Continuous and Discrete Data Rebinning in Time-of-Flight PET

• Published in: IEEE transactions on medical imaging 2008-09, Vol.27 (9), p.1310-1322
• Main Authors: Defrise, M., Panin, V., Michel, C., Casey, M.E.
• Format: Article
• Language: English
• Subjects: Algorithm design and analysis; Algorithms; Cost function; Data compression; Humans; Image Enhancement - methods; Image Interpretation, Computer-Assisted - methods; Image reconstruction; Imaging phantoms; Imaging, Three-Dimensional - methods; Partial differential equations; Phantoms, Imaging; Positron emission tomography; positron emission tomography (PET); Positron-Emission Tomography - methods; Prototypes; Reproducibility of Results; Sampling methods; Sensitivity and Specificity; Signal Processing, Computer-Assisted; Studies; Thorax; Thorax - diagnostic imaging; Time measurement
• ISSN: 0278-0062; 1558-254X
• DOI: 10.1109/TMI.2008.922688

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 re- binning 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.