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摘要:
深度展开网络由于可解释性高和学习能力强的特点受到广泛关注。现有CT图像重建算法的正则化项大多只关注某一类域中的信息，重建结果常存在边缘模糊等信息丢失的问题。基于此，提出一种基于稀疏变换先验约束的深度展开网络，用于进行稀疏角度CT重建。考虑像素域信息和变换域信息对图像重建具有重要作用，构建结合变换域稀疏正则化项和像素域一致性正则化项2种具有信息互补作用的正则化项，据此重新设计稀疏角度CT重建的目标函数。根据所构建的目标函数进行迭代优化求解，将得到的一系列约束关系映射为新的深度展开网络，用于低剂量CT图像的迭代重建。实验结果表明：所换算法得到的重建结果与经典的FISTA算法相比，平均峰值信噪比(PSNR)和视觉信息保真度(VIF)均有较大改善。
Abstract:Deep iterative unfolding networks have garnered a lot of attention lately because of their great learning capabilities and good interpretability. The regularization terms in existing CT image reconstruction methods mostly focus on information within a specific domain, leading to issues such as edge blurring and information loss in the reconstructed results. Therefore, a sparse transform prior constrain based deep unfolding network is proposed for sparse-view CT reconstruction. Two regularization terms with complementary information—transform-domain sparse regularization and pixel-domain consistency regularization—are created in consideration of the important roles that both pixel-domain and transform-domain information play in picture reconstruction. Based on these, the objective function for sparse-view CT reconstruction is redesigned. Furthermore, a new deep unfolding network for iterative reconstruction of low-dose CT is created by mapping a set of constraint relationships established from an iterative optimization solution for the constructed objective function. Experimental results demonstrate that the algorithm presented in this paper achieves a great improvement on average peak signal to noise ratio (PSNR) and visual information fidelity (VIF) compared to the classical FISTA algorithms.
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图 1 稀疏变换先验约束的深度展开网络整体框架
Figure 1. Overall structure diagram of sparse transform priors constrained deep unfolding network
图 4 采样角度数为60时，不同算法的重建结果和差值图结果示意图
Figure 4. Schematic diagrams of reconstruction results and difference using different algorithms on 60 views
图 5 采样角度数分别为90、180、270时，不同算法所获腹部CT重建结果示意图
Figure 5. Schematic diagrams of abdominal CT reconstruction results by different algorithms on 90, 180 and 270 views
图 6 60个采样角度下的消融网络重建结果及ROI
Figure 6. Reconstruction results and ROI using ablation networks on 60 views
表 1 不同算法在4种采样角度数下的重建结果量化分析值
Table 1. Quantitative values for reconstruction results by different algorithms on 4 kinds of views
采样角度数 重建算法 SSIM(均值±标准差)↑ PSNR(均值±标准差)/dB↑ VIF(均值±标准差)↑ MSE(均值±标准差)↓ 60 FBP 0.4557 ±0.0512 14.5076 ±1.1519 0.2234 ±0.0174 2386.2 ±646.8316 RED-CNN[44] 0.7775 ±0.0355 27.9191 ±2.2010 0.2792 ±0.0161 121.3903 ±79.5000 FBP ConvNet[45] 0.8078 ±0.0294 30.8149 ±1.6828 0.3346 ±0.0197 58.1162 ±23.9885 Learned Primal-Dual[23] 0.8475 ±0.0144 31.3078 ±1.3920 0.3445 ±0.0186 50.8037 ±18.5659 AirNet[46] 0.8434 ±0.0229 32.0765 ±1.7189 0.3744 ±0.0214 44.1415 ±23.2134 FISTA-Net[39] 0.8865 ±0.0171 31.8418 ±2.0896 0.3413 ±0.0177 48.3184 ±27.7186 STPC-DUN 0.8927 ±0.0155 33.0876 ±1.8421 0.5152 ±0.0398 35.4286 ±19.8697 90 FBP 0.5181 ±0.0455 16.9089 ±1.1465 0.2861 ±0.0193 1373.2 ±381.6216 RED-CNN[44] 0.8348 ±0.0273 31.5023 ±1.8976 0.3667 ±0.0170 50.8892 ±25.9904 FBP ConvNet[45] 0.8443 ±0.0243 32.6084 ±1.8659 0.3932 ±0.0224 39.4103 ±19.6849 Learned Primal-Dual[23] 0.8456 ±0.0245 32.7864 ±1.9438 0.5123 ±0.0261 39.4386 ±33.4385 AirNet[46] 0.8880± 0.0201 35.1691 ±1.7574 0.4933 ±0.0199 21.7726 ±11.9778 FISTA-Net[39] 0.9073 ±0.0128 34.5148 ±1.8938 0.3957 ±0.0192 25.6160 ±14.1523 STPC-DUN 0.9125 ±0.0169 35.7043 ±1.6713 0.5859 ±0.0360 18.9724 ±8.8451 180 FBP 0.6452 ±0.0423 20.9855 ±2.0037 0.3567 ±0.0251 576.4639 ±280.3785 RED-CNN[44] 0.9012 ±0.0159 35.2431 ±1.6113 0.5601 ±0.0188 20.9099 ±8.9502 FBP ConvNet[45] 0.9016 ±0.0215 36.5055 ±2.0669 0.6022 ±0.0289 16.3913 ±9.1723 Learned Primal-Dual[23] 0.9413 ±0.0174 36.7753 ±2.6183 0.5958 ±0.0259 16.9274 ±13.9621 AirNet[46] 0.9223 ±0.0215 38.0494 ±2.0437 0.6384 ±0.0253 11.6899 ±8.4169 FISTA-Net[39] 0.9408 ±0.0090 37.1486 ±2.1449 0.5500 ±0.0252 14.3909 ±8.8337 STPC-DUN 0.9460 ±0.0082 39.1352 ±1.5893 0.7603 ±0.0380 8.5092 ±3.4297 270 FBP 0.6627 ±0.0308 21.9470 ±1.6608 0.4109 ±0.0210 447.6719 ±181.3476 RED-CNN[44] 0.9443 ±0.0089 38.6660 ±1.4345 0.7015 ±0.0189 9.3455 ±3.3080 FBP ConvNet[45] 0.9339 ±0.0228 38.9396 ±2.5118 0.7026 ±0.0294 10.1832 ±8.7321 Learned Primal-Dual[23] 0.9449 ±0.0207 39.5926 ±1.9604 0.7279 ±0.0232 7.9585 ±4.3854 AirNet[46] 0.9441 ±0.0203 40.2075 ±2.2539 0.7585 ±0.0218 7.2035 ±4.7297 FISTA-Net[39] 0.9583 ±0.0071 40.1174 ±1.7459 0.6765 ±0.0222 6.9175 ±3.3517 STPC-DUN 0.9637 ±0.0076 40.9253 ±1.6207 0.8256 ±0.0384 5.6504 ±2.3047 注：“↑”表示该指标数值越大，图像与真实图像越接近；“↓”表示该指标数值越小，图像与真实图像越接近；加粗数值表示最优值。 
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表 2 不同消融网络所获重建结果的平均量化分析值
Table 2. Average quantitative values for reconstruction results by different ablation networks
采样角度数 正则化类型 PSNR/dB↑ SSIM↑ VIF↑ MSE↓ FSNet PDCNet 90 √ × 34.7607 0.8946 0.5360 24.7216 × √ 35.1753 0.9056 0.5662 21.1300 √ √ 35.7043 0.9125 0.5859 18.9724 180 √ × 37.7035 0.9419 0.6871 13.2066 × √ 37.6831 0.9242 0.7152 11.9676 √ √ 39.1352 0.9460 0.7603 8.5092
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