Fast and accurate motion-corrected reconstruction with motion-correcting Implicit GROG (motion-iGROG)

Motivation: Emerging motion-tracking strategies provide high-temporal-motion information, but full-motion-corrected reconstruction time scales poorly, increasing linearly with the number of motion-states due to accounting for changes in relative-position between coils and patient, and background-image-phase. Goal(s): Develop a fast and accurate motion-corrected reconstruction suitable for Cartesian and non-Cartesian sampling, where reconstruction time remains similar to non-motion-corrected cases. Approach: This work proposes applying implicit-GROG, a technique for rapidly generating GRAPPA-kernels, to unify motion-corrupted k-space data across variations in coil-sensitivity-shading and image-phase. Results: Across simulated and real motion-corrupted brain-data at 3T and 7T, motion-iGROG achieves comparable reconstruction to full motion-corrected reconstruction with an order of magnitude-faster speed. Impact: Motion-iGROG enables rapid and accurate motion-corrected and background-phase-changed reconstruction, which could be employed synergistically with emerging high-temporal motion-tracking methods, such as pilot tone and advanced motion navigators, where 100s of motion states are obtained across each imaging scan.