Self-Calibrated GRAPPA Operator Gridding (SC-GROG) for radially encoded Multi-Slice (SMS) Imaging



This work proposes a novel approach using Self-calibrating GRAPPA operator gridding (SC-GROG) for radially encoded simultaneous multi-slice imaging (SMS). The proposed method is implemented by combining non-Cartesian (NC) under-sampling (radial) with CAIPRINHA phase manipulation to accelerate data acquisition in SMS. Radial datasets are gridded using SC-GROG and reconstructed iteratively using Projection onto convex sets (POCS) algorithm. The results are compared with conventional NUFFT with POCS at increasing accelerations factors and quantified in terms of SSIM, PSNR and Artifact Power. It can be inferred from the results that the proposed method produces accurate reconstructions of SMS datasets.


Multi-slice excitation (SMS) is a rapidly advancing medical imaging technique which involves simultaneous sampling of multiple parallel slices. SMS accelerates MR data acquisition and the acceleration depends on the number of excited slices. Non-Cartesian (NC) trajectories (such as radial, spiral etc) can be used to achieve higher acceleration factors (AF) for multi-slice MR imaging [3]. However, NC trajectories need an extra pre-reconstruction interpolation step called “gridding”. Self-calibrating GRAPPA Operator Gridding (SC-GROG) [2] can be applied to map the NC samples to the closest Cartesian locations. In this work, we propose the use of SC-GROG based gridding for radially encoded SMS data. In the proposed method, we combine the phase manipulation used in CAIPIRINHA with NC (radial) under-sampling to achieve high acceleration factors (AF). Projection onto Convex Sets (POCS) (an iterative reconstruction algorithm) is used to remove the streaking artifacts produced due to radial under-sampling. For comparison purposes, NUFFT (a gold-standard gridding method) [1] interpolation is performed on the multi-slice data with POCS reconstruction. Several experiments are performed using in-vivo datasets containing multiple slices to evaluate the efficacy of the proposed technique (SC-GROG with POCS reconstruction). The reconstructed images are evaluated using Structural Similarity Index Measure (SSIM), Peak signal-to-noise ratio (PSNR) and Artifact Power (AP).


The following steps describe the methodology of the proposed method (Figure 1): (i) Radial CAIPRINHA phase cycling shifts each slice in the phase encoding direction according to Fourier shift theorem [4], (ii) SC-GROG grids the under-sampled NC samples to their nearest Cartesian locations (iii) POCS (an iterative reconstruction technique) is employed on the gridded multi-slice data for the recovery of true slices (iv) the process repeats until it reaches maximum number of iterations which are determined using the “maximum iterations” check (stopping criteria in this work) [4]. The proposed method SC-GROG gridding using POCS reconstruction for multi-slice images is tested on in vivo T2 weighted TSE multi-slice datasets acquired at Siemens Tim Trio 3T scanner with 32 channel head-coil having dimensions(256x256x32x7), compressed to 12 PCA channels to reduce memory requirements. The data was obtained online from (ISMRM workshop, 19-22 July 2015, Pacific Grove, CA, USA https://www.ismrm.org/workshops/MultiSlice15/stream.htm [7]).For experimentation purpose all the seven slices were tested but only four simultaneous slices (3,4,5,6) are displayed in Figure 2(a), 2(b) and 2(c). The multi-slice data sets are retrospectively under-sampled at various acceleration factors, i.e., (AF=2,4,8,10,14). The maximum number of iterations (stopping criteria) for POCS reconstruction are optimally selected to minimize the reconstruction errors empirically. All the methods in this work were implemented in MATLAB (Mathworks, Natick, MA) and run on Intel(R) Core (TM) i3-4010U CPU @1.70 GHz with 4GBMemory.


We performed several experiments on in-vivo 3T human head data to validate the performance of the proposed method on multi-slice data for different acceleration factors compared with gold standard NUFFT gridding. Figure 2(a) shows the reconstructed slices using the proposed method (top row) and conventional NUFFT reconstruction with POCS (bottom row) at AF=2. Results show that SC-GROG gridding using POCS reconstruction produces artifact free images as compared to pre-reconstruction using NUFFT where some artifacts are still visible. Figure 2(b) and 2(c) show the results for AF=8 and AF=14. It can be deduced by visual inspection that the proposed method produces better reconstructions and the artifacts are clearly removed. However, in the case of conventional NUFFT method, the artifacts keep on increasing with higher acceleration factors and the reconstructed images get degraded visibly. The quality of the reconstructed images is further evaluated using SSIM, PSNR and AP. The results show that the proposed method provides considerable improvement in the reconstructed images as compared to conventional NUFFT with POCS reconstruction, i.e., improvement in terms of SSIM, PSNR and AP (Table 1).


This work presents an implementation of self-calibrating GRAPPA operator gridding (SC-GROG) with POCS reconstructions for under-sampled radial multi-slice acquisitions. The proposed method achieves a significant removal of artifacts in the reconstructed slices without compromising the reconstruction accuracy at different acceleration factors.


No acknowledgement found.


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2. Seiberlich, N., Breuer, F. A., Blaimer, M., Barkauskas, K., Jakob, P. M. and Griswold, M. A. (2007), Non-Cartesian data reconstruction using GRAPPA operator gridding (GROG). Magn. Reson. Med., 58: 1257–1265. doi:10.1002/mrm.21435

3. Barth, M., Breuer, F., Koopmans, P. J., Norris, D. G. and Poser, B. A. (2016), Simultaneous multislice (SMS) imaging techniques. Magn. Reson. Med., 75: 63–81. doi:10.1002/mrm.25897

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7. ISMRM workshop 19-22 July 2015, Pacific Grove, CA,USA


Figure 1: Block diagram of SC-GROG gridding with POCS reconstruction (proposed method) explaining all steps involved in the reconstruction process, where slice 1-slice N are the T2 weighted TSE multi-slice datasets acquired at Siemens Tim Trio 3T scanner with 32 channel head-coil having dimensions(256x256x32x7), compressed to 12 PCA channels, the datasets are phase shifted using radial CAIPRINHA and retrospectively under-sampled, SC-GROG grids the non-Cartesian data points by shifting to the nearest Cartesian locations, POCS reconstruction algorithm iteratively reconstructs the gridded datasets and terminates once the stopping criteria has been met.

FIGURE 2(a): Proposed method (A-D) and conventional NUFFT (E-H) reconstructions for 3T human head images consisting of slices [3,4,5,6] for acceleration factor=2. The proposed method reconstructs images with better visual quality, while the conventional NUFFT shows appearance of some streaking artifacts.

FIGURE 2(b): Proposed method (A-D) and conventional NUFFT (E-H) reconstructions for 3T human head images consisting of slices [3,4,5,6] for acceleration factor= 8. As acceleration increases the proposed method reconstructs images removing most of the artifacts, while the conventional NUFFT reconstructions show an increase in the appearance of some streaking artifacts.

FIGURE 2(c): Proposed method (A-D) and conventional NUFFT (E-H) reconstructions for 3T human head images consisting of slices [3,4,5,6] for acceleration factor of 14. Note that proposed SC-GROG gridding with POCS reconstruction clearly removes the artifacts, while the conventional NUFFT reconstructions show further increase in the appearance of streaking artifacts.

TABLE 1: SSIM, PSNR and Artifact power values with increasing acceleration factors comparing SC-GROG gridding with POCS reconstruction (proposed) and conventional NUFFT for a randomly selected slice (slice 6) from the reconstruction results. The fully sampled 3T human head multi-slice dataset is used as a reference. Both techniques exhibit consistency in SSIM values however, there are small differences in the PSNR values for both methods. The AP values for the proposed method stay low even at high accelerations. However, the conventional NUFFT technique shows increased artifact power at high acceleration factors.

Proc. Intl. Soc. Mag. Reson. Med. 27 (2019)