Accurate attenuation modeling of rebinned 3D PET data

Rebinning is used in PET to reduce three-dimensional (3D) data to a set of stacked two-dimensional (2D) slices that can be reconstructed using a conventional 2D algorithm. Rebinning is an attractive alternative to 3D reconstruction for time-of-flight PET data because the errors made by rebinning are much smaller while the data size is much larger than for conventional 3D PET. For rebinning algorithms that require consistent projection data, attenuation correction is performed prior to rebinning. However, statistical reconstruction algorithms assume Poisson-distributed data with uncorrected data as the input and incorporate attenuation effects in the system model. The usual assumption with rebinned data is that the attenuation factor for direct 2D lines of response (LORs) is close to that for the oblique LORs that contribute to the 2D LOR during rebinning. This approximation breaks down for objects with non-uniform attenuation distributions and sharp axial attenuation discontinuities, especially for large axial acceptance angles. Average 2D attenuation factors, calculated as the weighted average of attenuation factors for LORs contributing to each rebinned LOR, is a more accurate representation of attenuation effects seen by rebinned data. The weighted attenuation factors are easily determined from the ratio of rebinned data with and without prior attenuation correction. Using the weighted attenuation factors leads to a modest reduction in image noise near attenuation discontinuities.