基于支撑先验与深度图像先验的无预训练磁共振图像重建方法

赵地; 赵莉芝; 甘永进; 覃斌毅

doi:10.7498/aps.71.20211761

摘要

基于深度学习的磁共振成像(magnetic resonance imaging, MRI)方法需要大规模、高质量的病患数据样本集进行预训练. 然而, 由于病患隐私及设备等因素限制, 获取大规模、高质量的磁共振数据集在实际临床应用中面临挑战. 本文提出一种新的基于深度学习的欠采样磁共振图像重建方法, 该方法无需预训练、不依赖训练数据集, 而是充分利用待重建的目标MR图像的结构先验和支撑先验, 并将其引入深度图像先验(deep image prior, DIP)框架, 从而削减对训练数据集的依赖, 提升学习效率. 基于参考图像与目标图像的相似性, 采用高分辨率参考图像作为深度网络输入, 将结构先验信息引入网络; 将参考图像在小波域中幅值大的系数索引集作为目标图像的已知支撑集, 构造正则化约束项, 将网络训练转化为网络参数的最优化求解过程. 实验结果表明, 本文方法可由欠采样k空间数据重建得到更精确的磁共振图像, 且在保留组织特征、细节纹理方面具有明显优势.

关键词:

Abstract

Magnetic resonance imaging (MRI) method based on deep learning needs large-quantity and high-quality patient-based datasets for pre-training. However, this is a challenge to the clinical applications because it is difficult to obtain a sufficient quantity of patient-based MR datasets due to the limitation of equipment and patient privacy concerns. In this paper, we propose a novel undersampled MRI reconstruction method based on deep learning. This method does not require any pre-training procedures and does not depend on training datasets. The proposed method is inspired by the traditional deep image prior (DIP) framework, and integrates the structure prior and support prior of the target MR image to improve the efficiency of learning. Based on the similarity between the reference image and the target image, the high-resolution reference image obtained in advance is used as the network input, thereby incorporating the structural prior information into network. By taking the coefficient index set of the reference image with large amplitude in the wavelet domain as the known support of the target image, the regularization constraint term is constructed, and the network training is transformed into the optimization process of network parameters. Experimental results show that the proposed method can obtain more accurate reconstructions from undersampled k-space data, and has obvious advantages in preserving tissue features and detailed texture.

Keywords:

作者及机构信息

1.
玉林师范学院, 广西高校复杂系统优化与大数据处理重点实验室, 玉林　537000

2.
中央民族大学信息工程学院, 北京　100081

3.
玉林师范学院物理与电信工程学院, 玉林　537000

通信作者: 赵莉芝, lizhi3285@126.com

基金项目: 国家自然科学基金(批准号: 62041111, 61701554)、广西自然科学基金(批准号: 2021GXNSFBA220056, 2019GXNSFBA245076)和玉林师范学院科研基金 (批准号: G2019ZK03)资助的课题

Authors and contacts

1.
Guangxi Colleges and Universities Key Laboratory of Complex System Optimization and Big Data Processing, Yulin Normal University, Yulin 537000, China

2.
School of Information Engineering, Minzu University of China, Beijing 100081, China

3.
School of Physics and Telecommunication Engineering, Yulin Normal University, Yulin 537000, China

Corresponding author: Zhao Li-Zhi, lizhi3285@126.com

Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 62041111, 61701554), the Natural Science Foundation of Guangxi, China (Grant Nos. 2021GXNSFBA220056, 2019GXNSFBA245076), and the Research Funds of Yulin Normal University, China (Grant No. G2019ZK03)

文章全文 : translate this paragraph

参考文献

[1]	Davenport M A, Duarte M F, Eldar Y C, et al. 2012 Compressed Sensing: Theory and Applications (Cambridge: Cambridge University Press) pp1–64
[2]	Lustig M, Donoho D L, Pauly J M 2007 Magn. Reson. Med. 58 1182 Google Scholar
[3]	Qu X B, Guo D, Ning B D, Hou Y K, et al. 2012 Magn. Reson. Imaging 30 964 Google Scholar
[4]	Liu J B, Wang S S, Peng X, Liang D 2015 Comput. Math. Methods Med. 2015 1
[5]	Zhan Z F, Cai J F, Guo D, Liu Y S, Chen Z, Qu X B 2016 IEEE Trans. Biomed. Eng. 63 1850 Google Scholar
[6]	Liu Q G, Wang S S, Ying L, Peng X, et al. 2013 IEEE Trans. Image Process. 22 4652 Google Scholar
[7]	Du H Q, Lam F 2012 Magn. Reson. Imaging 30 954 Google Scholar
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[9]	Manduca A, Trzasko J D, Li Z B. 2010 In: Proceedings of SPIE, The International Society for Optical Engineering (California-2010.2.13) p762223
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[11]	Stojnic M, Parvaresh F, Hassibi B 2009 IEEE Trans. Signal Process. 57 3075 Google Scholar
[12]	Usman M, Prieto C, Schaeffter T, et al. 2011 Magn. Reson. Med. 66 1163 Google Scholar
[13]	Blumensath T 2011 IEEE Trans. Inf. Theory 57 4660 Google Scholar
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[15]	Wang S S, Xiao T H, Liu Q G, Zheng H R 2021 Biomed. Signal Process. Control 68 102579 Google Scholar
[16]	Liang D, Cheng J, Ke Z W, Ying L 2020 IEEE Signal Processing Mag. 37 141 Google Scholar
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[19]	Wang S S, Su Z H, Ying L, Peng X, Zhu S, Liang F, Feng D G, Liang D 2016 In: IEEE 13th International Symposium on Biomedical Imaging Prague, Czech Republic, April 01, 2016 p514
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施引文献

图 1 方法总览图　(a)本文重建方法总体步骤; (b)本文重建方法采用的网络架构^[24]

Fig. 1. Overview of the proposed method: (a) Overall process for the proposed reconstruction method; (b) network architecture^[24] used in the proposed method.

下载: 全尺寸图片幻灯片

图 2 参考图像和目标图像的结构相似性及小波域支撑分布　(a), (b)同一病人的脑部扫描MR图像; (c), (d)对应的小波系数分布(Haar小波, 9层小波分解)

Fig. 2. Structural similarity between the reference and target images and support distributions in the wavelet domain: (a), (b) Brain MR images from the same patient; (c), (d) corresponding wavelet coefficient distributions (Using Haar wavelet at level 9).

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图 3 实验数据. 第一组　(a)参考图像; (b)待重建的目标图像1. 第二组　(c)参考图像; (d)待重建的目标图像2; (e)待重建的目标图像3

Fig. 3. MR images used in the experiments. Group one: (a) Reference image; (b) target image 1. Group two: (c) Reference image; (d) target image 2; (e) target image 3.

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图 4 降采样模板　(a)笛卡尔采样模板; (b)径向采样模板; (c)变密度采样模板

Fig. 4. Undersampling masks used in the experiments: (a) Cartesian mask; (b) radial mask; (c) variable density mask.

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图 5 笛卡尔采样模板40%采样率下目标图像1的重建结果对比. 第一行为目标图像1与各方法重建结果, 第二行为对应的误差图像, 第三行为对应的局部放大图

Fig. 5. Comparison of reconstructions of target image 1 using Cartesian undersampled mask with 40% sampling rate: Target image 1 and reconstruction results (1st row), the corresponding error images (2nd row), and the corresponding zoom-in images (3rd row)

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图 6 笛卡尔采样模板20%采样率下目标图像2的重建结果对比. 第一行为目标图像2与各方法重建结果, 第二行为对应的误差图像, 第三行为对应的局部放大图

Fig. 6. Comparison of reconstructions of target image 2 using Cartesian undersampled mask with 20% sampling rate: Target image 2 and reconstruction results (1st row), the corresponding error images (2nd row), and the corresponding zoom-in images (3rd row)

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图 7 笛卡尔采样模板30%采样率下目标图像3的重建结果对比. 第一行为目标图像3与各方法重建结果, 第二行为对应的误差图像, 第三行为对应的局部放大图

Fig. 7. Comparison of reconstructions of target image 3 using Cartesian undersampled mask with 30% sampling rate: Target image 3 and reconstruction results (1st row), the corresponding error images (2nd row), and the corresponding zoom-in images (3rd row)

下载: 全尺寸图片幻灯片

图 8 变密度采样模板30%采样率下目标图像1的重建结果对比. 第一行为目标图像1与各方法重建结果, 第二行为对应的误差图像, 第三行为对应的局部放大图

Fig. 8. Comparison of reconstructions of target image 1 using variable density undersampled mask with 30% sampling rate: Target image 1 and reconstruction results (1st row), the corresponding error images (2nd row), and the corresponding zoom-in images (3rd row).

下载: 全尺寸图片幻灯片

图 9 径向采样模板10%采样率下目标图像3的重建结果对比. 第一行为目标图像3与各方法重建结果, 第二行为对应的误差图像, 第三行为对应的局部放大图

Fig. 9. Comparison of reconstructions of target image 3 using radial undersampled mask with 10% sampling rate: Target image 3 and reconstruction results (1st row), the corresponding error images (2nd row), and the corresponding zoom-in images (3rd row).

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图 10 笛卡尔采样模板下本文方法的相对误差曲线

Fig. 10. Relative errors curves of the proposed method under Cartesian undersampled mask

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图 11 参考图像与目标图像间存在对比度差异及运动偏移情况下本文方法的重建结果　(a)参考图像; (b)待重建目标图像; (c)本文方法对(b)的重建结果; (d)待重建目标图像(存在运动偏移); (e)本文方法对(d)的重建结果; (a)—(c) 相对误差为2.19%, PSNR = 40.8788 dB, SSIM = 0.9937; (d), (e) 相对误差为2.54%, PSNR = 39.0825 dB, SSIM = 0.9937

Fig. 11. Reconstructions of the proposed method when there is contrast difference and motion between the reference image and the target image: (a) Reference image; (b) target image to be reconstructed; (c) reconstruction of (b) by the proposed method; (d) target image to be reconstructed(with motion effects); (e) reconstruction of (d) by the proposed method; (a)—(c) the relative error is 2.19%, PSNR = 40.8788 dB, SSIM = 0.9937; (d), (e) relative error 2.54%, PSNR = 39.0825 dB, SSIM = 0.9937.

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表 1 实验参数设置

Table 1. Parameter setting for experiments

参数		图像
参数		目标图像1	目标图像2	目标图像3
网络超参数	学习率	0.005	0.003	0.003
	L	6	6	6
	$n_{\rm{d}}$	[32, 64, 64, 64, 128, 128]	[16, 32, 64, 64, 128, 128]	[16, 32, 64, 64, 128, 128]
	$n_{\rm{u}}$	[32, 64, 64, 64, 128, 128]	[16, 32, 64, 64, 128, 128]	[16, 32, 64, 64, 128, 128]
	$n_{\rm{s}}$	[16, 16, 16, 16, 16, 16]	[16, 16, 16, 16, 16, 16]	[16, 16, 16, 16, 16, 16]
	$k_{\rm{d}}$	[3, 3, 3, 3, 3, 3]	[3, 3, 3, 3, 3, 3]	[3, 3, 3, 3, 3, 3]
	$k_{\rm{u}}$	[3, 3, 3, 3, 3, 3]	[3, 3, 3, 3, 3, 3]	[3, 3, 3, 3, 3, 3]
	$k_{\rm{s}}$	[1, 1, 1, 1, 1, 1]	[1, 1, 1, 1, 1, 1]	[1, 1, 1, 1, 1, 1]
迭代次数		5000	3000	3000
小波参数	小波函数	Haar	Haar	Haar
小波参数	分解层数	7	8	8
P		13500	55000	52000
λ		1 × 10^–10	1 × 10^–6	1 × 10^–9

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表 2 笛卡尔采样模板下不同重建方法的相对误差、PSNR及SSIM

Table 2. Relative errors, PSNR and SSIM values of reconstruction by different methods under Cartesian undersampled mask

待重建MR图像	重建方法	10%			20%
待重建MR图像	重建方法	相对误差/%	PSNR/dB	SSIM	相对误差/%	PSNR/dB	SSIM
目标图像1	零填充	35.64	18.7365	0.5543	16.14	25.6185	0.7135
	CS-WS	34.53	19.0101	0.5590	13.74	27.0139	0.7998
	DIP	32.51	19.5344	0.6666	12.49	27.8440	0.8989
	本文方法	19.89	23.8004	0.8172	9.43	30.2852	0.9793
目标图像2	零填充	19.66	22.5625	0.7550	13.36	25.9204	0.8065
	CS-WS	17.14	23.7530	0.7654	10.34	28.1426	0.8507
	DIP	15.09	24.9087	0.8473	5.41	33.7814	0.9619
	本文方法	7.51	30.9288	0.9454	3.48	37.5915	0.9788
目标图像3	零填充	17.64	23.5716	0.7857	12.76	26.3807	0.8266
	CS-WS	15.24	24.8395	0.8139	9.87	28.6144	0.8774
	DIP	14.90	25.0660	0.8585	5.43	33.8264	0.9607
	本文方法	7.31	31.2228	0.9491	3.53	37.5488	0.9806
待重建MR图像	重建方法	30%			40%
待重建MR图像	重建方法	相对误差/%	PSNR/dB	SSIM	相对误差/%	PSNR/dB	SSIM
目标图像1	零填充	11.53	28.5361	0.7657	7.71	32.0337	0.8087
	CS-WS	9.40	30.3126	0.8689	6.68	33.2736	0.9136
	DIP	9.05	30.6386	0.9342	6.98	32.8933	0.9605
	本文方法	7.06	32.7970	0.9590	5.64	34.7395	0.9728
目标图像2	零填充	4.61	35.1677	0.8677	3.46	37.6630	0.8830
	CS-WS	2.61	40.0883	0.9377	1.95	42.6338	0.9438
	DIP	2.80	39.4992	0.9858	2.33	41.1008	0.9892
	本文方法	2.08	42.0469	0.9905	1.73	43.6437	0.9931
目标图像3	零填充	4.31	35.8182	0.8813	3.24	38.2961	0.8997
	CS-WS	2.45	40.7193	0.9444	1.84	43.1958	0.9601
	DIP	3.22	38.5632	0.9824	2.54	40.4324	0.9885
	本文方法	2.05	42.2484	0.9908	1.64	44.2051	0.9939

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表 3 径向采样模板及变密度采样模板下不同重建方法的相对误差、PSNR及SSIM

Table 3. Relative errors, PSNR and SSIM values of reconstruction by different methods under radial undersampled mask and variable density undersampled mask

待重建MR图像	采样模板(采样率)	重建方法	相对误差/%	PSNR/dB	SSIM
目标图像1	径向(20%)	零填充	14.34	26.6426	0.7852
		CS-WS	12.11	28.1129	0.8519
		DIP	10.95	28.9845	0.9169
		本文方法	7.92	31.7960	0.9547
	变密度(30%)	零填充	15.03	26.2373	0.7735
		CS-WS	11.15	28.8264	0.8662
		DIP	9.26	30.4441	0.9321
		本文方法	6.43	33.6199	0.9648
目标图像2	径向(10%)	零填充	8.05	30.3202	0.7960
		CS-WS	5.73	33.2803	0.9010
		DIP	4.40	35.5814	0.9662
		本文方法	3.54	37.4434	0.9760
	变密度(20%)	零填充	6.47	32.2213	0.8778
		CS-WS	3.56	37.4195	0.9625
		DIP	3.15	38.4764	0.9821
		本文方法	2.57	40.2243	0.9850
目标图像3	径向(10%)	零填充	7.03	31.5576	0.8177
		CS-WS	5.18	34.2111	0.9158
		DIP	4.73	35.0303	0.9629
		本文方法	3.55	37.4852	0.9751
	变密度(20%)	零填充	5.82	33.2106	0.8978
		CS-WS	3.27	38.2161	0.9675
		DIP	3.01	38.9786	0.9819
		本文方法	2.54	40.4229	0.9852

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表 4 径向采样模板及变密度采样模板下不同重建方法的相对误差、PSNR及SSIM

Table 4. Relative errors, PSNR and SSIM values of reconstructions by different methods under radial undersampled mask and variable density undersampled mask

采样模板(采样率)	重建方法	相对误差/%	PSNR/dB	SSIM
径向 (20%)	DIP + Ref	8.88	30.9180	0.9478
	DIP + Sup	10.35	29.4739	0.9264
	DIP + Ref + Sup	8.24	31.5530	0.9512
	DIP + Ref + Sup + Cor	7.92	31.7960	0.9547
变密度 (30%)	DIP + Ref	7.38	32.4116	0.9583
	DIP + Sup	9.08	30.6104	0.9583
	DIP + Ref + Sup	6.71	33.2360	0.9620
	DIP + Ref + Sup + Cor	6.43	33.6199	0.9648

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表 5 笛卡尔采样下不同重建方法的计算时间

Table 5. Computational time for different reconstruction methods under the Cartesian mask

待重建MR图像	重建方法	计算时间
待重建MR图像	重建方法	10%	20%	30%	40%
目标图像1	CS-WS	46 s	46 s	49 s	46 s
	DIP	2 min 53 s	2 min 43 s	2 min 47 s	2 min 45 s
	本文方法	3 min 55 s	3 min 56 s	3 min 54 s	3 min 56 s
图11(d)所示目标图像	CS-WS	42 s	42 s	45 s	44 s
	DIP	2 min 33 s	2 min 35 s	2 min 35 s	2 min 34 s
	本文方法	3 min 14 s	3 min 15 s	3 min 15 s	3 min 13 s

下载: 导出CSV

[1]	Davenport M A, Duarte M F, Eldar Y C, et al. 2012 Compressed Sensing: Theory and Applications (Cambridge: Cambridge University Press) pp1–64
[2]	Lustig M, Donoho D L, Pauly J M 2007 Magn. Reson. Med. 58 1182 Google Scholar
[3]	Qu X B, Guo D, Ning B D, Hou Y K, et al. 2012 Magn. Reson. Imaging 30 964 Google Scholar
[4]	Liu J B, Wang S S, Peng X, Liang D 2015 Comput. Math. Methods Med. 2015 1
[5]	Zhan Z F, Cai J F, Guo D, Liu Y S, Chen Z, Qu X B 2016 IEEE Trans. Biomed. Eng. 63 1850 Google Scholar
[6]	Liu Q G, Wang S S, Ying L, Peng X, et al. 2013 IEEE Trans. Image Process. 22 4652 Google Scholar
[7]	Du H Q, Lam F 2012 Magn. Reson. Imaging 30 954 Google Scholar
[8]	Peng X, Du H Q, Lam F, Babacan D, Liang Z P 2011 In: Proceedings of IEEE International Symposium on Biomedical Imaging Chicago, USA, March 30, 2011 p89
[9]	Manduca A, Trzasko J D, Li Z B. 2010 In: Proceedings of SPIE, The International Society for Optical Engineering (California-2010.2.13) p762223
[10]	Han Y, Du H Q, Gao X Z, Mei W B 2017 IET Image Proc. 11 155 Google Scholar
[11]	Stojnic M, Parvaresh F, Hassibi B 2009 IEEE Trans. Signal Process. 57 3075 Google Scholar
[12]	Usman M, Prieto C, Schaeffter T, et al. 2011 Magn. Reson. Med. 66 1163 Google Scholar
[13]	Blumensath T 2011 IEEE Trans. Inf. Theory 57 4660 Google Scholar
[14]	Litjens G, Kooi T, Bejnordi B E, Setio A A A, Ciompi F, Ghafoorian M, van der Laak J A W M, van Ginneken B, Sánchez C I 2017 Med. Image Anal. 42 60 Google Scholar
[15]	Wang S S, Xiao T H, Liu Q G, Zheng H R 2021 Biomed. Signal Process. Control 68 102579 Google Scholar
[16]	Liang D, Cheng J, Ke Z W, Ying L 2020 IEEE Signal Processing Mag. 37 141 Google Scholar
[17]	Schlemper J, Caballero J, Hajnal J V, Price A N, Rueckert D 2018 IEEE Trans. Med. Imaging 37 491 Google Scholar
[18]	Yang G, Yu S, Dong H, Slabaugh G, Dragotti P L, Ye X J, Liu F D, Arridge S, Keegan J, Guo Y K, Firmin D 2018 IEEE Trans. Med. Imaging 37 1310 Google Scholar
[19]	Wang S S, Su Z H, Ying L, Peng X, Zhu S, Liang F, Feng D G, Liang D 2016 In: IEEE 13th International Symposium on Biomedical Imaging Prague, Czech Republic, April 01, 2016 p514
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