A Novel Iterative Image Reconstruction Method for High-Resolution PET Imaging with a Monte Carlo Based Positron Range Model

Positron range is one of the fundamental factors that limit the spatial resolution of positron emission tomography (PET). While empirical expressions are available to describe positron range in homogenous media, analytical calculation of positron range in biological objects where complex bone/tissue/air boundaries exist is extremely difficult. One solution is to use Monte Carlo (MC) simulation. However, on-the-fly MC simulation of positron migration is computationally intensive and is impractical to be used in every forward and back projection operation in an iterative image reconstruction algorithm. To address this problem, we have developed a maximum a posteriori (MAP) reconstruction algorithm with residual correction capability. To reduce the computational cost, the new algorithm uses a simplified, but computationally efficient system model in reconstruction and uses MC simulation to remove the reconstruction artifacts caused by the simplified system model. We performed computer simulations using the Geant4 MC simulation package to validate the proposed method. The results demonstrate that the proposed method is much more computationally efficient than the traditional MC-based MAP algorithm, and produces higher resolution images than the method that uses the simplified system matrix alone.