  To correct for respiratory motion in PET imaging, an interpretable and
unsupervised deep learning technique, FlowNet-PET, was constructed. The network
was trained to predict the optical flow between two PET frames from different
breathing amplitude ranges. The trained model aligns different
retrospectively-gated PET images, providing a final image with similar counting
statistics as a non-gated image, but without the blurring effects. FlowNet-PET
was applied to anthropomorphic digital phantom data, which provided the
possibility to design robust metrics to quantify the corrections. When
comparing the predicted optical flows to the ground truths, the median absolute
error was found to be smaller than the pixel and slice widths. The improvements
were illustrated by comparing against images without motion and computing the
intersection over union (IoU) of the tumors as well as the enclosed activity
and coefficient of variation (CoV) within the no-motion tumor volume before and
after the corrections were applied. The average relative improvements provided
by the network were 64%, 89%, and 75% for the IoU, total activity, and CoV,
respectively. FlowNet-PET achieved similar results as the conventional
retrospective phase binning approach, but only required one sixth of the scan
duration. The code and data have been made publicly available
(https://github.com/teaghan/FlowNet_PET).
