SPOT: SPIRiT Image Reconstruction with Custom Kernel Geometry
Yulin V Chang1, Marta Vidorreta2, Ze Wang3, and John A Detre2

1Radiology, University of Pennsylvania, Philadelphia, PA, United States, 2Neurology, University of Pennsylvania, Philadelphia, PA, United States, 3Hangzhou Normal University, Hangzhou, Zhejiang, China, People's Republic of

Synopsis

In SPIRiT image reconstruction the kernel usually consists of all elements within a square. The number of elements in such a kernel increases rapidly as the kernel size increases, especially for 3D reconstructions. Thus, a large kernel requires a sizable calibration region in k-space and demands significant time for calibration. In this work we proposed and validated a new image reconstruction approach that uses a custom SPIRiT kernel geometry, which we call SPOT. We show that a SPOT kernel is much faster to compute and results in no loss of image quality compared to the traditional SPIRiT kernel.

Purpose

SPIRiT1 is a self-calibrated parallel imaging reconstruction method that is flexible on sampling patterns. The number of elements in the reconstruction kernel (the SPIRiT kernel) increases rapidly as the kernel becomes larger, especially for 3D imaging – a kernel of 5X5X5 for a 32-channel head coil contains about 4000 elements. A large kernel generally prompts two problems for self-calibrated parallel imaging. First, a sizable calibration region/volume is required for kernel calibration, which ultimately limits the achievable acceleration. Second, calibration of a large kernel requires solving a large set of linear equations and can be computationally time consuming. A complete set of the 5X5X5X32(channel) kernel takes minutes to compute using a modern desktop computer. Therefore it is desirable to reduce the number of elements in a SPIRiT kernel without compromising its performance. In this work we sought such possibility by exploring the geometry of the SPIRiT kernels. We refer to this technique as SPOT (SPIRiT with custOm kernel geomeTry).

Theory

It was known that for a 2D SPIRiT1 or GRAPPA2,3 kernel the elements that are closer to the missing sampling point are generally more important in computing the missing point4,5. Therefore it may be feasible to remove the corner elements of a kernel without affecting the kernel performance. By doing so a 2D kernel is similar to a disk rather than a square, which we call a SPOT, as illustrated in Fig. 1. Likewise a 3D SPOT kernel is ball-shaped. The 2D and 3D SPOT kernels constructed this way contain approximately 79% (π/4) and 52% (π/6) of the elements of the original kernel, respectively. Since the computation complexity is roughly proportional to N3, where N is the number of unknowns6, such reduction in the number of elements may significantly shorten the calibration time.

Methods

We tested SPOT in both 2D and 3D imaging on a 3T whole-body scanner (Siemens Tim Trio) with a 32-channel coil. For 2D, a RARE image was acquired with a FOV of 256x256 mm2 and matrix size of 448X448 on a healthy volunteer. A random-sampling mask was applied to the k-space data to obtain a 3X under-sampled data. The images were reconstructed using both the SPIRT and SPOT 7X7 kernels shown in Fig. 1.

For 3D, stack-of-spirals7 were used for a 3D pCASL arterial spin labeling (ASL) acquisition of 2 mm isotropic resolution, collected in 4 segments (4-shot) in 35 s on a healthy volunteer. The sequence was highly accelerated and self-calibrated: the effective acceleration factor is 2.4 in the partition direction and is about 3 within each 2D axial partition. The variable-density spiral interleaves for each partition acquisition is shown in Fig. 2. The FOV is 216X216X144 mm3 (108X108X72 matrix). To maintain the high effective acceleration a moderate volume not large enough for the 7X7X7 SPIRiT kernel calibration was fully sampled and images were reconstructed using the 5X5X5 SPIRiT kernel and a 187-element 7X7X7 SPOT kernel.

Results

Figure 3 summarizes the results of 2D SPOT validation, showing that the 7X7 SPIRiT and SPOT kernels have very similar performance – their 10X magnified difference maps from the original image showed no visible difference. However, the SPIRiT calibration took 85 s while the SPOT only took 38 s. Figure 4 compares the control-label different maps of the 3D ASL image in the sagittal view. Arrows indicate improvement of image quality by using the 7X7X7 SPOT kernel.

Discussion

Our results in this study showed that for the same kernel size, a SPOT kernel a) permits a smaller calibration region (3D example) and b) significantly speeds up calibration (2D example). Conversely, for the same calibration data, SPOT may allow for a larger kernel to be used (3D example). There are potentially more benefits of SPOT that are yet to be explored. For example, a larger kernel is possibly more effective at computing missing data in each iteration and therefore fewer iterations may be required to reach the desired image quality1. The kernel geometry in SPOT is also not limited to disks or balls. In a sense, GRAPPA is a special case of SPOT where the kernel geometry is custom to the sampling pattern.

Conclusions

We showed that SPIRiT image reconstruction can be accelerated with little loss of image quality by adjusting the SPIRiT kernel geometry.

Acknowledgements

NIH P41EB015893, MH080729, 5T32HL007954

References

(1) Lustig and Pauly, MRM 2010;64:457 (2) Griswold et al. MRM 2002;47:1202 (3) Wang et al. MRM 2005;54:738 (4) Yeh et al. MRM 2005;53:1383 (5) Samsonov, MRM 2008;59:156 (6) Beatty et al. IEEE TMI 2005;24:799 (7) Vidorreta et al. NMR Biomed 2014;27:1387

Figures

Figure 1 A conventional 2D 7X7 SPIRiT kernel and an example of a 2D 7X7 SPOT kernel. The open-symbol elements outside the circle are removed.

Figure 2 The variable-density spiral interleaves used for the 3D ASL data acquisition in each axial partition.

Figure 3 Comparison of 2D SPIRiT and SPOT reconstructions for a 3X retrospectively randomly under-sampled image. The SPIRiT and SPOT images show no visible difference. All difference images were obtained by comparing with the fully sampled image.

Figure 4 Sagittal view of the difference maps of a single-pair, 4-shot accelerated stack-of-2D-axial-spirals ASL at 2 mm isotropic resolution. Images were reconstructed using a 5X5X5 SPIRiT kernel and a 7X7X7 SPOT kernel. Arrows indicate improvement by using the larger SPOT kernel.



Proc. Intl. Soc. Mag. Reson. Med. 24 (2016)
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