Fast Parallel Magnetic Resonance Imaging Reconstruction Based on Sparsifying Transform Learning and Structured Low-Rank Model

doi:10.1007/s12204-023-2647-2

Abstract

Abstract: The structured low-rank model for parallel magnetic resonance (MR) imaging can efficiently reconstruct MR images with limited auto-calibration signals. To improve the reconstruction quality of MR images, we integrate the joint sparsity and sparsifying transform learning (JTL) into the simultaneous auto-calibrating and k-space estimation (SAKE) structured low-rank model, named JTLSAKE. The alternate direction method of multipliers is exploited to solve the resulting optimization problem, and the optimized gradient method is used to improve the convergence speed. In addition, a graphics processing unit is used to accelerate the proposed algorithm. The experimental results on four in vivo human datasets demonstrate that the reconstruction quality of the proposed algorithm is comparable to that of JTL-based low-rank modeling of local k-space neighborhoods with parallel imaging (JTL-PLORAKS), and the proposed algorithm is 46 times faster than the JTL-PLORAKS, requiring only 4 s to reconstruct a 200 × 200 pixels MR image with 8 channels.

Key words: structured low-rank, parallel magnetic resonance imaging, sparsifying transform learning, alternating direction method of multipliers, optimized gradient method

摘要： 结构化低秩并行磁共振成像模型在自校准信号受限的情况下，可以有效地重构出磁共振图像，但其计算量大导致重构时间长，而难以得到临床应用。为了提高并行磁共振图像的重构质量和重构速度，将联合稀疏变换学习(JTL)与SAKE结构化低秩重构模型结合，使用交替方向乘子法对模型进行求解，并引入优化梯度法提高收敛速度。另外，使用图形处理器进行加速，从而得到一种并行磁共振成像快速重构算法JTLSAKE。通过对四组人类活体的并行磁共振成像数据集进行重构实验可以看出，提出的JTLSAKE算法可以获得与基于JTL的PLORAKS算法相当的重构质量，并且重构速度提高了43倍以上，重构200×200 pixels的8通道磁共振图像仅需4 s。

关键词: 结构化低秩，并行磁共振成像，联合稀疏变换学习，交替方向乘子法，优化梯度法

CLC Number:

TP391
R45

Duan Jizhong, Xu Yuhán, Huang Huan. Fast Parallel Magnetic Resonance Imaging Reconstruction Based on Sparsifying Transform Learning and Structured Low-Rank Model[J]. J Shanghai Jiaotong Univ Sci, 2025, 30(3): 499-509.

References

[1] DONOHO D L. Compressed sensing [J]. IEEE Transactions on Information Theory, 2006, 52(4): 1289- 1306.

[2] PRUESSMANN K P, WEIGER M, SCHEIDEGGER M B, et al. SENSE: Sensitivity encoding for fast MRI [J]. Magnetic Resonance in Medicine, 1999, 42(5): 952-962.

[3] CANDES E J, ROMBERG J, TAO T. Robust uncertainty principles: Exact signal reconstruction from highly incomplete frequency information [J]. IEEE Transactions on Information Theory, 2006, 52(2): 489-509.

[4] LUSTIG M, DONOHO D, PAULY J M. Sparse MRI: The application of compressed sensing for rapid MR imaging [J]. Magnetic Resonance in Medicine, 2007, 58(6): 1182-1195.

[5] YANG J F, ZHANG Y, YIN W T. A fast alternating direction method for TVL1-L2 signal reconstruction from partial Fourier data [J]. IEEE Journal of Selected Topics in Signal Processing, 2010, 4(2): 288-297.

[6] RAVISHANKAR S, BRESLER Y. MR image reconstruction from highly undersampled k-space data by dictionary learning [J]. IEEE Transactions on Medical Imaging, 2011, 30(5): 1028-1041.

[7] RAVISHANKAR S, BRESLER Y. Efficient blind compressed sensing using sparsifying transforms with convergence guarantees and application to MRI [J]. SIAM Journal on Imaging Sciences, 2015, 8(4): 2519-2557.

[8] WEN B H, LI Y J, BRESLER Y. Image recovery via transform learning and low-rank modeling: The power of complementary regularizers [J]. IEEE Transactions on Image Processing, 2020, 29: 5310-5323.

[9] WEN B H, RAVISHANKAR S, PFISTER L, et al. Transform learning for magnetic resonance image reconstruction: From model-based learning to building neural networks [J]. IEEE Signal Processing Magazine, 2020, 37(1): 41-53.

[10] GRISWOLD M A, JAKOB P M, HEIDEMANN R M, et al. Generalized autocalibrating partially parallel acquisitions (GRAPPA) [J]. Magnetic Resonance in Medicine, 2002, 47(6): 1202-1210.

[11] LUSTIG M, PAULY J M. SPIRiT: Iterative selfconsistent parallel imaging reconstruction from arbitrary k-space [J]. Magnetic Resonance in Medicine, 2010, 64(2): 457-471.

[12] SHIN P J, LARSON P E Z, OHLIGER M A, et al. Calibrationless parallel imaging reconstruction based on structured low-rank matrix completion [J]. Magnetic Resonance in Medicine, 2014, 72(4): 959-970.

[13] HALDAR J P, ZHUO J W. P-LORAKS: Low-rank modeling of local k-space neighborhoods with parallel imaging data [J]. Magnetic Resonance in Medicine, 2016, 75(4): 1499-1514.

[14] KIM T H, HALDAR J P. LORAKS software version 2.0: Faster implementation and enhanced capabilities [R]. Los Angeles: University of Southern California, 2018.

[15] HALDAR J P. Autocalibrated loraks for fast constrained MRI reconstruction [C]//2015 IEEE 12th International Symposium on Biomedical Imaging. Brooklyn: IEEE, 2015: 910-913.

[16] LIU Y L, YI Z Y, ZHAO Y J, et al. Calibrationless parallel imaging reconstruction for multislice MR data using low-rank tensor completion [J]. Magnetic Resonance in Medicine, 2021, 85(2): 897-911.

[17] DUAN J Z, LIU C, LIU Y, et al. Adaptive transform learning and joint sparsity based PLORAKS parallel magnetic resonance image reconstruction [J]. IEEE Access, 2020, 8: 212315-212326.

[18] CHANG C H, YU X D, JI J X. Compressed sensing MRI reconstruction from 3D multichannel data using GPUs [J]. Magnetic Resonance in Medicine, 2017, 78(6): 2265-2274.

[19] ULLAH I, NISAR H, RAZA H, et al. QRdecomposition based SENSE reconstruction using parallel architecture [J]. Computers in Biology and Medicine, 2018, 95: 1-12.

[20] MURPHY M, ALLEY M, DEMMEL J, et al. Fast 1-SPIRiT compressed sensing parallel imaging MRI: Scalable parallel implementation and clinically feasible runtime [J]. IEEE Transactions on Medical Imaging, 2012, 31(6): 1250-1262.

[21] KIM D, FESSLER J A. On the convergence analysis of the optimized gradient method [J]. Journal of Optimization Theory and Applications, 2017, 172(1): 187-205.

[22] GOLDSTEIN T, O’DONOGHUE B, SETZER S, et al. Fast alternating direction optimization methods [J]. SIAM Journal on Imaging Sciences, 2014, 7(3): 1588- 1623.

[23] FESSLER J A. Optimization methods for magnetic resonance image reconstruction: Key models and optimization algorithms [J]. IEEE Signal Processing Magazine, 2020, 37(1): 33-40.