  Purpose: To investigate motion compensated, self-supervised, model based deep
learning (MBDL) as a method to reconstruct free breathing, 3D Pulmonary
ultrashort echo time (UTE) acquisitions.
  Theory and Methods: A self-supervised eXtra Dimension MBDL architecture
(XD-MBDL) was developed that combined respiratory states to reconstruct a
single high-quality 3D image. Non-rigid, GPU based motion fields were
incorporated into this architecture by estimating motion fields from a low
resolution motion resolved (XD-GRASP) iterative reconstruction. Motion
Compensated XD-MBDL was evaluated on lung UTE datasets with and without
contrast and was compared to constrained reconstructions and variants of
self-supervised MBDL that do not consider respiratory motion.
  Results: Images reconstructed using XD-MBDL demonstrate improved image
quality as measured by apparent SNR, CNR and visual assessment relative to
self-supervised MBDL approaches that do not account for dynamic respiratory
states, XD-GRASP and a recently proposed motion compensated iterative
reconstruction strategy (iMoCo). Additionally, XD-MBDL reduced reconstruction
time relative to both XD-GRASP and iMoCo.
  Conclusion: A method was developed to allow self-supervised MBDL to combine
multiple respiratory states to reconstruct a single image. This method was
combined with GPU-based image registration to further improve reconstruction
quality. This approach showed promising results reconstructing a user-selected
respiratory phase from free breathing 3D pulmonary UTE acquisitions.
