Discrete axial rebinning for time-of-flight PET

Recent developments in PET allow the measurement of the time-of-flight (TOF) difference between the two coincident photons with a resolution between 500 ps and 1 ns FWHM. This information leads to improved signal-to-noise ratio when imaging large patients [Ref. l]-[Ref. 4], see [Ref. 5] for additional references. The additional TOF measurement also has some side benefits, including faster convergence of iterative reconstruction algorithms and, when working with histogrammed data, an improved robustness to angular undersampling. The latter property has been exploited to reduce the number of axial and transaxial angular samples without compromising spatial resolution, thereby allowing a significant acceleration of fully 3D iterative reconstruction. This work pursues the study of 2D rebinning for TOF-PET. We investigate algorithms in which rebinning is performed separately for each axial plane parallel to the axis of the scanner, that is, for each pair of sinogram variables (s, phi). Such algorithms will be called axial rebinning algorithms. The TOF-SSRB method, for example, belongs to that family. Axial rebinning algorithms are attractive because they can be applied directly to the raw (s,phi) samples defined by the transaxial arrangement of the detectors in each ring. This eliminates the need to pre-interpolate the data on a grid of uniformly spaced s samples (the arc correction) or to fill gaps in the data due to missing detectors. In addition, maintaining the native (s, phi) sampling should allow a more accurate modeling of the transaxial point-spread-function (PSF) during 2D iterative reconstruction. The goal of this work, therefore, is to develop axial rebinning algorithms that are more accurate than TOF-SSRB. Two approaches are explored: an analytical approach (section II) and a discrete approach (section III).