title: Continuous and discrete data rebinning in time-of-flight PET.
abstract: 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.
authors.affiliation: Department of Nuclear Medicine, Vrije Universiteit Brussel, B-1090 Brussels, Belgium. michel.defrise@vub.ac.be
authors.forename: Michel
authors.initials: M
authors.lastname: Defrise
authors.forename: Vladimir
authors.initials: V
authors.lastname: Panin
authors.forename: Christian
authors.initials: C
authors.lastname: Michel
authors.forename: Michael E
authors.initials: ME
authors.lastname: Casey
mesh_terms: D000465:Algorithms; D006801:Humans; D007089:Image Enhancement / Q000379:methods*; D007090:Image Interpretation, Computer-Assisted / Q000379:methods*; D021621:Imaging, Three-Dimensional / Q000379:methods*; D019047:Phantoms, Imaging; D049268:Positron-Emission Tomography / Q000379:methods*; D015203:Reproducibility of Results; D012680:Sensitivity and Specificity; D012815:Signal Processing, Computer-Assisted; D013909:Thorax / Q000000981:diagnostic imaging*