Reconstruction algorithm for highly undersampled magnetic resonance images based on residual graph convolutional neural network

doi:10.11772/j.issn.1001-9081.2022020309

Journal of Computer Applications ›› 2023, Vol. 43 ›› Issue (4): 1261-1268.DOI: 10.11772/j.issn.1001-9081.2022020309

• Multimedia computing and computer simulation • Previous Articles

Reconstruction algorithm for highly undersampled magnetic resonance images based on residual graph convolutional neural network

Xiaoyu FAN¹, Suzhen LIN¹(), Yanbo WANG¹, Feng LIU², Dawei LI¹

^1.School of Data Science and Technology，North University of China，Taiyuan Shanxi 030051，China
^2.School of Information Technology and Electrical Engineering，The University of Queensland，Brisbane Queensland 4072，Australia

Received:2022-03-16 Revised:2022-06-08 Accepted:2022-06-08 Online:2022-08-16 Published:2023-04-10
Contact: Suzhen LIN
About author:FAN Xiaoyu， born in 1998， M. S. candidate. His research interests include image processing， Magnetic Resonance Imaging （MRI） reconstruction.
WANG Yanbo， born in 1984， Ph. D.， lecturer. His research interest include graph model， image processing.
LIU Feng， born in 1968， Ph. D.， professor. His research interests include MRI hardware design， electromagnetic analysis， cardiac electrical functional imaging.
LI Dawei， born in 1980， Ph. D.， associate professor. His research interests include image processing.
Supported by:
Graduate Innovation Project of Shanxi Province(2021Y623)

基于残差图卷积神经网络的高倍欠采样核磁共振图像重建算法

樊小宇¹, 蔺素珍¹(), 王彦博¹, 刘峰², 李大威¹

^1.中北大学大数据学院，太原 030051
^2.昆士兰大学信息技术与电子工程学院，昆士兰布里斯班4072，澳大利亚

通讯作者: 蔺素珍
作者简介:樊小宇（1998—），男，山西原平人，硕士研究生，CCF会员，主要研究方向：图像处理、磁共振成像（MRI）重建；
王彦博（1984—），男，山西运城人，讲师，博士，CCF会员，主要研究方向：图模型、图像处理；
刘峰（1968—），男，澳大利亚人，教授，博士，主要研究方向：MRI硬件设计、电磁分析、心电功能成像；
李大威（1980—），男，河北衡水人，副教授，博士，主要研究方向：图像处理。
基金资助:
山西省研究生创新项目(2021Y623)

Abstract

Abstract:

Magnetic Resonance Imaging （MRI） is widely used in the diagnosis of complex diseases because of its non-invasiveness and good soft tissue contrast. Due to the low speed of MRI， most of the acceleration is currently performed by highly undersampled Magnetic Resonance （MR） signals in k-space. However， the representative algorithms often have the problem of blurred details when reconstructing highly undersampled MR images. Therefore， a highly undersampled MR image reconstruction algorithm based on Residual Graph Convolutional Neural nETwork （RGCNET） was proposed. Firstly， auto-encoding technology and Graph Convolutional neural Network （GCN） were used to build a generator. Secondly， the undersampled image was input into the feature extraction （encoder） network to extract features at the bottom layer. Thirdly， the high-level features of MR images were extracted by the GCN block. Fourthly， the initial reconstructed image was generated through the decoder network. Finally， the final high-resolution reconstructed image was obtained through a dynamic game between the generator and the discriminator. Test results on FastMRI dataset show that at 10%， 20%， 30%， 40% and 50% sampling rates， compared with spatial orthogonal attention mechanism based MRI reconstruction algorithm SOGAN（Spatial Orthogonal attention Generative Adversarial Network）， the proposed algorithm decreases 3.5%， 26.6%， 23.9%， 13.3% and 14.3% on Normalized Root Mean Square Error （NRMSE）， increases 1.2%， 8.7%， 6.9%， 2.9% and 3.2% on Peak Signal-to-Noise Ratio （PSNR） and increases 0.8%， 2.9%， 1.5%， 0.5% and 0.5% on Structural SIMilarity （SSIM） respectively. At the same time， subjective observation also proves that the proposed algorithm can preserve more details and have more realistic visual effects.

Key words: image reconstruction, highly undersampled image, Generative Adversarial Network (GAN), Graph Convolutional neural Network (GCN), deep learning

摘要：

磁共振成像（MRI）因其无创伤和较高的软组织对比度而被广泛地用于复杂疾病诊断。目前多通过在k空间高倍欠采样磁共振（MR）信号解决MRI速度较慢的问题，然而代表性算法重建高倍欠采样的MR图像时往往存在细节模糊的问题。因此，提出一种基于残差图卷积神经网络（RGCNET）的高倍欠采样MR图像重建算法。首先，使用自编码技术与图卷积神经网络（GCN）构建生成器；其次，将欠采样图像输入特征提取（编码）网络中从底层提取特征；接着，通过GCN块提取MR图像的高层特征；然后，通过解码网络生成初始的重建图像；最后，经过生成器和鉴别器的动态博弈得到最终的高分辨率重建图像。在FastMRI数据集上的测试结果表明，与基于空间正交注意力机制的MRI重建算法SOGAN（Spatial Orthogonal attention Generative Adversarial Network）相比，在10%、20%、30%、40%和50%的采样率下，所提算法在标准均方根误差（NRMSE）指标上分别下降了3.5%、26.6%、23.9%、13.3%和14.3%，在峰值信噪比（PSNR）指标上分别提升了1.2%、8.7%、6.9%、2.9%和3.2%，而结构相似性（SSIM）指标上分别提升了0.8%、2.9%、1.5%、0.5%和0.5%。同时，主观观察也验证了所提算法能保留更多细节和取得更逼真的视觉效果。

关键词: 图像重建, 高倍欠采样图像, 生成对抗网络, 图卷积神经网络, 深度学习

CLC Number:

TP183

Xiaoyu FAN, Suzhen LIN, Yanbo WANG, Feng LIU, Dawei LI. Reconstruction algorithm for highly undersampled magnetic resonance images based on residual graph convolutional neural network[J]. Journal of Computer Applications, 2023, 43(4): 1261-1268.

樊小宇, 蔺素珍, 王彦博, 刘峰, 李大威. 基于残差图卷积神经网络的高倍欠采样核磁共振图像重建算法[J]. 《计算机应用》唯一官方网站, 2023, 43(4): 1261-1268.

Figures/Tables 12

References 29

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采样模式	算法	NRMSE	PSNR/dB	SSIM
1DGaussian	ZF	0.129±0.046	29.618±2.836	0.892±0.044
1DGaussian	RGCNET	0.085±0.033	33.335±2.876	0.935±0.032
2DGaussian	ZF	0.139±0.044	28.844±2.892	0.839±0.070
2DGaussian	RGCNET	0.089±0.034	32.944±3.241	0.923±0.039
POSSION	ZF	0.109±0.033	30.930±3.075	0.884±0.058
POSSION	RGCNET	0.074±0.029	34.555±3.655	0.940±0.037
Radial	ZF	0.128±0.039	29.583±2.939	0.873±0.061
Radial	RGCNET	0.069±0.028	35.257±3.629	0.949±0.031

采样模式	算法	NRMSE	PSNR/dB	SSIM
1DGaussian	ZF	0.129±0.046	29.618±2.836	0.892±0.044
1DGaussian	RGCNET	0.085±0.033	33.335±2.876	0.935±0.032
2DGaussian	ZF	0.139±0.044	28.844±2.892	0.839±0.070
2DGaussian	RGCNET	0.089±0.034	32.944±3.241	0.923±0.039
POSSION	ZF	0.109±0.033	30.930±3.075	0.884±0.058
POSSION	RGCNET	0.074±0.029	34.555±3.655	0.940±0.037
Radial	ZF	0.128±0.039	29.583±2.939	0.873±0.061
Radial	RGCNET	0.069±0.028	35.257±3.629	0.949±0.031

采样率/%	算法	NRMSE	PSNR/dB	SSIM
10	ZF	0.197±0.067	25.900±3.019	0.757±0.087
	DAGAN	0.167±0.057	27.378±3.104	0.803±0.080
	RefineGAN	0.165±0.056	27.430±3.094	0.800±0.082
	ESSGAN	0.157±0.050	27.855±3.165	0.833±0.074
	SOGAN	0.142±0.047	28.718±3.154	0.854±0.066
	RGCNET	0.137±0.047	29.050±3.218	0.861±0.063
20	ZF	0.128±0.039	29.583±2.939	0.873±0.061
	DAGAN	0.088±0.034	33.050±3.597	0.918±0.049
	RefineGAN	0.085±0.031	33.241±3.331	0.929±0.040
	ESSGAN	0.094±0.036	32.394±2.911	0.922±0.035
	SOGAN	0.094±0.036	32.444±3.023	0.922±0.038
	RGCNET	0.069±0.028	35.257±3.629	0.949±0.031
30	ZF	0.096±0.029	32.039±3.504	0.917±0.046
	DAGAN	0.062±0.023	36.077±3.578	0.958±0.026
	RefineGAN	0.071±0.029	34.843±2.899	0.946±0.027
	ESSGAN	0.056±0.023	36.988±3.860	0.965±0.024
	SOGAN	0.067±0.027	35.483±3.227	0.956±0.024
	RGCNET	0.051±0.021	37.943±3.862	0.970±0.020
40	ZF	0.074±0.022	34.332±3.209	0.945±0.034
	DAGAN	0.047±0.018	38.434±3.654	0.975±0.017
	RefineGAN	0.059±0.024	36.392±2.809	0.964±0.017
	ESSGAN	0.049±0.019	38.103±3.351	0.974±0.016
	SOGAN	0.045±0.018	38.942±3.665	0.976±0.016
	RGCNET	0.039±0.016	40.081±3.755	0.981±0.012
50	ZF	0.057±0.017	36.631±3.413	0.965±0.025
	DAGAN	0.037±0.014	40.460±3.573	0.982±0.010
	RefineGAN	0.045±0.018	38.843±2.918	0.978±0.011
	ESSGAN	0.048±0.021	38.346±2.766	0.978±0.011
	SOGAN	0.035±0.016	41.112±3.573	0.984±0.015
	RGCNET	0.030±0.012	42.411±3.688	0.989±0.007

采样率/%	算法	NRMSE	PSNR/dB	SSIM
10	ZF	0.197±0.067	25.900±3.019	0.757±0.087
	DAGAN	0.167±0.057	27.378±3.104	0.803±0.080
	RefineGAN	0.165±0.056	27.430±3.094	0.800±0.082
	ESSGAN	0.157±0.050	27.855±3.165	0.833±0.074
	SOGAN	0.142±0.047	28.718±3.154	0.854±0.066
	RGCNET	0.137±0.047	29.050±3.218	0.861±0.063
20	ZF	0.128±0.039	29.583±2.939	0.873±0.061
	DAGAN	0.088±0.034	33.050±3.597	0.918±0.049
	RefineGAN	0.085±0.031	33.241±3.331	0.929±0.040
	ESSGAN	0.094±0.036	32.394±2.911	0.922±0.035
	SOGAN	0.094±0.036	32.444±3.023	0.922±0.038
	RGCNET	0.069±0.028	35.257±3.629	0.949±0.031
30	ZF	0.096±0.029	32.039±3.504	0.917±0.046
	DAGAN	0.062±0.023	36.077±3.578	0.958±0.026
	RefineGAN	0.071±0.029	34.843±2.899	0.946±0.027
	ESSGAN	0.056±0.023	36.988±3.860	0.965±0.024
	SOGAN	0.067±0.027	35.483±3.227	0.956±0.024
	RGCNET	0.051±0.021	37.943±3.862	0.970±0.020
40	ZF	0.074±0.022	34.332±3.209	0.945±0.034
	DAGAN	0.047±0.018	38.434±3.654	0.975±0.017
	RefineGAN	0.059±0.024	36.392±2.809	0.964±0.017
	ESSGAN	0.049±0.019	38.103±3.351	0.974±0.016
	SOGAN	0.045±0.018	38.942±3.665	0.976±0.016
	RGCNET	0.039±0.016	40.081±3.755	0.981±0.012
50	ZF	0.057±0.017	36.631±3.413	0.965±0.025
	DAGAN	0.037±0.014	40.460±3.573	0.982±0.010
	RefineGAN	0.045±0.018	38.843±2.918	0.978±0.011
	ESSGAN	0.048±0.021	38.346±2.766	0.978±0.011
	SOGAN	0.035±0.016	41.112±3.573	0.984±0.015
	RGCNET	0.030±0.012	42.411±3.688	0.989±0.007

算法	GCN	ResBlock	L_ssim+ L_grad	L_FFL	NRMSE	PSNR/dB	SSIM
ZF					0.128± 0.039	29.583± 2.939	0.873± 0.061
RGCNET-A	×	√	√	√	0.081± 0.029	33.751± 3.636	0.943± 0.032
RGCNET-B	√	√	×	√	0.085± 0.032	33.320± 3.470	0.938± 0.033
RGCNET-C	√	√	√	×	0.081± 0.029	33.737± 3.618	0.944± 0.032
RGCNET-D	√	×	√	√	0.076± 0.029	34.388± 3.300	0.942± 0.032
RGCNET	√	√	√	√	0.069± 0.028	35.257± 3.630	0.949± 0.032

Reconstruction algorithm for highly undersampled magnetic resonance images based on residual graph convolutional neural network

基于残差图卷积神经网络的高倍欠采样核磁共振图像重建算法

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References 29

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Metrics

var	算法	NRMSE	PSNR/dB	SSIM
1	ZF	0.128±0.039	29.541±2.894	0.873±0.056
	DAGAN	0.089±0.034	32.894±3.462	0.915±0.048
	RefineGAN	0.087±0.032	33.093±3.205	0.927±0.039
	ESSGAN	0.095±0.036	32.291±2.835	0.921±0.035
	SOGAN	0.095±0.036	32.327±2.932	0.919±0.037
	RGCNET	0.070±0.029	35.001±3.390	0.946±0.030
3	ZF	0.133±0.041	29.186±2.622	0.865±0.047
	DAGAN	0.098±0.037	31.981±2.837	0.898±0.045
	RefineGAN	0.096±0.036	32.206±2.615	0.910±0.036
	ESSGAN	0.103±0.041	31.603±2.415	0.907±0.032
	SOGAN	0.103±0.041	31.596±2.468	0.903±0.033
	RGCNET	0.081±0.034	33.662±2.504	0.930±0.027
5	ZF	0.143±0.046	28.580±2.269	0.846±0.040
	DAGAN	0.113±0.044	30.736±2.246	0.870±0.040
	RefineGAN	0.110±0.043	30.970±2.042	0.881±0.032
	ESSGAN	0.116±0.048	30.568±1.945	0.882±0.028
	SOGAN	0.116±0.048	30.523±1.965	0.876±0.028
	RGCNET	0.098±0.042	32.051±1.843	0.903±0.022
7	ZF	0.155±0.052	27.845±1.952	0.819±0.035
	DAGAN	0.130±0.051	29.468±1.855	0.837±0.037
	RefineGAN	0.127±0.051	29.689±1.643	0.846±0.028
	ESSGAN	0.131±0.056	29.441±1.583	0.850±0.024
	SOGAN	0.132±0.056	29.373±1.588	0.842±0.023
	RGCNET	0.116±0.050	30.529±1.454	0.872±0.018
10	ZF	0.176±0.061	26.677±1.595	0.771±0.030
	DAGAN	0.158±0.061	27.700±1.508	0.785±0.034
	RefineGAN	0.155±0.062	27.913±1.280	0.788±0.025
	ESSGAN	0.157±0.067	27.825±1.239	0.798±0.023
	SOGAN	0.158±0.067	27.748±1.238	0.790±0.020
	RGCNET	0.144±0.060	28.577±1.165	0.824±0.015

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