## 2 Method
### Joint Training Process  
In order to achieve collaborative optimization between the projection domain and the image domain, we devised a joint training strategy. This strategy involves optimizing the parameters of the UNet network and the ResNet network through a unified loss function. The loss function consists of multiple components aimed at evaluating several key aspects of artifact correction, including the following:  
Mean Square Error (MSE) loss, denoted as \(Loss_{MSE}\). \[Loss_{MSE}=\frac{\sum_{i=1}^{n}\left(y_{i}-y_{i}^{p}\right)^{2}}{n}\]  
where \(y_{i}\) represents the ground truth value and \(y_{i}^{p}\) represents the predicted value. \(Loss_{MSE}\) evaluates and minimizes the overall pixel density error between the corrected image and \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter** & **Numeric Value** \\ \hline Source-to-detector distance & 1200 (mm) \\ Source-to-rotation distance & 600 (mm) \\ Object size & \(512\times 512\) \\ Pixel size & \(0.1\times 0.1\) (mm\({}^{2}\)) \\ Number of detector units & 704 \(\times\) 1 \\ Detector size & \(0.1\times 0.1\) (mm\({}^{2}\)) \\ Projection angles & 320 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Main parameters of simulation CT system. Figure 5: Partial projection data in the training set, reconstructed CT images containing metal artifacts, and corresponding ideal CT images. The materials corresponding to the CT images in the picture are iron, aluminum, and brass-zinc alloy. the ground truth image, helping adjust the global intensity values and suppress global distortions caused by metal artifacts. L\({}_{1}\) loss, denoted as \(Loss_{L1}\). \[Loss_{L_{1}}=\sum_{i=1}^{n}\lvert y_{i}-y_{i}^{p}\rvert\]  
\(Loss_{L_{1}}\) is more sensitive to edges in the image, which is beneficial for preserving image details and textures, especially when it is necessary to retain object edges and details during the correction process. Structural Similarity Index (SSIM) loss [25], denoted as \(Loss_{SSIM}\). \[Loss_{SSIM}=1-SSIM(x,y)\]  
\[SSIM(x,y)=\frac{\left(2\mu_{x}\mu_{y}+C_{1}\right)\left(2\sigma_{x}\sigma_{y} +C_{2}\right)}{\left(\mu_{x}^{2}+\mu_{y}{}^{2}+C_{1}\right)\left(\sigma_{x}{}^ {2}+\sigma_{y}{}^{2}+C_{2}\right)}\]  
\(SSIM(x,y)\) measures the similarity between the test image x and the reference image y, where higher values indicate better structural similarity. \(\mu_{x}\), \(\mu_{y}\) are the mean luminance values, \(\sigma_{x}\), \(\sigma_{y}\) are the standard deviations with respect to \(\mu_{x}\), \(\mu_{y}\), and \(C_{1}\) and \(C_{2}\) are constants representing contrast factors. By comparing the brightness, contrast, and structure of the images, \(Loss_{SSIM}\) helps ensure visual realism and attractiveness in the corrected images. Additionally, it preserves the structural information of non-metallic regions in the images, preventing excessive smoothing or the loss of details while removing metal-induced artifacts. The total loss function, denoted as \(Loss_{Total}\), is a weighted combination of the aforementioned losses. \[Loss_{Total}=\alpha Loss_{MSE}+\beta Loss_{L1}+\lambda Loss_{SSIM}\]  
The joint loss function enables the model to reduce pixel-level errors while maintaining image structure and details, leading to comprehensive performance improvements. In this study, the MSE loss is assigned the highest weight of 0.8, while the L\({}_{1}\) loss and SSIM loss are assigned weights of 0.1 each. The MSE loss focuses on the global average error at the pixel level. In the early stage of metal artifact correction, it is typically more important to reduce the large-scale deviations caused by artifacts rather than handle details or structure. Assigning a higher weight to the MSE loss and lower weights to the L\({}_{1}\) and SSIM losses prevents the model from excessively focusing on image details and structural fidelity during the early training stage, ensuring that the model does not overlook large-scale correction due to details. The optimizer is Adam, with an initial learning rate of 0.0001.