Low-dose CT Reconstruction Based on Deep Energy Models
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摘要: 降低计算机断层扫描（CT）的剂量对于降低临床应用中的辐射风险至关重要，深度学习的快速发展和广泛应用为低剂量CT成像算法的发展带来了新的方向。与大多数受益于手动设计的先验函数或有监督学习方案的现有先验驱动算法不同，本文使用基于深度能量模型来学习正常剂量CT的先验知识，然后在迭代重建阶段，将数据一致性作为条件项集成到低剂量CT的迭代生成模型中，通过郎之万动力学迭代更新训练的先验，实现低剂量CT重建。实验比较，证明所提方法的降噪和细节保留能力优良。Abstract: Reducing the dose of computed tomography (CT) is essential for reducing the radiation risk in clinical applications. With the rapid development and wide application of deep learning, it has brought new directions for the development of low-dose CT imaging algorithms. Unlike most existing prior-driven algorithms that benefit from manually designed prior functions or supervised learning schemes, in this paper, we use an energy-based deep model to learn the prior knowledge of normal-dose CT, and then in the iterative reconstruction phase, we integrate data consistency as a conditional item into the iterative generation model of low-dose CT, and realize the low-dose CT reconstruction through the prior experience of iterative updating training of Langevin dynamics. The experimental results show that the proposed method hold excellent noise reduction and detail retention capabilities.
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Key words:
- low-dose CT /
- deep learning /
- Langevin dynamics /
- deep energy based model
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图 3 不同方法的CIRS挑战数据的重建结果
Figure 3. Reconstruction results of CIRS challenge data by different methods
图 4 原始CT图像与不同算法重建的CT图像之间的残差图
Figure 4. The residual plot of the reference CT images and the CT images reconstructed by different algorithms
图 6 不同方法的AAPM数据集的重建结果
Figure 6. Reconstruction results of AAPM challenge data by different methods
图 7 使用AAPM数据集的原始CT图像与不同算法重建结果之间的残差图
Figure 7. The residual plot of the original CT images using AAPM dataset and the CT images reconstructed by different algorithms
表 1 EBM-LDCT算法的重建过程
Table 1. The reconstruction process of the EBM-LDCT algorithm
算法1 初始化：输入数据${\tilde x^0}\sim N(0,{\boldsymbol{I}})$，动量项${{\boldsymbol{w}}^0}$，参数$ \beta $，松弛因子$ \gamma $，迭代次数$ T $
开始循环：$t = 1,{\text{ }}2,{\text{ }} \cdots ,{\text{ }}T$
设定$ { {\boldsymbol{z} }^t}\sim N(0,{\boldsymbol{I} }) $
根据公式（10）更新：$ {\tilde {\boldsymbol{u} }^t} = {\tilde {\boldsymbol{x} }^{t - 1} } - \displaystyle\dfrac{ {\,\varepsilon \,} }{2}{\nabla _x}E{}_\theta \left( { { {\tilde {\boldsymbol{x} } }^{t - 1} } } \right) + \sqrt \varepsilon { {\boldsymbol{z} }^t} $
根据公式（8）更新：$ {\tilde {\boldsymbol{x} }^t} = { {\boldsymbol{w} }^{t - 1} } - \displaystyle\dfrac{ { {\kern 1 pt} { {\boldsymbol{A} }^{\rm{T} } }\left( { {\boldsymbol{A} }{ {\tilde {\boldsymbol{x} } }^{t - 1} } - {\boldsymbol{y} } } \right) + \beta \left( { { {\tilde {\boldsymbol{x} } }^{t - 1} } - { {\tilde {\boldsymbol{u} } }^t} } \right){\kern 1 pt} } }{ { { {\boldsymbol{A} }^{\rm{T} } }{\boldsymbol{A} }{\boldsymbol{1} } + \beta {\boldsymbol{1} } } } $
最后更新：${{\boldsymbol{w}}^t} = {\tilde {\boldsymbol{x}}^t} + \gamma \left( { { {\tilde {\boldsymbol{x}}}^t} - { {\tilde {\boldsymbol{x}}}^{t - 1} } } \right)$
${\tilde {\boldsymbol{x}}^t} \leftarrow {{\boldsymbol{w}}^t}$
结束
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表 2 使用CIRS数据集的多种低剂量CT重建方法定量结果比较
Table 2. Comparison of quantitative results of multiple LDCT reconstruction methods using CIRS dataset
方法 MAE PSNR/dB SSIM/10-2 FBP（Ramp-filter） 9.48±0.64 40.67±0.59 94.36±0.87 TV 7.64±0.41 42.12±0.35 96.58±0.51 K-SVD 7.01±0.19 42.86±0.34 97.01±0.36 RED-CNN 6.74±0.07 41.76±0.12 97.47±0.16 EBM-LDCT 6.29±0.23 42.73±0.20 97.81±0.27
下载: 导出CSV
表 3 使用AAPM数据集的多种LDCT重建方法定量结果比较
Table 3. Comparison of quantitative results of multiple LDCT reconstruction methods using AAPM dataset
方法 MAE PSNR/dB SSIM/10-2 FBP（Ramp-filter） 67.69±13.16 28.68±2.03 44.43±7.18 TV 29.65±4.60 34.98±1.32 86.10±3.48 K-SVD 21.00±1.04 35.68±2.26 81.98±2.41 RED-CNN 16.97±1.02 39.37±1.87 94.78±0.56 EBM-LDCT 18.75±1.31 39.56±0.54 94.16±0.68
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