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A GPU-based Modified Conjugate Gradient Method for Accelerating Wave-CAIPI Reconstruction

Haifeng Wang¹, Shi Su¹, Xin Liu¹, Yuchou Chang², and Dong Liang¹

¹Shenzhen Institutes of Advanced Technology, Chinese Academy of Sciences, Shenzhen, China, ²Department of Computer Science and Technology Engineering, University of Houston-Downtown, Houston, TX, United States

Synopsis

Wave-CAIPI is a novel 3D imaging method with corkscrew trajectory in k-space to speed up MRI acquisition. However, the 3D data acquisitions of Wave-CAIPI are also tremendous for reconstruction calculations. In order to accelerate the reconstruction procedure, we realized a Wave-CAIPI reconstruction using a modified GPU-based conjugate gradient (CG) algorithm to reduce time cost of reconstructions. The experiments of in vivo human brain dataset show that using our GPU-based Wave-CAIPI reconstruction can achieve similar image results as the conventional CPU-based Wave-CAIPI reconstruction with less time cost than the conventional CPU-based Wave-CAIPI reconstruction.

Introduction

Recently, Wave-CAIPI is a new 3D imaging method with corkscrew trajectory in k-space to speed up MRI acquisition ¹. Different from the traditional parallel imaging methods ^2-4, Wave-CAIPI combines and extends the 2D-CAIPI ⁵ and Bunched phase encoding (BPE) ⁶ strategies by simultaneously playing sinusoidal Gy and Gz gradients. However, the 3D data acquisitions of Wave-CAIPI are tremendous for reconstruction calculations, which cannot achieve real-time processing. Currently, the modern competitive platforms of graphics processing unit (GPU) become more and more powerful to accelerate reconstruction computations for the real-time needs of clinical applications. So, in this work, we developed a GPU-based Wave-CAIPI reconstruction using modified conjugate gradient (CG) algorithm ⁷ based on NVIDIA CUDA platforms ⁸ to reduce time cost of Wave-CAIPI reconstructions. The experiments of in vivo 7T dataset of human brain show that using our GPU-based Wave-CAIPI reconstruction can achieve similar image results as the conventional CPU-based Wave-CAIPI reconstruction and reduce more 70.9% computation time cost than the conventional CPU-based reconstruction. Moreover, the modified GPU-based CG algorithm can be easy to be transplanted to other similar applications.

Theory and Methods

It is known that the CG method 7 is an optimization algorithm for the numerical solution of linear equations which is implemented as an iterative algorithm. The Wave-CAIPI reconstruction is a optimization problem that can be formulated as a least-squares minimization problem solved by an iterative LSQR algorithm ¹. Here, the iterative LSQR algorithm minimizes $$$\parallel A(x)-y\parallel_2^2$$$ , where $$$A(\cdot)$$$ is the encoding function of Wave-CAIPI reconstruction, while x and y are respectively the unknown image rows and the wave coil data in this equation. Because data is tremendous and every unknown image row has to solve an iterative minimization problem, the reconstruction procedure of CPU-based Wave-CAIPI is frequently slower than CPU-based 2D-CAIPI ⁵. In order to accelerate reconstruction calculation speed of Wave-CAIPI, we solve the least-squares problem with the GPU-based a modified CG method ^7-10. As seen as the Fig. 1, the algorithm flow of the modified GPU-based CG method is expressed, and the encoding function $$$A(\cdot)$$$ of the Wave-CAIPI applications on GPU is also described. Here, retrospectively acceleration factor was Ry×Rz=3×3. And, the center 48×48 region of k-space was applied to estimate the sensitivity maps by ESPIRiT ¹¹. The current point spread function (PSF) estimation uses three fully sampled calibration scans (i.e. no wave, wave gradient y, wave gradient z).

Results

The dataset were scanned at 7T MR scanners (Siemens AG, Erlangen, Germany) with 32-channel head coils and 3D Wave-CAIPI sequence (FOV: 224×224×120 mm³; voxel size: 1×1×2 mm³; maximum wave gradient amplitude: 6 mT/m; maximum slew rate: 50 mT/m; 7 sinusoidal wave cycles per readout) ¹. All reconstruction calculations were running on the MATLAB (MathWorks Inc., Natick, Massachusetts, USA) and CUDA (NVIDIA Corp., Santa Clara, California, USA) platforms. Here, the workstation platform has CPU is Intel (R) Core(TM) i7-4770 Dual-Core (3.4G Hz, 8M Cache); GPU is NVIDIA GTX770 (1536 CUDA Cores, 1.2G Hz); RAM is 8G; OS is Microsoft Windows 6 64-bit. Here, the acceleration factors are all Rz× Ry = 3×3; Rz is the acceleration factor along Z direction; Ry is the acceleration factor along Y direction. Fig. 2 shows the comparison of the BPE and Wave-CAIPI reconstruction with GPU-based CG methods. The GPU-based Wave-CAIPI reconstruction only spends 9 seconds which is about 70.9% time cost of the previous CPU-based Wave-CAIPI reconstruction. At the same time, the GPU-based BPE reconstruction also spends about 55.6% time cost of the corresponding CPU-based reconstructions. And, Fig. 3 shows that the reconstruction results of 2D CAIPI, CPU-based and GPU-based BPE, and CPU-based and GPU-based Wave-CAIPI. Here, they show very similar reconstruction results visually. To quantitatively compare them, Fig.4 illustrated that the difference maps between Wave-CAPI and 2D CAIPI respectively based on GPU and CPU. Simultaneously, the difference maps between BPE and 2D CAIPI also present for comparisons. The proposed GPU-based Wave-CAPI reconstruction with the modified CG reconstruction method has less computational time cost than the conventional CPU-based reconstruction and still reserves the similar details as the conventional CPU-based results.

Discussion and Conclusion

In sum, we implement the proposed GPU-based Wave-CAPI reconstruction with the modified CG minimization algorithm to accelerate the conventional CPU-based Wave-CAIPI reconstruction. The current reconstruction results of the proposed methods have shown the attractive potential of reducing time cost of the Wave-CAPI reconstruction from tremendous dataset. In the future, more optimal GPU-based algorithm of the Wave-CAIPI reconstruction will be studied to achieve faster data processing.

Acknowledgements

The authors also thank Dr. Berkin Bilgic, Michael Saunders and Chris Fougner for their open-source codes. This study is partial supported by the grant from the National Science Foundation of China (No. 61471350, No. 81729003, No. 61871373), Guangdong Provincial Key Laboratory of Medical Image Processing (No. 2017A050501026), National Science Foundation of Guangdong (No. 2018A0303130132).

References

1. Bilgic B, Gagoski BA, Cauley SF, Fan AP, Polimeni JR, Grant PE, Wald LL, Setsompop K. Wave-CAIPI for highly accelerated 3D imaging. Magn Reson Med. 2015 Jun;73(6):2152-62.

2. Sodickson DK, Manning WJ. Simultaneous acquisition of spatial harmonics (SMASH): fast imaging with radiofrequency coil arrays. Magn Reson Med. 1997 Oct;38(4):591-603.

3. Pruessmann KP, Weiger M, Scheidegger MB, Boesiger P. SENSE: sensitivity encoding for fast MRI.Magn Reson Med. 1999 Nov;42(5):952-62.

4. Griswold MA, Jakob PM, Heidemann RM, Nittka M, Jellus V, Wang J, Kiefer B, Haase A. Generalized autocalibrating partially parallel acquisitions (GRAPPA). Magn Reson Med. 2002 Jun;47(6):1202-10.

5. Breuer FA, Blaimer M, Mueller MF, Seiberlich N, Heidemann RM, Griswold MA, Jakob PM. Controlled aliasing in volumetric parallel imaging (2D CAIPIRINHA). Magn Reson Med. 2006 Mar; 55(3):549-56.

6. Moriguchi H, Duerk J. Bunched phase encoding (BPE): a new fast data acquisition method in MRI. Magn Reson Med 2006; 55.3:633-648.

7. Hestenes MR, Stiefel E, Methods of conjugate gradients for solving linear systems. Journal of Research of the National Bureau of Standards. 1952 Dec; 49 (6). doi:10.6028/jres.049.044.

8. NVIDIA Corp., 2017. GPU-Accelerated Libraries https://developer.nvidia.com/

9. Saunders M, CGLS: CG method for Ax = b and Least Squares, 2017; http://web.stanford.edu/group/SOL/software/cgls/.

10. Fougner C, Conjugate Gradient for Least Squares in CUDA, 2017; https://github.com/foges/cgls_cuda.

11. Uecker M, Lai P, Murphy MJ, Virtue P, Elad M, Pauly JM, Vasanawala SS, Lustig M. ESPIRiT-An Eigenvalue Approach to Autocalibrating Parallel MRI: Where SENSE Meets GRAPPA. Magnet Reson Med 2014;71(3):990-1001.

Figures

Fig 1. Algorithm flow of the proposed GPU-based Wave-CAIPI reconstruction with the modified CG algorithm on the NVIDIA CUDA platform.

Fig 2. Time-cost comparison of the BPE and Wave-CAIPI reconstructions based CPU and GPU on the MATLAB and NVIDIA CUDA platforms. Here, the acceleration factors are all Rz× Ry = 3×3; Rz is the acceleration factor along Z direction; Ry is the acceleration factor along Y direction.

Fig 3. Reconstruction comparison of 2D CAIPI, BPE and Wave-CAIPI reconstructions based on CPU and GPU at the acceleration factors of Rz× Ry = 3×3.

Fig 4. Difference maps between 2D CAIPI and the two reconstruction methods, BPE and Wave-CAIPI, respectively based on CPU and GPU at the acceleration factors of Rz× Ry = 3×3.

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

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