7T ultra-high field magnetic resonance parallel imaging algorithm based on residual complex convolution network

doi:10.11772/j.issn.1001-9081.2024101501

Journal of Computer Applications ›› 2025, Vol. 45 ›› Issue (10): 3381-3389.DOI: 10.11772/j.issn.1001-9081.2024101501

• Frontier and comprehensive applications • Previous Articles

7T ultra-high field magnetic resonance parallel imaging algorithm based on residual complex convolution network

Zhaoyao GAO¹^,², Zhan ZHANG²(), Liangliang HU³, Guangyu XU¹, Sheng ZHOU⁴, Yuxin HU¹^,², Zijie LIN⁵, Chao ZHOU²^,⁵

^1.School of Computer Science and Engineering，Anhui University of Science and Technology，Huainan Anhui 232001，China
^2.Center for Applied Research of Superconducting Technology，Institute of Energy，Hefei Comprehensive National Science Center （Anhui Energy Laboratory），Hefei Anhui 230031，China
^3.School of Instrument Science and Opto-electronics Engineering，Hefei University of Technology，Hefei Anhui 230009，China
^4.Hefei Xihe Superconducting Technology Company Limited，Hefei Anhui 230031，China
^5.Institute of Plasma Physics，Chinese Academy of Sciences，Hefei Anhui 230031，China

Received:2024-10-24 Revised:2025-01-10 Accepted:2025-01-16 Online:2025-02-07 Published:2025-10-10
Contact: Zhan ZHANG
About author:GAO Zhaoyao， born in 1999， M. S. candidate. His research interests include signal processing， magnetic resonance imaging reconstruction.
ZHANG Zhan， born in 1986， Ph. D.， associate research fellow. His research interests include superconducting magnet， superconducting magnetic resonance systems.
HU Liangliang， born in 1981， Ph. D.， lecturer. His research interests include magnetic resonance instruments， magnetic resonance elastography.
XU Guangyu， born in 1976， Ph. D.， associate professor. His research interests include digital image processing， machine learning.
Supported by:
Research Project of Hefei Comprehensive National Science Center （Anhui Energy Laboratory）(24JYCD01);Collaborative Innovation Project of Anhui Universities(GXXT-2022-011)

基于残差复卷积网络的7T超高场磁共振并行成像算法

高照耀¹^,², 张展²(), 胡亮亮³, 许光宇¹, 周胜⁴, 胡雨欣¹^,², 林子捷⁵, 周超²^,⁵

^1.安徽理工大学计算机科学与工程学院，安徽淮南 232001
^2.合肥综合性国家科学中心能源研究院（安徽省能源实验室）超导技术应用研究中心，合肥 230031
^3.合肥工业大学仪器科学与光电工程学院，合肥 230009
^4.合肥曦合超导科技有限公司，合肥 230031
^5.中国科学院等离子体物理研究所，合肥 230031

通讯作者: 张展
作者简介:高照耀（1999—），男，安徽滁州人，硕士研究生，主要研究方向：信号处理、核磁共振图像重建
张展（1986—），男，河北邢台人，副研究员，博士，主要研究方向：超导磁体、超导核磁共振系统 Email:zhanzhang@ie.ah.cn
胡亮亮（1981—），男，安徽岳西人，讲师，博士，主要研究方向：核磁共振仪器、磁共振弹性成像
许光宇（1976—），男，安徽合肥人，副教授，博士，CCF会员，主要研究方向：数字图像处理、机器学习。
基金资助:
合肥综合性国家科学中心能源研究院（安徽省能源实验室）项目(24JYCD01);安徽高校协同创新项目(GXXT-2022-011)

Abstract

Abstract:

Parallel imaging techniques can help solving problems of radiofrequency energy deposition and image inhomogeneity， reducing scan time， lowering motion artifacts， and accelerating data acquisition in ultra-high field Magnetic Resonance Imaging （MRI）. To enhance feature extraction ability to MRI complex-valued data and reduce wrap-around artifacts caused by under-sampling in parallel imaging， a Residual Complex convolution scan-specific Robust Artificial-neural-networks for K-space Interpolation （RCRAKI） was proposed. In the algorithm， the raw under-sampled MRI scan data was taken as input， and the advantages of both linear and nonlinear reconstruction methods were combined with a residual structure. In the residual connection part， convolution was used to create a linear reconstruction baseline， while multiple layers of complex convolution were utilized in the main path to compensate for baseline defects， ultimately reconstructing Magnetic Resonance （MR） images with fewer artifacts. Experiments were conducted on data acquired from a 7T ultra-high field MR device developed by the Institute of Energy of Hefei Comprehensive National Science Center， and RCRAKI was compared with residual scan-specific Robust Artificial-neural-networks for K-space Interpolation （rRAKI） under a sampling rate of 40 Automatic Calibration Signals （ACSs） and 8 speedup ratio for mouse imaging quality across different anatomical planes. Experimental results show that in sagittal plane， the proposed algorithm has the Normalized Root Mean Squared Error （NRMSE） decreased by 59.74%， the Structural SIMilarity （SSIM） increased by 0.45%， and the Peak Signal-to-Noise Ratio （PSNR） increased by 13.04%； in axial plane， the proposed algorithm has the NRMSE decreased by 7.97%， the SSIM improved slightly （by 0.005%）， and the PSNR increased by 1.09%； in coronal plane， the proposed algorithm has the NRMSE decreased by 35.03%， the PSNR increased by 5.60%， and the SSIM increased by 0.98%. It can be seen that RCRAKI performs well on all the different anatomical planes of MRI data， can reduce the influence of noise amplification at high speedup ratio， and reconstruct MR images with clearer details.

Key words: ultra-high field Magnetic Resonance (MR), parallel imaging, under-sampled image, complex convolution, deep learning

摘要：

并行成像技术可以帮助解决超高场强磁共振成像（MRI）中的射频能量沉积、图像均匀性的问题，缩短扫描时间，减少运动伪影，并提升数据采集速度。为了提高对MRI复值数据的特征提取能力，减少并行成像欠采样所引起的卷褶伪影，提出基于K空间插值的残差复卷积鲁棒人工神经网络（RCRAKI）。所提算法将原始欠采样MRI扫描数据作为输入，利用残差结构结合线性与非线性重建方法的优势，在残差连接部分利用卷积创建线性重建基线，主路径利用多层复卷积补偿基线缺陷，最终重建出伪影更少的磁共振（MR）图像。在合肥综合性国家科学中心能源研究院自主研发的7T超高场磁共振设备采集的数据上进行实验，并将RCRAKI与基于K空间插值的残差鲁棒人工神经网络（rRAKI）在自动校准信号（ACS）数为40、加速比为8的采样率下进行小鼠不同解剖切面成像质量对比。实验结果表明：在矢状位下，所提算法的标准化均方根误差（NRMSE）指标下降了59.74%，结构相似度（SSIM）指标提升了0.45%，峰值信噪比（PSNR）指标提升了13.04%；在横断位下，所提算法的NRMSE指标降低了7.97%，SSIM指标略有改善（提高了0.005%），PSNR指标提升了1.09%；在冠状位下，所提算法的NRMSE指标下降了35.03%，PSNR指标提升了5.60%，SSIM指标提升了0.98%。可见，RCRAKI在不同解剖切面的MRI数据上均表现出良好的性能，在高加速比采样率下能够减小噪声放大的影响，并重建出细节更清晰的MR图像。

关键词: 超高场磁共振, 并行成像, 欠采样图像, 复卷积, 深度学习

CLC Number:

TP391.41

Zhaoyao GAO, Zhan ZHANG, Liangliang HU, Guangyu XU, Sheng ZHOU, Yuxin HU, Zijie LIN, Chao ZHOU. 7T ultra-high field magnetic resonance parallel imaging algorithm based on residual complex convolution network[J]. Journal of Computer Applications, 2025, 45(10): 3381-3389.

高照耀, 张展, 胡亮亮, 许光宇, 周胜, 胡雨欣, 林子捷, 周超. 基于残差复卷积网络的7T超高场磁共振并行成像算法[J]. 《计算机应用》唯一官方网站, 2025, 45(10): 3381-3389.

Figures/Tables 14

References 26

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采样模式		算法	NRMSE	SSIM	PSNR/dB
N_ACS	rate	算法	NRMSE	SSIM	PSNR/dB
30	2	ZF	0.142 458 01	0.915 087 82	23.902 764 04
		GRAPPA	0.003 541 90	0.972 988 01	39.990 581 44
		RAKI	0.007 244 31	0.973 258 07	36.839 659 80
		rRAKI	0.003 688 19	0.974 834 25	39.818 398 06
		RCRAKI	0.003 418 73	0.975 292 60	40.035 774 10
	3	ZF	0.202 789 48	0.886 558 14	22.520 205 89
		GRAPPA	0.007 667 29	0.954 258 17	36.636 524 31
		RAKI	0.034 356 36	0.953 532 86	30.230 589 10
		rRAKI	0.009 670 57	0.957 742 94	35.970 478 28
		RCRAKI	0.006 940 29	0.957 969 19	37.176 881 87
40	2	ZF	0.127 766 00	0.926 240 51	24.267 329 98
		GRAPPA	0.003 187 30	0.976 947 79	40.448 718 44
		RAKI	0.003 727 72	0.974 463 85	40.165 202 34
		rRAKI	0.003 251 53	0.972 707 06	40.365 474 12
		RCRAKI	0.003 123 91	0.975 651 90	40.492 646 53
	4	ZF	0.210 604 28	0.888 745 30	22.204 960 71
		GRAPPA	0.019 037 45	0.906 617 11	32.686 857 65
		RAKI	0.052 912 92	0.934 690 09	28.828 713 09
		rRAKI	0.024 772 03	0.937 842 32	31.415 594 25
		RCRAKI	0.018 092 50	0.944 431 33	32.731 004 45
	8	ZF	0.200 982 87	0.880 228 27	22.408 042 13
		GRAPPA	0.085 235 68	0.779 268 26	26.176 731 60
		RAKI	0.157 800 38	0.870 278 07	23.458 552 16
		rRAKI	0.081 201 84	0.888 080 79	26.851 648 46
		RCRAKI	0.032 691 56	0.892 073 63	30.352 650 32

采样模式		算法	NRMSE	SSIM	PSNR/dB
N_ACS	rate	算法	NRMSE	SSIM	PSNR/dB
30	2	ZF	0.142 458 01	0.915 087 82	23.902 764 04
		GRAPPA	0.003 541 90	0.972 988 01	39.990 581 44
		RAKI	0.007 244 31	0.973 258 07	36.839 659 80
		rRAKI	0.003 688 19	0.974 834 25	39.818 398 06
		RCRAKI	0.003 418 73	0.975 292 60	40.035 774 10
	3	ZF	0.202 789 48	0.886 558 14	22.520 205 89
		GRAPPA	0.007 667 29	0.954 258 17	36.636 524 31
		RAKI	0.034 356 36	0.953 532 86	30.230 589 10
		rRAKI	0.009 670 57	0.957 742 94	35.970 478 28
		RCRAKI	0.006 940 29	0.957 969 19	37.176 881 87
40	2	ZF	0.127 766 00	0.926 240 51	24.267 329 98
		GRAPPA	0.003 187 30	0.976 947 79	40.448 718 44
		RAKI	0.003 727 72	0.974 463 85	40.165 202 34
		rRAKI	0.003 251 53	0.972 707 06	40.365 474 12
		RCRAKI	0.003 123 91	0.975 651 90	40.492 646 53
	4	ZF	0.210 604 28	0.888 745 30	22.204 960 71
		GRAPPA	0.019 037 45	0.906 617 11	32.686 857 65
		RAKI	0.052 912 92	0.934 690 09	28.828 713 09
		rRAKI	0.024 772 03	0.937 842 32	31.415 594 25
		RCRAKI	0.018 092 50	0.944 431 33	32.731 004 45
	8	ZF	0.200 982 87	0.880 228 27	22.408 042 13
		GRAPPA	0.085 235 68	0.779 268 26	26.176 731 60
		RAKI	0.157 800 38	0.870 278 07	23.458 552 16
		rRAKI	0.081 201 84	0.888 080 79	26.851 648 46
		RCRAKI	0.032 691 56	0.892 073 63	30.352 650 32

采样模式		算法	NRMSE	SSIM	PSNR/dB
N_ACS	rate	算法	NRMSE	SSIM	PSNR/dB
30	2	ZF	0.211 770 56	0.912 599 84	24.521 678 76
		GRAPPA	0.002 643 45	0.979 180 56	43.558 617 44
		RAKI	0.004 877 09	0.975 954 82	40.898 720 70
		rRAKI	0.002 120 70	0.986 610 08	44.515 535 79
		RCRAKI	0.002 115 99	0.986 735 50	44.525 187 70
	3	ZF	0.302 426 83	0.902 198 04	22.753 947 17
		GRAPPA	0.005 269 48	0.956 157 82	40.562 653 78
		RAKI	0.016 427 03	0.963 051 33	35.404 559 67
		rRAKI	0.004 555 08	0.969 976 73	40.972 257 38
		RCRAKI	0.004 863 32	0.974 765 66	40.690 430 18
40	2	ZF	0.145 095 88	0.938 843 77	26.163 783 79
		GRAPPA	0.002 494 39	0.978 611 48	43.810 677 93
		RAKI	0.003 309 85	0.973 819 37	42.582 248 75
		rRAKI	0.002 100 74	0.985 028 08	44.556 403 15
		RCRAKI	0.001 954 27	0.988 486 69	44.870 490 21
	4	ZF	0.410 778 12	0.903 930 86	21.644 261 61
		GRAPPA	0.011 571 58	0.928 763 84	37.146 405 88
		RAKI	0.012 008 34	0.962 025 96	36.985 504 06
		rRAKI	0.008 300 74	0.962 333 01	38.589 163 75
		RCRAKI	0.009 064 88	0.964 618 39	38.206 709 43
	8	ZF	0.433 850 05	0.901 630 24	21.406 938 09
		GRAPPA	0.061 405 57	0.860 340 73	29.898 256 81
		RAKI	0.055 075 52	0.932 176 01	30.370 748 11
		rRAKI	0.028 887 94	0.946 611 09	33.173 168 66
		RCRAKI	0.026 586 84	0.946 658 07	33.533 666 67

采样模式		算法	NRMSE	SSIM	PSNR/dB
N_ACS	rate	算法	NRMSE	SSIM	PSNR/dB
30	2	ZF	0.211 770 56	0.912 599 84	24.521 678 76
		GRAPPA	0.002 643 45	0.979 180 56	43.558 617 44
		RAKI	0.004 877 09	0.975 954 82	40.898 720 70
		rRAKI	0.002 120 70	0.986 610 08	44.515 535 79
		RCRAKI	0.002 115 99	0.986 735 50	44.525 187 70
	3	ZF	0.302 426 83	0.902 198 04	22.753 947 17
		GRAPPA	0.005 269 48	0.956 157 82	40.562 653 78
		RAKI	0.016 427 03	0.963 051 33	35.404 559 67
		rRAKI	0.004 555 08	0.969 976 73	40.972 257 38
		RCRAKI	0.004 863 32	0.974 765 66	40.690 430 18
40	2	ZF	0.145 095 88	0.938 843 77	26.163 783 79
		GRAPPA	0.002 494 39	0.978 611 48	43.810 677 93
		RAKI	0.003 309 85	0.973 819 37	42.582 248 75
		rRAKI	0.002 100 74	0.985 028 08	44.556 403 15
		RCRAKI	0.001 954 27	0.988 486 69	44.870 490 21
	4	ZF	0.410 778 12	0.903 930 86	21.644 261 61
		GRAPPA	0.011 571 58	0.928 763 84	37.146 405 88
		RAKI	0.012 008 34	0.962 025 96	36.985 504 06
		rRAKI	0.008 300 74	0.962 333 01	38.589 163 75
		RCRAKI	0.009 064 88	0.964 618 39	38.206 709 43
	8	ZF	0.433 850 05	0.901 630 24	21.406 938 09
		GRAPPA	0.061 405 57	0.860 340 73	29.898 256 81
		RAKI	0.055 075 52	0.932 176 01	30.370 748 11
		rRAKI	0.028 887 94	0.946 611 09	33.173 168 66
		RCRAKI	0.026 586 84	0.946 658 07	33.533 666 67

采样模式		算法	NRMSE	SSIM	PSNR/dB
N_ACS	rate	算法	NRMSE	SSIM	PSNR/dB
30	2	ZF	0.055 123 71	0.959 548 79	33.172 203 32
		GRAPPA	0.002 713 90	0.992 051 37	46.270 613 44
		RAKI	0.003 545 20	0.991 787 10	45.089 176 06
		rRAKI	0.002 631 07	0.993 117 37	46.384 379 77
		RCRAKI	0.002 594 87	0.993 451 56	46.444 500 00
	3	ZF	0.112 634 96	0.929 946 24	30.020 655 43
		GRAPPA	0.007 139 27	0.981 853 30	42.070 025 26
		RAKI	0.010 104 12	0.980 954 10	40.492 387 14
		rRAKI	0.005 730 24	0.985 881 26	42.955 433 68
		RCRAKI	0.005 675 46	0.987 121 30	42.997 396 27
40	2	ZF	0.033 361 68	0.972 235 18	35.353 109 07
		GRAPPA	0.002 573 55	0.992 027 74	46.501 233 27
		RAKI	0.002 873 33	0.991 949 45	46.001 754 51
		rRAKI	0.002 377 84	0.992 461 47	46.833 736 85
		RCRAKI	0.002 371 69	0.993 160 54	46.835 004 86
	4	ZF	0.077 271 58	0.947 333 11	31.705 390 53
		GRAPPA	0.018 849 08	0.957 162 85	37.853 659 80
		RAKI	0.013 300 72	0.974 484 10	39.346 810 24
		rRAKI	0.008 718 41	0.980 464 71	41.185 102 87
		RCRAKI	0.009 801 50	0.980 654 14	40.672 661 27
	8	ZF	0.121 397 84	0.932 714 97	29.743 478 68
		GRAPPA	0.084 294 66	0.880 373 03	31.348 562 93
		RAKI	0.053 645 78	0.935 678 45	33.288 645 10
		rRAKI	0.045 854 56	0.947 206 90	33.985 345 78
		RCRAKI	0.029 791 42	0.956 521 47	35.887 412 78

7T ultra-high field magnetic resonance parallel imaging algorithm based on residual complex convolution network

基于残差复卷积网络的7T超高场磁共振并行成像算法

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Figures/Tables 14

References 26

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算法	网络参数量/MB	推理时间/s
GRAPPA	/	35.966 4
RAKI	493.40	5.033 4
rRAKI	580.99	5.177 8
RCRAKI	1 837.64	7.270 4

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采样模式		算法	NRMSE	SSIM	PSNR/dB
N_ACS	rate	算法	NRMSE	SSIM	PSNR/dB
30	2	ZF	0.054 106 65	0.923 798 36	28.839 310 01
		无复数BN	0.002 836 50	0.982 833 48	41.643 986 89
		复数BN	0.002 721 08	0.984 933 01	41.824 398 02
	3	ZF	0.103 255 29	0.898 279 57	26.048 375 28
		无复数BN	0.006 121 38	0.964 682 15	38.319 002 83
		复数BN	0.005 975 10	0.965 684 36	38.424 040 75
40	2	ZF	0.031 483 25	0.945 242 90	31.191 020 40
		无复数BN	0.002 537 30	0.984 837 13	42.128 097 84
		复数BN	0.002 484 74	0.986 850 29	42.218 996 66
	4	ZF	0.072 034 77	0.915 817 72	27.596 395 04
		无复数BN	0.013 275 19	0.952 071 74	34.941 409 45
		复数BN	0.012 951 17	0.947 192 09	35.048 725 94
	8	ZF	0.093 905 28	0.900 484 19	26.444 916 45
		无复数BN	0.033 284 44	0.905 816 68	30.949 404 39
		复数BN	0.029 758 18	0.908 226 31	31.435 752 41

采样模式		算法	NRMSE	SSIM	PSNR/dB
N_ACS	rate	算法	NRMSE	SSIM	PSNR/dB
30	2	ZF	0.054 106 65	0.923 798 36	28.839 310 01
		无复数BN	0.002 836 50	0.982 833 48	41.643 986 89
		复数BN	0.002 721 08	0.984 933 01	41.824 398 02
	3	ZF	0.103 255 29	0.898 279 57	26.048 375 28
		无复数BN	0.006 121 38	0.964 682 15	38.319 002 83
		复数BN	0.005 975 10	0.965 684 36	38.424 040 75
40	2	ZF	0.031 483 25	0.945 242 90	31.191 020 40
		无复数BN	0.002 537 30	0.984 837 13	42.128 097 84
		复数BN	0.002 484 74	0.986 850 29	42.218 996 66
	4	ZF	0.072 034 77	0.915 817 72	27.596 395 04
		无复数BN	0.013 275 19	0.952 071 74	34.941 409 45
		复数BN	0.012 951 17	0.947 192 09	35.048 725 94
	8	ZF	0.093 905 28	0.900 484 19	26.444 916 45
		无复数BN	0.033 284 44	0.905 816 68	30.949 404 39
		复数BN	0.029 758 18	0.908 226 31	31.435 752 41