Motion correction based on an appropriate system matrix for statistical reconstruction of respiratory-correlated PET acquisitions

Respiratory motion correction in positron emission tomography (PET) seeks to incorporate motion information into an image reconstruction algorithm by using the full counting statistics of an acquisition to generate a single, motion-free volume. Here, we present a motion-incorporated ordered subsets expectation maximization (MOSEM) reconstruction based on a device-dedicated tomographic projector in which each matrix element is calculated directly from the voxels' Cartesian coordinates alone. The motion is corrected by updating this projector as a function of the respiratory level. The performance of the reconstruction method was investigated with three datasets: two simulations of a transaxially or axially moving lesion on a patient acquisition and a third acquisition of a moving sphere. After the 16th sub-iteration, the normalized mean square error (NMSE, with a motionless acquisition as reference) was 0.20 for the non-corrected (ungated) image and 0.01 for the MOSEM image with transaxial motion simulation. Likewise, NMSE was 0.30 for the ungated image and 0.03 for MOSEM image with axial motion simulation. For the phantom, ungated reconstruction yielded an error of 0.78, whereas MOSEM yielded 0.43. The error reduction resulted from enhancement and reduced spreading of the moving uptake. Our results show that MOSEM reconstruction yields motion-corrected images which are similar to motionless reference images.