3D PET reconstruction with FORE and WLS-OS-EM

2D PET reconstructions by the ordered subsets version of the AIL-EM algorithm (typically referred to as "OS-EM") assume that the random- and scattered-corrected coincidence data retain their Poisson statistics. Negative projection values, which are possible after these subtractive corrections, are either truncated at zero counts or accommodated by adding an offset to the projection data, and to the corresponding forward-projected values, during the algorithm. These methods are effective due to the relatively low scatter and random fractions of most 2D PET acquisitions. In 3D PET data, particularly in acquisitions in the body, the scatter and random fractions are much higher. As a result, the OS-EM algorithm may not be the most appropriate for reconstruction for rebinned 3D PET data. We have implemented an ordered-subsets version of the weighted least-squares expectation maximization (WLS-EM) algorithm, or WLS-OS-EM, which is based on a Gaussian approximation to the statistics of the rebinned data. The weights used in the algorithm are based on the attenuation correction factors applied to the data. WLS-OS-EM exhibits faster, and more consistent, convergence than ML-OS-EM for projection data sets with substantial negative projection values created by subtractive data corrections.