To compare four parallel imaging reconstruction algorithms for simultaneous multi-slice (SMS) imaging $$$^{1,2}$$$. Algorithms under consideration include SENSE/GRAPPA combination $$$^3$$$, slice-GRAPPA $$$^4$$$, split-slice-GRAPPA $$$^5$$$ and hybrid-space SENSE $$$^6$$$.

Brain data from a regular single-slice acquisition are used to simulate SMS acquisitions. The single-slice data are acquired on a GE 3T MR750 scanner (GE Healthcare, Waukesha, WI) with a SMS gradient echo EPI sequence using a 32-channel head coil (Nova Medical, Wilminton, MA). Experiments are approved by our university's institutional review board. The simulated CAIPI $$$^{4,7}$$$ acquisition has 5 simultaneous slices, no inplane-acceleration, a FOVy/3 interslice shift, and a 100$$$\times$$$100 matrix size.

Reconstructions are offline in Matlab (the MathWorks, Natick, MA). Geometric-decomposition coil compression $$$^8$$$ is applied to compress the 32 channels into 10 channels. Sensitivity maps for hybrid-space SENSE are computed using an eigenvalue approach $$$^9$$$.

A region of interest (ROI) is defined for the head. The relative root-mean-squared errors (RRMS) $$$^{10}$$$ inside the ROI are calculated between the reconstructed and the ground truth single-slice images. The simulation is then repeated 100 times with injected random noise. The pseudo-multiple replica method $$$^{11}$$$ is used to calculate the g-factor basing on the 100 repeated reconstructions. Finally, signal leakage $$$^{5,12}$$$ from the 2nd band into the other bands is calculated. The leaked signals are normalized by the amplitude of the original single-slice data to generate values for display.

Images from all reconstructions exhibit no visual differences (Fig. 1). Although the noise pattern outside the brain is different for GRAPPA-type than for SENSE reconstructions, the errors inside the brain are small and exhibit no structural patterns across all reconstruction algorithms (Fig. 1). Compared to the three GRAPPA-type reconstructions, whose g-factor maps are very similar, hybrid-space SENSE shows relatively elevated g-factor values (Fig. 2). Slice-GRAPPA shows a high signal leakage level, whereas all the other reconstruction methods have similarly low leakage level (Fig. 3).

For SENSE/GRAPPA combination, slice-GRAPPA, split-slice-GEAPPA and hybrid-space SENSE respectively, the mean RRMS error inside the head ROI is 0.0470, 0.0371, 0.0384 and 0.0398 (Fig. 4a). The mean g-factor inside the head ROI is 1.0760, 1.0886, 1.0879 and 1.1763 (Fig. 4b). The mean signal leakage is 0.0442, 0.2632, 0.0377 and 0.0367 (Fig. 4c). SENSE/GRAPPA combination is fast to reconstruct 1 replica, but relatively slow to reconstruct 100 replicas (Fig. 4d). The reason is that its kernel fitting process is fast but its data interpolating process is slow because the interpolation is conducted on big matrices corresponding to a concatenation of all simultaneous slices and additional zero matrices. Split-slice-GRAPPA is slower than slice-GRAPPA by a fixed amount of time which corresponds to the difference in their kernel training processes (Fig. 4d). Hybrid-space SENSE is slow to reconstruct 1 replica because of the time needed for the sensitivity map calculation. Once the sensitivity maps are calculated, adding more replicas imposes small impact on the reconstruction time (Fig. 4d). It is worth pointing out that the above results are reported for our current implementation and that implementation details may dramatically affect the reconstruction time. For example, when we changed the Matlab 'pinv' function used in hybrid-space SENSE to a backslash operator, the reconstruction time for 1 replica reduced from approximately 60 seconds to approximately 30 seconds.

All four algorithms provide good reconstruction quality with reasonable computation time. Overall speaking, split-slice-GRAPPA appears to be the best among the four to reconstructe data from CAIPI acquisions. Slice-GRAPPA provides very similar reconstruction quality to split-slice-GRAPPA but exhibits high signal leakage problem, which indicates it allows more signal from the wrong sources to go into the reconstructed images. SENSE/GRAPPA combination exhibits slightly higher RRMS errors than split-slice-GRAPPA but also provides slightly better SNR. The main drawback is that it may take longer to reconstruct a time seires. Hybrid-space SENSE performs well except for higher noise amplification. We think the noise enhancement originates from the difficulty to get an accurate sensitivity estimation given imperfections in the calibration data. For example, residual Nyquist ghosting in the single-slice EPI data used in this simulation may contribute to errors in the sensitivity map estimation. It is worth noting that only hybrid-space SENSE is compatible with arbitrary Cartesian SMS undersampling patterns, including incoherent non-CAIPI type patterns such as the zigzag $$$^{13}$$$ and MICA $$$^6$$$ patterns. It therefore has value to serve as a more generic reconstruction method for Cartesian SMS acquisitions.