Fast volumetric Cartesian MRI with auto-calibrated local B0 coil array – a reproducing kernel Hilbert space perspective

Motivation: The local B0 coil array has been shown to speed up 2D Cartesian MRI and provides a platform for investigating the most efficient B0 encoding fields. Nevertheless, optimizing the rapid modulations for accelerating volumetric scans without introducing additional artifacts becomes more challenging. Goal(s): We explore distinct nonlinear modulation B0 fields and reconstruct artifact-free accelerated images. Approach: With a recent RKHS framework, the k-space efficiency maps for various modulation fields are analyzed, and a novel auto-calibration reconstruction method is introduced. Results: Our k-space analysis provides insights validating optimal modulation fields, and the ex-vivo and in-vivo scans demonstrate the robustness of the proposed reconstruction technique. Impact: We demonstrate the RKHS formalism as a valuable tool for understanding 3D MRI scans encoded with nonlinear modulation fields. Our auto-calibration reconstruction, analogous to GRAPPA in parallel imaging, offers a promising approach for image acceleration with rapid B0 modulation.