Estimation of and correction for finite motion sampling errors in small animal PET rigid motion correction

Motion tracking with finite time sampling causing an associated unknown residual motion between two motion measurements is one of the factors contributing to resolution loss in small animal PET motion correction. The aim of this work is (i) to provide a means to estimate the effect of the finite motion sampling on the spatial resolution of the motion correction reconstructions and (ii) to correct for this residual motion thereby minimizing resolution loss. We calculate a tailored spatially variant deconvolution kernel from the measured motion data which is then used to deconvolve the motion corrected image using a 3D Richardson-Lucy algorithm. A simulation experiment of numerical phantoms as well as a microDerenzo phantom experiment wherein the phantom was manually moved at different speeds was performed to assess the performance of our proposed method. In the motion corrected images of the microDerenzo phantom there was an average rod FWHM differences between the slow and fast motion cases of 9.7%. This difference was reduced to 5.8% after applying the residual motion deconvolution. In awake animal experiments, the proposed method can serve to mitigate the finite sampling factor degrading the spatial resolution as well as the resolution differences between fast-moving and slow-moving animals. Graphical abstract Motion correction of positron emission tomography (PET) scans of moving subjects can be performed by measuring the motion of the subject during the PET scan with an optical tracking camera. The motion tracking data obtained from the tracking camera is then used to correct the PET image reconstructions for motion. Due to finite time sampling of the motion data, the motion corrected reconstructions suffer from loss of spatial resolution. In the proposed method, a spatially variant deconvolution kernel is calculated from the motion tracking data, which is then used to correct the motion-corrected PET reconstructions for the blurring effect of the finite motion sampling through a Richardson-Lucy deconvolution.