET imaging are the data storage with either list-mode or binned formats, and the reconstruction time using iterative algorithms. Previously, we derived the Fourier rebinning and consistency equations (FORCEs), and showed 3D TOF data can be fully characterized by two consistency equations. In this work, we present an exact Fourier rebinning for 3D TOF data based on the axial consistency equation to dramatically reduce the data storage and the reconstruction time. Starting from pre-corrected 3D TOF data, the axial Fourier rebinning algorithm estimates a 2D TOF sinogram for each transverse slice without information loss. Since the 3D TOF data are axially truncated, we provide a solution to estimate the missing portion in the oblique TOF projection data. The proposed axial Fourier rebinning for TOF data (axFRT) can take advantage of all the 3D TOF data statistics, and the rebinned 2D TOF data can then be reconstructed using any algorithms for 2D or 2.5D TOF reconstructions. The axFRT algorithm allows the axial data sets being rebinned independently, and there are tens of thousands of such data sets which can naturally take advantage of the massively parallel processors to dramatically speedup the rebinning. We show numerical simulations to demonstrate that axFRT produces accurate and unbiased rebinned sinograms even for TOF PET with large axial acceptance angle. The axFRT will be particularly useful for 3D TOF PET with large axial field of view for PET imaging applications including dynamic, whole- or total-body imaging.