Efficient Constrained Reconstruction of Non-Cartesian Time-Segmented Data with Implicit GROG and Polynomial Preconditioning

Motivation: Fast, regularized subspace reconstruction would enable the acquisition and synthesis of a standard clinical brain protocol in mere minutes. Goal(s): Our goal is to make high-resolution, image reconstruction faster and more robust to $$$B_0$$$ inhomogeneities. Approach: Our reconstruction alternates between data consistency (DC) and spatio-temporal low rank regularization. We leverage coil sensitivities to "snap" non-Cartesian trajectories to the kspace grid, speeding up DC steps and enabling $$$B_0$$$-robust reconstructions with fewer time segments. Polynomial preconditioning enables convergence in up to 2x fewer iterations, reducing expensive proximal updates. Results: Our method reduces the reconstruction time by an order of magnitude while retaining quality. Impact: The ability to reconstruct MRF quickly should make integration of MRF into clinical workflows not just possible, but convenient. Additionally, the efficiency gains from this framework can make even the most sophisticated and expensive regularizers computationally feasible.