Fourier rebinning of time-of-flight PET data

This paper explores fast reconstruction strategies for 3D time-of-flight (TOF) positron emission tomography (PET), based on 2D data rebinning. Starting from pre-corrected 3D TOF data, a rebinning algorithm estimates for each transaxial slice the 2D TOF sinogram that would have been acquired by a single-ring scanner. The rebinned sinograms can then be reconstructed using any algorithm for 2D TOF reconstruction. We introduce TOF-FORE, an approximate rebinning algorithm obtained by extending the Fourier rebinning method for non-TOF data. In addition, we identify two partial differential equations that must be satisfied by consistent 3D TOF data, and use them to derive exact rebinning algorithms and to characterize the degree of the approximation in TOF-FORE. Numerical simulations demonstrate that TOF-FORE is more accurate than two different TOF extensions of the single-slice rebinning method, and suggest that TOF-FORE will be a valuable tool for practical TOF PET in the range of axial apertures and time resolutions typical of current scanners.