Self-calibrated interpolation of non-Cartesian data with GRAPPA in parallel imaging

Purpose: To develop a non-Cartesian k-space reconstruction method using self-calibrated region-specific interpolation kernels for highly accelerated acquisitions. Methods: In conventional non-Cartesian GRAPPA with through-time GRAPPA (TT-GRAPPA), the use of region-specific interpolation kernels has demonstrated improved reconstruction quality in dynamic imaging for highly accelerated acquisitions. However, TT-GRAPPA requires the acquisition of a large number of separate calibration scans. To reduce the overall imaging time, we propose Self-calibrated Interpolation of Non-Cartesian data with GRAPPA (SING) to self-calibrate region-specific interpolation kernels from dynamic undersampled measurements. The SING method synthesizes calibration data to adapt to the distinct shape of each region-specific interpolation kernel geometry, and uses a novel local k-space regularization through an extension of TT-GRAPPA. This calibration approach is used to reconstruct non-Cartesian images at high acceleration rates while mitigating noise amplification. The reconstruction quality of SING is compared with conjugate-gradient SENSE and TT-GRAPPA in numerical phantoms and in vivo cine data sets. Results: In both numerical phantom and in vivo cine data sets, SING offers visually and quantitatively similar reconstruction quality to TT-GRAPPA, and provides improved reconstruction quality over conjugate-gradient SENSE. Furthermore, temporal fidelity in SING and TT-GRAPPA is similar for the same acceleration rates. G-factor evaluation over the heart shows that SING and TT-GRAPPA provide similar noise amplification at moderate and high rates. Conclusion: The proposed SING reconstruction enables significant improvement of acquisition efficiency for calibration data, while matching the reconstruction performance of TT-GRAPPA.