Continuous and discrete data rebinning in time-of-flight PET

This paper investigates data compression methods for time-of-flight (TOF) positron emission tomography (PET), which rebin the 3-D TOF measurements into a set of 2-D TOF data for a stack of transaxial slices. The goal of this work is to develop rebinning algorithms that are more accurate than the TOF single-slice-rebinning (TOF-SSRB) method proposed by Mullani in 1982. Two approaches are explored. The first one is based on a partial differential equation, which expresses a consistency condition for TOF-PET data with a Gaussian TOF profile. From this equation we derive an analytical rebinning algorithm, which is unbiased in the limit of continuous sampling. The second approach is discrete: each 2-D rebinned data sample is calculated as a linear combination of the 3-D TOF samples in the same axial plane parallel to the axis of the scanner. The coefficients of the linear combination are precomputed by optimizing a cost function which enforces both accuracy and good variance reduction, models the TOF profile, the axial PSF of the LORs, and the specific sampling scheme of the scanner. Measurements of a thorax phantom on a prototype TOF-PET scanner with a resolution of 550 ps show that the proposed discrete method improves the bias-variance trade-off and is a promising alternative to TOF-SSRB when data compression is required to achieve clinically acceptable reconstruction time.