Learning efficient non-rigid registration in k-space for accelerated Magnetic Resonance Imaging

Non-rigid motion estimation at high temporal resolution is essential for dynamic and real-time Magnetic Resonance Imaging (MRI), yet remains challenging due to the spatio-temporal sampling limitations of accelerated acquisitions. Conventional motion estimation pipelines typically reconstruct images before performing registration. However, the high undersampling required to achieve high temporal resolution degrades image quality and introduces artifacts that corrupt the spatial structures needed for reliable feature matching. Direct k-space-based registration approaches bypass image reconstruction, but often require auxiliary prior information or rely on localized processing, limiting their ability to capture global contextual representations while increasing workflow and computational complexity. In this work, we propose the Local-All Pass Attention Network (LAPANet), an image registration framework for direct non-rigid motion estimation from accelerated multi-coil k-space data. LAPANet learns a global, multi-scale decomposition of the spectral phase structure, where non-rigid motion is modeled as spatially varying phase variations in k-space. Evaluated on cardiac MRI, the proposed method accurately recovers motion from as few as 2 lines/frame in a Cartesian trajectory and 3 spokes/frame in a non-Cartesian radial trajectory. Under these high acceleration settings, existing image-based and k-space-based registration methods fail to maintain anatomically plausible motion estimates. LAPANet enables reconstruction-free non-rigid motion estimation at sub-5 ms temporal resolution with inference times suitable for online deployment, supporting real-time tracking, motion-robust reconstruction, and interventional MRI.