Motion compensation during image reconstruction with the standard maximum likelihood-expectation maximization (ML-EM) algorithm can successfully reduce the effects of rigid object motion. Any errors in the pose measurements, however, can themselves degrade the reconstructed image – and ML-EM provides little information regarding the precision of activity values.

Researchers from the University of Sydney's Brain and Mind Centre are investigating an alternative: the origin ensembles (OE) algorithm, which provides image reconstruction along with uncertainty estimates for quantitative values extracted from the measured data. They extended the OE algorithm to incorporate motion compensation and used this to study the impact of pose data precision on awake small-animal PET (Phys. Med. Biol. 62 715).

"We investigated OE for motion compensation for two main reasons," explained first author John Gillam. "First, OE uses an ensemble of point-like emission locations, which seemed a natural fit for motion compensation without the need for interpolation in the image-space. Secondly, OE explores the full posterior and provides information about the precision of the reconstruction, which is particularly important in awake animal imaging, as each data set is affected by unique animal motion."

Scan simulations

To simulate awake small-animal PET, Gillam and colleagues measured the pose of an optical marker attached to an awake rat during a PET scan. They replayed this measured motion using a six-axis robot, and tracked the robot's motion with a large, high-accuracy marker and a small marker with greater uncertainty. The true robot pose was also measured to provide ground truth (exact) motion data.

The team generated two further precision levels: temporally filtering the small marker data to increase pose measurement precision; and generating measurements with greater uncertainty via random perturbations of the exact data. This provided five levels of pose measurement precision – exact, large-marker, small-marker, filtered small-marker and randomized exact – for use during image reconstruction.

The researchers used the GATE toolkit to simulate a microPET system with a hot rod phantom insert. They simulated data from a static and a moving phantom, using exact pose data to guide the motion, and reconstructed images using ML-EM and OE. The detected emission counts for ML-EM reconstructions, with and without motion, lay almost entirely within the uncertainty of the MMSE-OE (the minimum mean square error point-estimate) reconstruction. These findings indicate that the motion compensation approach developed for OE agrees with that used in ML-EM.

To examine the impact of voxel size and count number, the researchers simulated small (low-count) and large (high-count) data sets, incorporating phantom motion. They reconstructed images using 0.5 mm3 voxels and, for the low-count set, also using 1.0 mm3 voxels. For high-count data with small voxels, and low-count data with large voxels, the ML-EM and MMSE-OE solutions were almost identical. However, for low-count data with small voxels, the two algorithms diverged.

"It might be possible to exploit this divergence effect, which is expected to occur at a specific transition point, by using it to identify when too few events are recorded to make reliable estimates for a specific region-of-interest or voxel size," noted Gillam.

Pose measurement precision

Gillam and colleagues used the OE algorithm to analyse uncertainties in regional activity estimates arising from changes in pose measurement precision. Examining regions-of-interest (ROIs) corresponding to individual hot-rods, they reconstructed images using the five different pose measurement precisions.

In the high-count data set, posterior intensity distributions showed that regional counts decreased as the uncertainty in motion measurement worsened, for all ROIs. Temporal filtering of the pose measurements recovered counts and reduced uncertainty. For the low-count data set, the small marker induced some count losses for only the largest ROI.

Finally, the team calculated pairwise correlations between ROIs corresponding to groups of hot-rods. For exact pose measurements, a strong negative correlation was seen between the background region and all hot-rod regions, as expected. A small positive correlation between all hot-rod regions was also seen. For randomized exact measurements with greater uncertainty, this positive correlation decreased.

"While positive feature correlation provides information regarding estimated cross-talk, it can be affected by the quantity and resolution of the detected measurements, as well as the distance between the features," said Gillam. He noted that such measurements enable trade-offs between feature separation, detection resolution and data set size to be explored for system analysis and design.

The authors concluded that OE provides a powerful framework for evaluating the statistical uncertainty of voxel and regional estimates. They note that OE can also be extended to non-rigid motion compensation of respiratory or cardiac motion. "OE is also very well suited to image reconstruction in time-of-flight PET," said Gillam.

Related articles in PMB
Motion compensation using origin ensembles in awake small animal positron emission tomography
John E Gillam et al Phys. Med. Biol. 62 715
Time-of-flight PET image reconstruction using origin ensembles
Christian Wülker et al Phys. Med. Biol. 60 1919
Simulated one-pass list-mode: an approach to on-the-fly system matrix calculation
J E Gillam et al Phys. Med. Biol. 58 2377

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