MARMI: Marginalizing Anatomical Uncertainty for MRI Motion Inference

Patient motion in multi-shot magnetic resonance imaging (MRI) introduces k-space inconsistencies that depend jointly on the motion trajectory and the underlying anatomy, making the two difficult to disentangle from the acquired measurements. A motion-free auto-calibration signal (ACS) anchors the reference pose but only partially constrains the corresponding anatomy, leaving motion estimation intrinsically ambiguous. We introduce MARMI (Marginalized Anatomical References for Motion Inference), a framework that models ACS-conditioned anatomical uncertainty and marginalizes it during amortized shot-wise motion inference on a compact central k-space representation. MARMI consists of two complementary components. Specifically, Conditional Anatomical Residual Sampling (CARS) generates plausible motion-free references by modeling the anatomical content not determined by the ACS, providing a direct physical interpretation of the unobserved frequencies. Reference-Marginalized Motion Inference (RAMI) then evaluates these references through a motion-aware MRI forward model and aggregates their physical evidence for motion estimation. On fastMRI FLAIR, marginalizing multiple ACS-conditioned references reduces normalized motion error by 10–13% relative to a single sampled reference. MARMI also outperforms JSMoCo and MoPED in motion-corrected reconstruction across the tested ACS and acceleration settings, and extends to 0.3 T M4Raw and an adapted in-house 0.55 T cohort. Together, these results show that modeling the partially observed reference as a latent distribution provides a principled strategy for disentangling motion from anatomy.