Following continuous improvement in PET spatial resolution, respiratory motion correction
has become an important task. Two of the most common approaches that utilize all detected
PET events to motion-correct PET data are the reconstruct-transform-average method
(RTA) and motion-compensated image reconstruction (MCIR). In RTA, separate images
are reconstructed for each respiratory frame, subsequently transformed to one reference
frame and finally averaged to produce a motion-corrected image. In MCIR, the projection
data from all frames are reconstructed by including motion information in the system
matrix so that a motion-corrected image is reconstructed directly. Previous theoretical
analyses have explained why MCIR is expected to outperform RTA. It has been suggested
that MCIR creates less noise than RTA because the images for each separate respiratory
frame will be severely affected by noise. However, recent investigations have shown
that in the unregularized case RTA images can have fewer noise artefacts, while MCIR
images are more quantitatively accurate but have the common salt-and-pepper noise.
In this paper, we perform a realistic numerical 4D simulation study to compare the
advantages gained by including regularization within reconstruction for RTA and MCIR,
in particular using the median-root-prior incorporated in the ordered subsets maximum
a posteriori one-step-late algorithm. In this investigation we have demonstrated that
MCIR with proper regularization parameters reconstructs lesions with less bias and
root mean square error and similar CNR and standard deviation to regularized RTA.
This finding is reproducible for a variety of noise levels (25, 50, 100 million counts),
lesion sizes (8 mm, 14 mm diameter) and iterations. Nevertheless, regularized RTA
can also be a practical solution for motion compensation as a proper level of regularization
reduces both bias and mean square error.