Monte-Carlo system modeling for PET reconstruction: A rotator approach

Statistical iterative reconstruction with Monte Carlo system modeling is an effective method in improving image quality in Positron Emission Tomography ( PET). However, this approach is quite complex in case of human PET imaging due to the large memory requirements in storage and computaionally expensive simulation of the system matrix. To address these problems, we adapted a rotator based maximum likelihood expectation maximum (ML-EM) reconstruction algorithm and a fast Monte Carlo simulator. In this paper, a Gaussian rotator is used with the ML-EM algorithm. This algorithm enables the full utilization of the rotational symmetry to reduce the storage of the system matrix, as well as the simulation cost. The fast system matrix simulator is based on egs pet, a Monte Carlo code using EGSnrc. For a brain-size field of view, the system matrix storage requirement is reduced by a factor of 131,083 with regard to that of the full system matrix. This reduction is achieved by using symmetries and a sparse matrix representation. This enables the system matrix to reside in the main memory of a modern desktop. By combining the symmetry with the fast system matrix simulator, the simulation time is reduced by a factor of 9,240 with regard to an analog GATE simulation. The quality of the reconstructed image was evaluated with the contrast recovery versus background noise. Significant improvements were found with regard to the standard ray-tracing ML-EM.