Unsupervised high-resolution 3D MRI motion correction via physics-informed implicit neural representations.

Motion-corrupted inverse problems remain a central bottleneck in magnetic resonance imaging (MRI), especially for high-resolution 3D acquisitions where long readouts couple rigid-body displacement with non-Cartesian k-space sampling. We present a physics-informed implicit neural representation (INR) that recasts 3D motion correction as continuous neural field estimation. The method embeds a differentiable rigid-body motion operator into the INR forward model, enabling joint, zero-shot optimization of the motion trajectory and motion-free volume directly from raw k-space, without external navigators or paired supervision. By enforcing strict data consistency in a coordinate-based representation, the framework yields globally coherent reconstructions and mitigates hallucination risks under severe motion. Across simulated perturbations and real in-vivo high-resolution radial scans, our approach consistently improves motion estimation accuracy, structural preservation, downstream segmentation, and generalizes across subjects and protocols. Remarkably, for kooshball acquisitions with motion severity up to 10°/20mm, our method outperforms the navigator-based method by approximately 2 dB in peak signal-to-noise ratio. These results establish a unified paradigm for unsupervised, physics-consistent artificial intelligence solving of motion-corrupted MRI inverse problems, with broad applicability beyond a single sequence or anatomy. The source code is available at: https://github.com/AMRI-Lab/MoCo-3DRadial.