Reconstruction in PET cameras with irregular sampling and depth of interaction capability

The authors present 2D reconstruction algorithms for a rectangular PET camera capable of measuring depth of interaction (DOI). The camera geometry leads to irregular radial and angular sampling of the tomographic data. DOI information increases sampling density, allowing the use of evenly spaced quartercrystal width radial bins with minimal interpolation of irregularly spaced data. In the regions where DOI does not increase sampling density (chords normal to crystal faces), fine radial sinogram binning leads to zero efficiency bins if uniform angular binning is used. These zero efficiency sinogram bins lead to streak artifacts if not corrected. To minimize these unnormalizable sinogram bins the authors use two angular binning schemes: Fixed Width and Natural Width. Fixed Width uses a fixed angular width except in the problem regions where appropriately chosen widths are applied. Natural Width uses angle widths which are derived from intrinsic detector sampling. Using a modified filtered-backprojection algorithm to accommodate these angular binning schemes, the authors reconstruct artifact free images with nearly isotropic and position independent spatial resolution. Results from Monte Carlo data indicate that the authors have nearly eliminated image degradation due to crystal penetration.