Maximum-Likelihood Joint Image Reconstruction/Motion Estimation in Attenuation-Corrected Respiratory Gated PET/CT Using a Single Attenuation Map

This work provides an insight into positron emission tomography (PET) joint image reconstruction/motion estimation (JRM) by maximization of the likelihood, where the probabilistic model accounts for warped attenuation. Our analysis shows that maximum-likelihood (ML) JRM returns the same reconstructed gates for any attenuation map (
$\mu$
-map) that is a deformation of a given
$\mu$
-map, regardless of its alignment with the PET gates. We derived a joint optimization algorithm accordingly, and applied it to simulated and patient gated PET data. We first evaluated the proposed algorithm on simulations of respiratory gated PET/CT data based on the XCAT phantom. Our results show that independently of which
$\mu$
-map is used as input to JRM: (i) the warped
$\mu$
-maps correspond to the gated
$\mu$
-maps, (ii) JRM outperforms the traditional post-registration reconstruction and consolidation (PRRC) for hot lesion quantification and (iii) reconstructed gated PET images are similar to those obtained with gated
$\mu$
-maps. This suggests that a breath-held
$\mu$
-map can be used. We then applied JRM on patient data with a
$\mu$
-map derived from a breath-held high resolution CT (HRCT), and compared the results with PRRC, where each reconstructed PET image was obtained with a corresponding cine-CT gated
$\mu$
-map. Results show that JRM with breath-held HRCT achieves similar reconstruction to that using PRRC with cine-CT. This suggests a practical low-dose solution for implementation of motion-corrected respiratory gated PET/CT.