High throughput CUDA implementation of accurate geometric modelling for iterative reconstruction of PET data

An approach to high throughput and high accuracy modelling of the geometric component of PET acquisition for the Siemens Biograph mMR PET/MR scanner is presented. The geometric components calculated in forward and back-projections are computationally expensive, however, they are inherently parallel and therefore, they are suitable for implementation on parallel computing platforms such as CUDA, consequently permitting more accurate and computationally involved system models. The key aspects of this work are: (1) accurate modelling of the geometric component of each tube of response (TOR) by tracing multiple lines for each TOR to account for the varying sensitivity along and across the TOR; (2) decomposition of the calculations into transaxial and axial components allowing the use of ray and voxel-driven methods optimal for forward and back-projection, respectively. Such decomposition also allows keeping exact correspondence between the ray and voxel-driven methods for forward and backprojection. (3) Due to the large axial field of view and the high number of crystal rings (64), the core ray-tracing is taking place in the axial dimension by projecting the transaxial calculations on each direct and oblique sinogram element. (4) Axially oriented arrangement of the images and sinograms in the GPU memory enables more efficient use of the L2 cache and together with point (3) it leads to more optimal performance even without the use of shared memory. Currently, for the Biograph mMR scanner geometry the projections are calculated within two seconds.