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Purpose, To develop a high scanning efficiency, motion corrected imaging strategy for free-breathing pulmonary MRI by combining a motion compensation reconstruction with a UTE acquisition, called iMoCo UTE. Methods, An optimized golden angle ordering radial UTE sequence was used to continuously acquire data for 5 minutes. All readouts were grouped to different respiratory motion states based on self-navigator signals, then motion resolved data was reconstructed by XD Golden angle RAdial Sparse Parallel reconstruction (XD GRASP). One state from the motion resolved images was selected as a reference, and motion fields from the other states to the reference were derived via non-rigid registration. Finally, all motion resolved data and motion fields were reconstructed by using an iterative motion compensation reconstruction with a total generalized variation sparse constraint. Results, The iMoCo UTE strategy was evaluated in volunteers and non-sedated pediatric patient(4-6 y/o) studies. Images reconstructed with iMoCo UTE provided sharper anatomical lung structures, and higher apparent SNR and CNR, compared to using other motion correction strategies, such as soft-gating, motion resolved reconstruction, and non-rigid motion compensation(MoCo). iMoCo UTE also showed promising results in an infant study. Conclusions, The proposed iMoCo UTE combines self-navigation, motion modeling, and a compressed sensing reconstruction to increase scan efficiency, SNR, and reduce respiratory motion in lung MRI. This proposed strategy shows improvements in free breathing lung MRI scans, especially in very challenging application situations, such as pediatric MRI studies.