Figure 2.

In‐plane kernel estimation in the presence of Nyquist ghosting. This figure shows how to preprocess reference data to obtain a kernel compatible with the ghosted, accelerated data. The procedure is depicted for a single slice but needs to be repeated for all slices before readout‐concatenation. Red and blue show k‐space samples that are shifted resulting in ghosting. Please note that any form of reference data could be used (here single shot EPI) as long as it can be made ghost‐free and the individual slice ghosting of the SMS data is known. A: The accelerated data together with an overlay of a 5x4 kernel. The lines indicate the source points that are needed to fill in the missing value at the location of the orange dot (please note that the coil dimension is omitted here for clarity). The gray line visualizes the frequency of the ghosting pattern. B: The reference data with the same kernel. Blue source points display a mismatch with the actual data. The cause is the higher frequency of the shifting pattern (grey zigzag line). The gray kernel outline indicates the next k_y‐location for a kernel of this polarity (i.e., within the odd–even framework), shown translated in the read dimension for better visualization. C: The proposed fix to the reference data. The ghosting pattern in panel B is corrected and a new pattern is introduced that matches that of panel A. The changed periodicity causes the k_y‐location of the next kernel (gray) to shift as well. This would reduce the number of equations in the inversion because, the purple samples are never used as source points. This can be avoided by introducing multiple shifting patterns, where the phase of the pattern is modified, and combining the sets of equations obtained before matrix inversion. D: A phase cycled variant of the zigzag pattern to increase the number of equations. The number of cycles required is equal to the in‐plane acceleration factor.