Restoration of lost frequency in OpenPET imaging: comparison between the method of convex projections and the maximum likelihood expectation maximization method.

We are developing a new PET scanner based on the "OpenPET" geometry, which consists of two detector rings separated by a gap. One item to which attention must be paid is that OpenPET image reconstruction is classified into an incomplete inverse problem, where low-frequency components are truncated. In our previous simulations and experiments, however, the OpenPET imaging was made feasible by application of iterative image reconstruction methods. Therefore, we expect that iterative methods have a restorative effect to compensate for the lost frequency. There are two types of reconstruction methods for improving image quality when data truncation exists: one is the iterative methods such as the maximum-likelihood expectation maximization (ML-EM) and the other is an analytical image reconstruction method followed by the method of convex projections, which has not been employed for the OpenPET. In this study, therefore, we propose a method for applying the latter approach to the OpenPET image reconstruction and compare it with the ML-EM. We found that the proposed analytical method could reduce the occurrence of image artifacts caused by the lost frequency. A similar tendency for this restoration effect was observed in ML-EM image reconstruction where no additional restoration method was applied. Therefore, we concluded that the method of convex projections and the ML-EM had a similar restoration effect to compensate for the lost frequency.