Unified Motion Correction and Reconstruction for Accelerated Zero Echo Time MRI

Zero echo time (ZTE) MRI is near-silent, but dead time gaps, head motion, and undersampling jointly degrade reconstruction. To develop an accelerated ZTE MRI reconstruction framework that jointly estimates the 3D image and rigid-motion parameters, this work introduces Energy-based Motion Correction (EnMoCo), a regularized maximum a posteriori (MAP) formulation that also compensates for missing k-space center data and angular undersampling artifacts. Solved by alternating between k-space rigid-motion updates and conjugate-gradient data-consistency updates, the framework incorporates regularization via a pre-trained Multi-Scale Energy-based model (MuSE) implemented in a data-efficient 2.5D form. Evaluations on simulated and in vivo 3D ZTE data, spanning dead time gaps of 1.5 to 5 samples, rotations up to 17 degrees and translations up to 10 mm, demonstrate that EnMoCo significantly improves PSNR and SSIM relative to CG-SENSE and Autofocusing baselines (achieving roughly 10 to 15 dB higher PSNR for gaps >= 3.5) while reducing motion blur and tissue contrast inconsistencies.