Pre-computed system matrix calculation based on a piece-wise method for PET

A system matrix (SM) is the basic component of iterative image reconstruction algorithms. Calculation of the SM needs a considerable amount of time due to an enormous number of lines of response (LORs) being modeled. In this study, we developed a technique based on a piece-wise calculation method in which symmetry and further division of the voxels are applied. The detector response function for all detectable pairs of photons along certain LORs originating from each voxel is calculated analytically. The total number of LORs in 300 × 300 × 120 voxels (with 2 × 2 × 2 mm(3)) is ~44 billion, and the SM was calculated by the use of three different computers independently; the calculation time was 5 h. The SM took 5 days when calculated by the use of the conventional method (where symmetry and the piece-wise method are not used). The sensitivity correction factor was stored; it had a size of 42 MB in a four-byte computer memory.