LOR-OSEM: statistical PET reconstruction from raw line-of-response histograms

Iterative statistical reconstruction methods are becoming the standard in positron emission tomography (PET). Conventional maximum-likelihood expectation-maximization (MLEM) and ordered-subsets (OSEM) algorithms act on data which have been pre-processed into corrected, evenly-spaced histograms; however, such pre-processing corrupts the Poisson statistics. Recent advances have incorporated attenuation, scatter and randoms compensation into the iterative reconstruction. The objective of this work was to incorporate the remaining pre-processing steps, including arc correction, to reconstruct directly from raw unevenly-spaced line-of-response (LOR) histograms. This exactly preserves Poisson statistics and full spatial information in a manner closely related to listmode ML, making full use of the ML statistical model. The LOR-OSEM algorithm was implemented using a rotation-based projector which maps directly to the unevenly-spaced LOR grid. Simulation and phantom experiments were performed to characterize resolution, contrast and noise properties for 2D PET. LOR-OSEM provided a beneficial noise-resolution tradeoff, outperforming AW-OSEM by about the same margin that AW-OSEM outperformed pre-corrected OSEM. The relationship between LOR-ML and listmode ML algorithms was explored, and implementation differences are discussed. LOR-OSEM is a viable alternative to AW-OSEM for histogram-based reconstruction with improved spatial resolution and noise properties.