Evaluation of two approaches to motion-corrected PET image reconstruction

Motion correction is a major task in PET. This study aims to understand the behaviour of different approaches to motion-corrected image reconstruction in terms of convergence rates and the properties of the images obtained. We have studied two approaches that have been suggested to motion-correct PET gated data. The first method, RRA, is based on independent reconstructions of each gate which are then registered to a reference gate and averaged. On the other hand, in the second method, MCIR, all data are used with the motion information within a single reconstruction. As a first step, this investigation compares the methods with no motion present. Multiple simulations have been produced with counts approximating a 5 min PET thorax acquisition. The image bias and variance are the main figures of merit. The results show different convergence and statistics performance between the two methods. RRA converges faster than MCIR but not at the correct value. Considering the trade-off between bias and variance, it is seen that MCIR outperforms RRA. It has been also demonstrated that, although at higher iterations RRA has lower variance and higher bias than MCIR, at a low number of iterations the performance of the methods becomes closer. This investigation has revealed the statistical and computational discrepancies between RRA and MCIR when motion is not present and MCIR is shown to be clearly superior.