Monte Carlo noise in full Monte Carlo ML-EM and dual matrix reconstructions in positron emission tomography

Monte Carlo (MC) simulations in positron emission tomography (PET) play an important role in detector modeling and algorithm testing. Nowadays, these simulation are also increasingly used for scatter correction during reconstruction. This can be done ideally by using MC simulations to calculate the system matrix including scatter (full matrix approach). Another approach to incorporate MC simulations into the reconstruction is using a MC based projector and attenuation based back-projector, avoiding the storage of the matrix (dual matrix (DM) approach). It appears desirable to compare these two methods for PET and investigate the reconstruction accuracy in the light of MC noise. For this purpose a method to estimate the error introduced by the matrix, the sinogram or the projector based on repeated simulations with different MC seeds is introduced. Simulations of a single ring scanner (due to storage limitations) were performed.