PET Reconstruction Using Generalized Natural Pixels and a Monte Carlo Generated System Matrix

The spatially variant detector response can reduce spatial resolution in PET imaging. In iterative reconstruction methods, the detector response can be modeled into the system response matrix (SRM). Unfortunately, the SRM for current PET scanners can be very large. We have been evaluating PET reconstruction using generalized natural pixel (GNP) functions. With these pixel functions, the SRM becomes block-circulant for a ring-PET scanner, thereby substantially reducing the number of non-redundant elements in the SRM. Application of the generalized natural pixel functions assumes a perfect rotationally symmetric system. There are no such PET scanners in reality. We developed a method to correct and match an actual PET scanner geometry to a virtual rotationally symmetric system. The Geant4 based GATE Monte Carlo simulation code was used to model a 2D version of the Philips Allegro PET scanner consisting of one ring with 616 GSO crystals. The simulation code modeled all interactions within the detector. To evaluate and compare reconstruction algorithms, a simulated 2D phantom and two physical phantoms were used to collect simulated or experimental LOR-binned fan beam sinogram data. Reconstruction was performed using either an algebraic reconstruction technique (ART) with generalized natural pixels, or a LOR-based maximum-likelihood expectation maximization algorithm (MLEM) using Siddon ray tracing. We studied the contrast versus noise as a function of iteration number. The GNP-ART method clearly outperforms the LOR-MLEM with higher contrast at the same noise level. This can be simply attributed to the improvement of spatial resolution in GNP-ART by modeling spatially variant detector response in the SRM.