Image-Space Gridding for Nonrigid Motion-Corrected MR Image Reconstruction

Motion remains a major challenge in magnetic resonance (MR) imaging, particularly in free-breathing cardiac MR imaging, where data are acquired over multiple heartbeats at varying respiratory phases. We adopt a model-based approach for nonrigid motion correction, addressing two challenges: (a) motion representation and (b) motion estimation. For motion representation, we derive image-space gridding by adapting the nonuniform fast Fourier transform (NUFFT) to represent and compute nonrigid motion, which provides an exact forward-adjoint pair of linear operators. We then introduce nonrigid SENSE operators that incorporate nonrigid motion into the multi-coil MR acquisition model. For motion estimation, we employ both low-resolution 3D image-based navigators (iNAVs) and high-resolution 3D self-navigating image-based navigators (self-iNAVs). During each heartbeat, data are acquired along two types of non-Cartesian trajectories: a subset of a high-resolution trajectory that sparsely covers 3D k-space, followed by a full low-resolution trajectory. We reconstruct 3D iNAVs for each heartbeat using the full low-resolution data, which are then used to estimate bulk motion and identify the respiratory phase of each heartbeat. By combining data from multiple heartbeats within the same respiratory phase, we reconstruct high-resolution 3D self-iNAVs, allowing estimation of nonrigid respiratory motion. For each respiratory phase, we construct the nonrigid SENSE operator, reformulating the nonrigid motion-corrected reconstruction as a standard regularized inverse problem. In a preliminary study, the proposed method enhanced sharpness of the coronary arteries and improved image quality in non-cardiac regions, outperforming translational motion-corrected reconstruction.