Reconstruction algorithm for undersampled magnetic resonance images based on complex convolution dual-domain cascade network

doi:10.11772/j.issn.1001-9081.2023020187

Journal of Computer Applications ›› 2024, Vol. 44 ›› Issue (2): 580-587.DOI: 10.11772/j.issn.1001-9081.2023020187

• Multimedia computing and computer simulation • Previous Articles

Reconstruction algorithm for undersampled magnetic resonance images based on complex convolution dual-domain cascade network

Hualu QIU¹, Suzhen LIN¹(), Yanbo WANG¹, Feng LIU², Dawei LI³

^1.College of Data Science and Technology，North University of China，Taiyuan Shanxi 030051，China
^2.College of Information Technology and Electrical Engineering，The University of Queensland，Brisbane Queensland 4702，Australia
^3.School of Electrical and Control Engineering，North University of China，Taiyuan Shanxi 030051，China

Received:2023-02-27 Revised:2023-05-14 Accepted:2023-05-18 Online:2024-02-22 Published:2024-02-10
Contact: Suzhen LIN
About author:QIU Hualu， born in 2000， M. S. candidate. His research interests include image processing， Magnetic Resonance Imaging （MRI） reconstruction.
WANG Yanbo， born in 1984， Ph. D.， lecturer. His research interests 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 pattern recognition， machine learning， image processing.
Supported by:
Fundamental Research Program of Shanxi Province(20210302123025)

基于复卷积双域级联网络的欠采样磁共振图像重建算法

邱华禄¹, 蔺素珍¹(), 王彦博¹, 刘峰², 李大威³

^1.中北大学计算机科学与技术学院, 太原 030051
^2.昆士兰大学信息技术与电子工程学院, 澳大利亚布里斯班 4702
^3.中北大学电气与控制工程学院, 太原 030051

通讯作者: 蔺素珍
作者简介:邱华禄（2000—），男，福建三明人，硕士研究生，CCF会员，主要研究方向：图像处理、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：磁共振成像硬件设计、电磁分析、心脏电功能成像
李大威（1980—），男，河北衡水人，副教授，博士，主要研究方向：模式识别、机器学习、图像处理。
基金资助:
山西省基础研究计划项目(20210302123025)

Abstract

Abstract:

At present， most accelerated Magnetic Resonance Imaging （MRI） reconstruction algorithms reconstruct undersampled amplitude images and use real-value convolution for feature extraction， without considering that the MRI data itself is complex， which limits the feature extraction ability of MRI complex data. In order to improve the feature extraction ability of single slice MRI complex data， and thus reconstruct single slice MRI images with clearer details， a Complex Convolution Dual-Domain Cascade Network （ComConDuDoCNet） was proposed. The original undersampled MRI data was used as input， and Residual Feature Aggregation （RFA） blocks were used to alternately extract the dual domain features of the MRI data， ultimately reconstructing the Magnetic Resonance （MR） images with clear texture details. Complex convolution was used as a feature extractor for each RFA block. Different domains were cascaded through Fourier transform or inverse transform， and data consistency layer was added to achieve data fidelity. A large number of experiments were conducted on publicly available knee joint dataset. The comparison results with the Dual-task Dual-domain Network （DDNet） under three different sampling masks with a sampling rate of 20% show that： under the two-dimensional Gaussian sampling mask， the proposed algorithm decreases Normalized Root Mean Square Error （NRMSE） by 13.6%， increases Peak Signal-to-Noise Ratio （PSNR） by 4.3%， and increases Structural SIMilarity （SSIM） by 0.8%； under the Poisson sampling mask， the proposed algorithm decreases NRMSE by 11.0%， increases PSNR by 3.5%， and increases SSIM by 0.1%； under the radial sampling mask， the proposed algorithm decreases NRMSE by 12.3%， increases PSNR by 3.8%， and increases SSIM by 0.2%. The experimental results show that ComConDuDoCNet， combined with complex convolution and dual-domain learning， can reconstruct MR images with clearer details and more realistic visual effects.

Key words: image reconstruction, undersampled image, complex convolution, dual-domain learning, deep learning

摘要：

目前，大多数加速磁共振成像（MRI）的重建算法通过重建欠采样幅值图像，利用实值卷积进行特征提取，没有考虑MRI数据本身是复数，从而限制了对MRI复值数据的特征提取能力。为了提高对单个切片MRI复值数据特征提取能力，从而重建出细节更为清晰的单切片磁共振（MR）图像，提出复卷积双域级联网络（ComConDuDoCNet）。将原始欠采样MRI数据作为输入，使用残差特征聚合（RFA）块交替提取MRI数据的双域特征，最终重建出具有清晰纹理细节的MR图像。每个RFA块使用复卷积作为特征提取器。不同域间通过傅里叶变换或逆变换进行级联，并加入数据一致性层实现数据保真。在公开的膝关节数据集上进行实验，与双任务双域网络（DDNet）在采样率为20%的三种不同采样掩码下的对比结果表明，在二维高斯采样掩码下，所提算法的标准均方根误差（NRMSE）下降了13.6%，峰值信噪比（PSNR）提升了4.3%，结构相似性指数（SSIM）提升了0.8%；在泊松采样掩码下，所提算法的NRMSE下降了11.0%，PSNR提升了3.5%，SSIM提升了0.1%；在径向采样掩码下，所提算法的NRMSE下降了12.3%，PSNR提升了3.8%，SSIM提升了0.2%。实验结果表明，ComConDuDoCNet结合复卷积与双域学习，能够重建出细节更加清晰、视觉效果更加逼真的MR图像。

关键词: 图像重建, 欠采样图像, 复卷积, 双域学习, 深度学习

CLC Number:

TP391.41

Hualu QIU, Suzhen LIN, Yanbo WANG, Feng LIU, Dawei LI. Reconstruction algorithm for undersampled magnetic resonance images based on complex convolution dual-domain cascade network[J]. Journal of Computer Applications, 2024, 44(2): 580-587.

邱华禄, 蔺素珍, 王彦博, 刘峰, 李大威. 基于复卷积双域级联网络的欠采样磁共振图像重建算法[J]. 《计算机应用》唯一官方网站, 2024, 44(2): 580-587.

Figures/Tables 11

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采样模式	算法	NRMSE	SSIM	PSNR/dB
10% 2DGaussian	ZF	0.223±0.131	0.777±0.068	24.867±3.069
	ReconResNet	0.135±0.062	0.884±0.065	28.912±2.885
	H-CNN	0.123±0.054	0.873±0.061	29.713±2.795
	DDNet	0.110±0.057	0.906±0.061	30.882±3.589
	ComConDuDoCNet	0.098±0.051	0.906±0.060	31.930±3.440
20% 2DGaussian	ZF	0.210±0.121	0.791±0.059	25.395±2.994
	ReconResNet	0.123±0.058	0.905±0.050	29.757±2.872
	H-CNN	0.108±0.045	0.892±0.047	30.773±2.832
	DDNet	0.088±0.044	0.932±0.043	32.834±3.761
	ComConDuDoCNet	0.076±0.041	0.939±0.042	34.239±3.665
30% 2DGaussian	ZF	0.179±0.096	0.823±0.053	26.639±2.921
	ReconResNet	0.111±0.055	0.924±0.039	30.685±2.921
	H-CNN	0.088±0.037	0.923±0.034	32.598±2.946
	DDNet	0.070±0.036	0.954±0.028	34.902±3.770
	ComConDuDoCNet	0.057±0.034	0.963±0.027	36.847±4.034
10% POSSION	ZF	0.208±0.122	0.787±0.068	25.437±3.114
	ReconResNet	0.139±0.066	0.883±0.065	28.717±2.811
	H-CNN	0.123±0.057	0.875±0.062	29.758±2.874
	DDNet	0.110±0.060	0.909±0.062	30.939±3.667
	ComConDuDoCNet	0.100±0.050	0.906±0.062	31.786±3.368
20% POSSION	ZF	0.165±0.089	0.834±0.056	27.287±3.042
	ReconResNet	0.115±0.058	0.916±0.048	30.462±3.011
	H-CNN	0.096±0.044	0.916±0.043	31.875±3.103
	DDNet	0.082±0.046	0.944±0.042	33.558±3.890
	ComConDuDoCNet	0.073±0.042	0.945±0.041	34.735±3.871
30% POSSION	ZF	0.127±0.059	0.876±0.046	29.440±2.888
	ReconResNet	0.094±0.048	0.945±0.030	32.228±3.056
	H-CNN	0.071±0.033	0.952±0.025	34.631±3.366
	DDNet	0.052±0.030	0.974±0.020	37.671±4.335
	ComConDuDoCNet	0.044±0.029	0.977±0.020	39.259±4.364
10% Radial	ZF	0.341±0.203	0.665±0.078	21.364±3.015
	ReconResNet	0.200±0.077	0.813±0.080	25.365±2.488
	H-CNN	0.183±0.063	0.780±0.082	26.017±2.488
	DDNet	0.162±0.076	0.837±0.080	27.311±3.200
	ComConDuDoCNet	0.151±0.059	0.824±0.079	27.861±2.764
20% Radial	ZF	0.207±0.121	0.815±0.057	25.525±3.174
	ReconResNet	0.113±0.056	0.923±0.043	30.636±2.862
	H-CNN	0.098±0.042	0.915±0.042	31.659±2.893
	DDNet	0.081±0.043	0.945±0.038	33.578±3.855
	ComConDuDoCNet	0.071±0.039	0.947±0.038	34.860±3.748
30% Radial	ZF	0.151±0.082	0.876±0.044	28.081±3.156
	ReconResNet	0.086±0.047	0.953±0.028	33.082±3.195
	H-CNN	0.075±0.035	0.953±0.026	33.994±3.227
	DDNet	0.054±0.031	0.973±0.021	37.329±4.289
	ComConDuDoCNet	0.048±0.030	0.974±0.021	38.379±4.064

采样模式	算法	NRMSE	SSIM	PSNR/dB
10% 2DGaussian	ZF	0.223±0.131	0.777±0.068	24.867±3.069
	ReconResNet	0.135±0.062	0.884±0.065	28.912±2.885
	H-CNN	0.123±0.054	0.873±0.061	29.713±2.795
	DDNet	0.110±0.057	0.906±0.061	30.882±3.589
	ComConDuDoCNet	0.098±0.051	0.906±0.060	31.930±3.440
20% 2DGaussian	ZF	0.210±0.121	0.791±0.059	25.395±2.994
	ReconResNet	0.123±0.058	0.905±0.050	29.757±2.872
	H-CNN	0.108±0.045	0.892±0.047	30.773±2.832
	DDNet	0.088±0.044	0.932±0.043	32.834±3.761
	ComConDuDoCNet	0.076±0.041	0.939±0.042	34.239±3.665
30% 2DGaussian	ZF	0.179±0.096	0.823±0.053	26.639±2.921
	ReconResNet	0.111±0.055	0.924±0.039	30.685±2.921
	H-CNN	0.088±0.037	0.923±0.034	32.598±2.946
	DDNet	0.070±0.036	0.954±0.028	34.902±3.770
	ComConDuDoCNet	0.057±0.034	0.963±0.027	36.847±4.034
10% POSSION	ZF	0.208±0.122	0.787±0.068	25.437±3.114
	ReconResNet	0.139±0.066	0.883±0.065	28.717±2.811
	H-CNN	0.123±0.057	0.875±0.062	29.758±2.874
	DDNet	0.110±0.060	0.909±0.062	30.939±3.667
	ComConDuDoCNet	0.100±0.050	0.906±0.062	31.786±3.368
20% POSSION	ZF	0.165±0.089	0.834±0.056	27.287±3.042
	ReconResNet	0.115±0.058	0.916±0.048	30.462±3.011
	H-CNN	0.096±0.044	0.916±0.043	31.875±3.103
	DDNet	0.082±0.046	0.944±0.042	33.558±3.890
	ComConDuDoCNet	0.073±0.042	0.945±0.041	34.735±3.871
30% POSSION	ZF	0.127±0.059	0.876±0.046	29.440±2.888
	ReconResNet	0.094±0.048	0.945±0.030	32.228±3.056
	H-CNN	0.071±0.033	0.952±0.025	34.631±3.366
	DDNet	0.052±0.030	0.974±0.020	37.671±4.335
	ComConDuDoCNet	0.044±0.029	0.977±0.020	39.259±4.364
10% Radial	ZF	0.341±0.203	0.665±0.078	21.364±3.015
	ReconResNet	0.200±0.077	0.813±0.080	25.365±2.488
	H-CNN	0.183±0.063	0.780±0.082	26.017±2.488
	DDNet	0.162±0.076	0.837±0.080	27.311±3.200
	ComConDuDoCNet	0.151±0.059	0.824±0.079	27.861±2.764
20% Radial	ZF	0.207±0.121	0.815±0.057	25.525±3.174
	ReconResNet	0.113±0.056	0.923±0.043	30.636±2.862
	H-CNN	0.098±0.042	0.915±0.042	31.659±2.893
	DDNet	0.081±0.043	0.945±0.038	33.578±3.855
	ComConDuDoCNet	0.071±0.039	0.947±0.038	34.860±3.748
30% Radial	ZF	0.151±0.082	0.876±0.044	28.081±3.156
	ReconResNet	0.086±0.047	0.953±0.028	33.082±3.195
	H-CNN	0.075±0.035	0.953±0.026	33.994±3.227
	DDNet	0.054±0.031	0.973±0.021	37.329±4.289
	ComConDuDoCNet	0.048±0.030	0.974±0.021	38.379±4.064

采样模式	算法	NRMSE	SSIM	PSNR/dB
10% 2DGaussian	ZF	0.372±0.104	0.626±0.054	20.721±2.326
	ReconResNet	0.179±0.042	0.908±0.022	26.942±2.088
	H-CNN	0.137±0.017	0.843±0.039	29.140±2.070
	DDNet	0.121±0.027	0.907±0.029	30.348±2.453
	ComConDuDoCNet	0.090±0.012	0.935±0.018	32.801±2.228
20% 2DGaussian	ZF	0.348±0.094	0.634±0.052	21.279±2.238
	ReconResNet	0.183±0.049	0.914±0.020	26.806±2.007
	H-CNN	0.118±0.013	0.844±0.040	30.391±2.088
	DDNet	0.081±0.015	0.928±0.025	33.732±2.416
	ComConDuDoCNet	0.065±0.009	0.951±0.013	35.604±2.222
30% 2DGaussian	ZF	0.292±0.071	0.669±0.051	22.726±2.143
	ReconResNet	0.151±0.045	0.931±0.016	28.527±1.850
	H-CNN	0.091±0.011	0.880±0.034	32.664±2.184
	DDNet	0.060±0.009	0.933±0.021	36.363±2.301
	ComConDuDoCNet	0.044±0.006	0.970±0.009	39.057±2.193
10% POSSION	ZF	0.342±0.091	0.642±0.055	21.412±2.377
	ReconResNet	0.167±0.041	0.917±0.020	27.554±2.079
	H-CNN	0.137±0.018	0.846±0.040	29.155±2.189
	DDNet	0.121±0.026	0.924±0.025	30.351±2.450
	ComConDuDoCNet	0.092±0.012	0.941±0.016	32.602±2.199
20% POSSION	ZF	0.256±0.063	0.700±0.055	23.889±2.441
	ReconResNet	0.160±0.051	0.936±0.016	28.081±1.955
	H-CNN	0.099±0.014	0.890±0.033	31.986±2.314
	DDNet	0.077±0.018	0.954±0.016	34.247±2.268
	ComConDuDoCNet	0.057±0.007	0.968±0.009	36.804±2.177
30% POSSION	ZF	0.182±0.039	0.749±0.051	26.792±2.259
	ReconResNet	0.132±0.045	0.958±0.010	29.845±2.332
	H-CNN	0.062±0.008	0.932±0.022	36.039±2.181
	DDNet	0.037±0.006	0.977±0.009	40.665±2.372
	ComConDuDoCNet	0.031±0.004	0.982±0.007	42.037±2.205
10% Radial	ZF	0.537±0.168	0.475±0.043	17.574±1.913
	ReconResNet	0.256±0.049	0.812±0.042	23.757±1.659
	H-CNN	0.219±0.024	0.717±0.057	25.054±1.966
	DDNet	0.200±0.040	0.801±0.052	25.962±2.541
	ComConDuDoCNet	0.181±0.023	0.800±0.043	26.724±2.088
20% Radial	ZF	0.359±0.093	0.644±0.053	20.980±2.325
	ReconResNet	0.163±0.048	0.945±0.011	27.864±1.927
	H-CNN	0.105±0.014	0.891±0.028	31.429±2.188
	DDNet	0.072±0.014	0.948±0.019	34.776±2.767
	ComConDuDoCNet	0.058±0.008	0.967±0.010	36.692±2.270
30% Radial	ZF	0.238±0.061	0.735±0.055	24.557±2.640
	ReconResNet	0.128±0.046	0.967±0.008	30.151±2.489
	H-CNN	0.077±0.013	0.938±0.018	34.227±2.362
	DDNet	0.040±0.009	0.977±0.010	40.052±2.999
	ComConDuDoCNet	0.034±0.005	0.984±0.005	41.284±2.179

采样模式	算法	NRMSE	SSIM	PSNR/dB
10% 2DGaussian	ZF	0.372±0.104	0.626±0.054	20.721±2.326
	ReconResNet	0.179±0.042	0.908±0.022	26.942±2.088
	H-CNN	0.137±0.017	0.843±0.039	29.140±2.070
	DDNet	0.121±0.027	0.907±0.029	30.348±2.453
	ComConDuDoCNet	0.090±0.012	0.935±0.018	32.801±2.228
20% 2DGaussian	ZF	0.348±0.094	0.634±0.052	21.279±2.238
	ReconResNet	0.183±0.049	0.914±0.020	26.806±2.007
	H-CNN	0.118±0.013	0.844±0.040	30.391±2.088
	DDNet	0.081±0.015	0.928±0.025	33.732±2.416
	ComConDuDoCNet	0.065±0.009	0.951±0.013	35.604±2.222
30% 2DGaussian	ZF	0.292±0.071	0.669±0.051	22.726±2.143
	ReconResNet	0.151±0.045	0.931±0.016	28.527±1.850
	H-CNN	0.091±0.011	0.880±0.034	32.664±2.184
	DDNet	0.060±0.009	0.933±0.021	36.363±2.301
	ComConDuDoCNet	0.044±0.006	0.970±0.009	39.057±2.193
10% POSSION	ZF	0.342±0.091	0.642±0.055	21.412±2.377
	ReconResNet	0.167±0.041	0.917±0.020	27.554±2.079
	H-CNN	0.137±0.018	0.846±0.040	29.155±2.189
	DDNet	0.121±0.026	0.924±0.025	30.351±2.450
	ComConDuDoCNet	0.092±0.012	0.941±0.016	32.602±2.199
20% POSSION	ZF	0.256±0.063	0.700±0.055	23.889±2.441
	ReconResNet	0.160±0.051	0.936±0.016	28.081±1.955
	H-CNN	0.099±0.014	0.890±0.033	31.986±2.314
	DDNet	0.077±0.018	0.954±0.016	34.247±2.268
	ComConDuDoCNet	0.057±0.007	0.968±0.009	36.804±2.177
30% POSSION	ZF	0.182±0.039	0.749±0.051	26.792±2.259
	ReconResNet	0.132±0.045	0.958±0.010	29.845±2.332
	H-CNN	0.062±0.008	0.932±0.022	36.039±2.181
	DDNet	0.037±0.006	0.977±0.009	40.665±2.372
	ComConDuDoCNet	0.031±0.004	0.982±0.007	42.037±2.205
10% Radial	ZF	0.537±0.168	0.475±0.043	17.574±1.913
	ReconResNet	0.256±0.049	0.812±0.042	23.757±1.659
	H-CNN	0.219±0.024	0.717±0.057	25.054±1.966
	DDNet	0.200±0.040	0.801±0.052	25.962±2.541
	ComConDuDoCNet	0.181±0.023	0.800±0.043	26.724±2.088
20% Radial	ZF	0.359±0.093	0.644±0.053	20.980±2.325
	ReconResNet	0.163±0.048	0.945±0.011	27.864±1.927
	H-CNN	0.105±0.014	0.891±0.028	31.429±2.188
	DDNet	0.072±0.014	0.948±0.019	34.776±2.767
	ComConDuDoCNet	0.058±0.008	0.967±0.010	36.692±2.270
30% Radial	ZF	0.238±0.061	0.735±0.055	24.557±2.640
	ReconResNet	0.128±0.046	0.967±0.008	30.151±2.489
	H-CNN	0.077±0.013	0.938±0.018	34.227±2.362
	DDNet	0.040±0.009	0.977±0.010	40.052±2.999
	ComConDuDoCNet	0.034±0.005	0.984±0.005	41.284±2.179

算法	网络参数量/MB	推理时间/ms
ReconResNet	16.71	24.59
H-CNN	0.38	20.56
DDNet	9.25	35.04
ComConDuDoCNet	0.89	110.04

Reconstruction algorithm for undersampled magnetic resonance images based on complex convolution dual-domain cascade network

基于复卷积双域级联网络的欠采样磁共振图像重建算法

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Figures/Tables 11

References 23

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Metrics

采样模式	卷积	NRMSE	SSIM	PSNR/dB
2DGaussian	ZF	0.210±0.121	0.791±0.059	25.395±2.994
	复卷积	0.076±0.041	0.939±0.042	34.239±3.665
	实值卷积	0.089±0.041	0.910±0.041	32.514±2.969
POSSION	ZF	0.165±0.089	0.834±0.056	27.287±3.042
	复卷积	0.073±0.042	0.945±0.041	34.735±3.871
	实值卷积	0.081±0.041	0.928±0.041	33.484±3.208
Radial	ZF	0.207±0.121	0.815±0.057	25.525±3.174
	复卷积	0.071±0.039	0.947±0.038	34.860±3.748
	实值卷积	0.079±0.038	0.933±0.037	33.608±3.183

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