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

Abstract

Monte Carlo (MC) simulations in positron emission tomography (PET) play an important role in detector modeling and algorithm testing. Whereas the simulations are widely used in a forward projection manner to accomplish this task, ideally they should be included into the reconstruction process itself. It is therefore desirable to investigate the convergence properties and the propagation of MC noise of these kinds of reconstruction algorithms. MC simulations were integrated into the maximum likelihood expectation maximization (ML-EM) algorithm in two different ways. In the full matrix approach the system matrix was calculated by running MC simulations, including scatter. This matrix was used in both the projector and the backprojector. In the dual matrix (DM) approach, MC simulations were used to incorporate scatter in the projector, whereas the backprojector only comprised attenuation. Repeated reconstructions with different MC seeds allowed a statistical analysis of the error at each iteration step and made it possible to investigate separately the propagation of the MC noise that was introduced by the sinogram, by the projector, and by the matrix. Both approaches resulted in similar images, but the DM approach with unmatched projector and backprojector yielded a faster initial convergence when compared to the ideal full matrix approach. The analysis of the noise sources for the modeled single ring scanner in full matrix reconstruction showed that the noise introduced by the matrix became comparable to the noise introduced by the sinogram when using a matrix that was simulated with 10,000 emissions/voxel.