## 2 Materials and Methods
### Neural Network Architecture  
#### 2.2.1 The Enhanced Network in the Projection Sinogram Domain  
As shown in Figure 1, the enhanced network in the projection sinogram domain is indicated with the larger blue solid rectangle, which adopts a multi-scale feature extraction network. PCCT is commonly used in medical diagnosis, where medical images often consist of tissue, organs, and structures of different scales. After projection, these different scales of information are distributed in the projected sinogram. Therefore, the network can effectively capture information at different scales from the projected sinogram, improving the accuracy of image feature extraction. Here, initialization is performed as the first step. Then, four downsamplings of different scales are performed for multi-scale feature extraction. Finally, the multi-scale features are fused using the concatenate block represented by the gray rectangle to output the restored sinogram. Initialization: Initialization is performed with the convolution filter to convert the corrupted PCCT projection sinogram into its feature image, which is represented with the green cuboid. Increasing the size of the convolution kernel could improve the effect of feature extraction, while it exponentially increases the learning parameters and even causes overfitting. Studies have shown that multi-layer convolutional filters with smaller-sized convolution kernels could enlarge the receptive field and decrease the parameters. Therefore, the convolution filter with a size of \(3\times 3\) is used as the feature extractor. The stride is set to 1 to ensure that the sinogram has the same size as its feature. Rectified linear units (ReLU) and batch normalization (BN) techniques are integrated into initialization, so as to overcome the problem of vanishing gradients and to greatly speed up training. Multi-scale feature extraction: Multi-scale feature extraction is performed by four downsampling branches, where each branch contains a different number of downsampling blocks and the subsequent ResNets. Each downsampling block has a convolution kernel size of \(3\times 3\) and a stride of 2, as represented with the pink cuboid in Figure 1. The downsampling convolution intersects the conventional downsampling methods in DL, such as max-pooling or mean-pooling operations, to achieve higher learning accuracy and efficiency. However, the multi-scale feature extraction may cause degradation problems due to the network depth. ResNet provides an effective solution to the degradation problem of deep neural networks and accelerates convergence. Therefore, ResNets are introduced for the multi-scale feature extraction to enable the convergence and the acceleration of network training. As shown in Figure 1, four ResNets labeled \"ResNet1\", \"ResNet2\", \"ResNet3\" and \"ResNet4\" are used, and each of them is connected after the previous downsampling blocks. ResNet consists of four layers of convolutions with the linear rectification function (ReLU) and batch normalization (BN), where each layer has the structure as shown in the lower right corner of Figure 1. It adopts the highway network architecture for introducing an additional identity mapping transmission, which is performed by directly transmitting each layer's input to its subsequent layer's outputs. ResNet keeps the integrity of information to a certain extent, ensuring that the performance of the deep network is at least the same as the performance of the shallow one, not worse. Moreover, it only requires learning the difference between the input and output to speed up the learning process by simplifying its objectives and difficulty. Feature restoration: Upsampling is required to restore low-resolution features of the downsampling branches, since the previous step yields features with four proportionally decreased sizes. As represented with the yellow cuboid, upsampling is performed with the deconvolution operation referred to as the transpose convolution (ConvTranspose),which is the reverse operation of convolution.