# Sparse-View Artifact Correction of High-Pixel-Number Synchrotron Radiation CT
## 2 Methods and Data  
### Method  
The method proposed in this paper is shown in Figure 2: First, the sparse-view slices are reconstructed with filtered back projection (FBP). The slices with aliasing artifacts of 1728 \(\times\)1728 pixels are cropped with overlap into patches of 480 \(\times\) 480 pixels. Cropping with pixel overlap avoids pixel discontinuity in image stitching. Then, these patches are passed through the neural network to start training and artifact-free patches as labels. Once all the patches of each slice have been trained, these patches are reintegrated to a complete CT slice, and we further expect the complete CT slice to be wirelessly close to the full-view CT slice in terms of feature structure. In other words, we add a \(Loss_{global}\) here (see Figure 2).  
Due to incorporating an attention mechanism in its network architecture (see Figure 3), the Attention U-Net [31] model demonstrates an enhanced capability in extracting detailed image features. Therefore, in this paper, the Attention U-Net is employed as the network model for artifact correction. In the left part of the network, two convolutions are first used in each dimension to extract image features. After down-sampling four times in the Max Pooling layer, the receptive field of the network increases continuously. The right part of the network is expanded by the up-sampled feature map to restore the image size. The introduction of the Attention-Gate module allows the model to focus on the target information, reduce the weight of irrelevant information, and improve the ability of the network to retain details. After the Attention-Gate module and concatenation with the up-sampled features on the feature channel, the image resolution can be recovered. The network model is implemented using the PyTorch framework, running on Intel Xeon Gold 6240 CPU and Nvidia V100 GPU. The Adam optimizer was used during training, with a total of 60 epochs, and the initial learning rate was 0.0001. Every 10 epochs, the learning rate was reduced to 0.8 times the original. The images in this dataset are all of 8-bit depth. Before training the network, we normalize their grayscale values by dividing by 255, thus scaling them to a range between 0 and 1.  
During training, the patch section uses the mean square error as the loss function:  
\[Loss_{local}(X^{\prime},X)=\left|X^{\prime}-X\right|^{2} \tag{1}\]  
Figure 3: Attention U-Net network structure.  
Figure 2: Flow chart of aliasing artifact correction method.  
where \(X^{\prime}\) is the neural network's patch output, and \(X\) represents the patch's label. In addition, the structural similarity index [32] integrates the brightness \(l(Y^{\prime},Y)\), contrast \(c(Y^{\prime},Y)\), and structure \(s(Y^{\prime},Y)\) of the two images, which can be used to evaluate the similarity between the \(Y^{\prime}\) (reintegrated CT slice)and the label image \(Y\) (full-view CT slice):  
\[l(Y^{\prime},Y)=\frac{2m_{Y^{\prime}}m_{Y}+c_{1}}{m_{Y^{\prime}}^{2}+m_{Y}^{2}+ c_{1}} \tag{2}\]  
\[c(Y^{\prime},Y)=\frac{2\sigma_{Y^{\prime}}\sigma_{Y}+c_{2}}{\sigma_{Y^{\prime }}^{2}+\sigma_{Y}^{2}+c_{2}} \tag{3}\]  
\[s(Y^{\prime},Y)=\frac{\sigma_{Y^{\prime}Y}+c_{3}}{\sigma_{Y^{\prime}}\sigma_{Y }+c_{3}} \tag{4}\]  
\[SSIM(Y^{\prime},Y)=\frac{(2m_{Y^{\prime}}m_{Y}+c_{1})(2\sigma_{Y^{\prime}}+c_{ 2})}{(m_{Y^{\prime}}^{2}+m_{Y}^{2}+c_{1})(\sigma_{Y^{\prime}}^{2}+\sigma_{Y}^ {2}+c_{2})} \tag{5}\]  
where \(m\) represents the mean, \(\sigma\) represents the standard deviation, \(c_{1}\), \(c_{2}\) and \(c_{3}\) are constants. We propose to use \(SSIM(Y^{\prime},Y)\) to further constrain the direction of network optimization:  
\[Loss_{global}(Y^{\prime},Y)=\lambda\cdot(1-SSIM(Y^{\prime},Y)) \tag{6}\]  
In this paper, the \(\lambda\) is 0.1. In summary, the loss function for network training consists of two parts:  
\[Loss=Loss_{local}(X^{\prime},X)+Loss_{global}(Y^{\prime},Y) \tag{7}\]