## 2 Materials and Methods
### Data and Settings  
In order to verify the effectiveness of the SIAR-GAN method proposed in this paper, we collected 13,120 CT lung images of patients from the well-known open source clinical medical image database DeepLesion [28] and 3400 CT head images from the LDCT and Projection data of the Cancer Archives [29]. We expanded the head dataset to 13,600 by data augmentation with direct copy. To facilitate the completion of the information near the 180\({}^{\circ}\) edge of the sinogram, CT image was transformed to sinogram with the size of \(512\times 192\) using Radon transform during training phase, and the sampling interval of the projected data was 1\({}^{\circ}\). Remove part view of the projected data to simulate limited-angle sinograms. This generated missing projection data of \([90^{\circ},180^{\circ}]\), \([120^{\circ},180^{\circ}]\), and \([150^{\circ},180^{\circ}]\), together with sinograms of full projection data, forming a training sample dataset to train SI-GAN. During the application phase, the \([0^{\circ},12^{\circ}]\) projection data of the sinogram were duplicated before the mirror and 180\({}^{\circ}\) rotation operations were performed, and then the results were used as the projection data corresponding to \([180^{\circ},192^{\circ}]\) of the sinogram. In the lung CT dataset and head CT dataset, 9000 images were used for training and the remaining images were used for testing. We extracted the \([0^{\circ},180^{\circ}]\) sinogram image from the output of SI-GAN network test set for FBP reconstruction. The reconstruction results and the collected original CT images of patients were used as AR-GAN unpaired datasets. The learning rate of the SI-GAN network was set to 0.0001, the number of epoch was 200, and the batch size was 16. The learning rate of the AR-GAN was 0.0002, the number of epoch was 200, and the batch size was 1. The training time of SI-GAN was 33 h, and the training time of AR-GAN was 95 h. To visualize the convergence of the network, we calculated the PSNR, SSIM, and RMSE Indicator values of the test set after each epoch. Figure 4 shows the averaged PSNR, SSIM, and RMSE Indicator values versus the number of epochs for SI-GAN and AR-GAN. For the sake of fairness to the SIN algorithm and the Tomo-GAN method, we used the same data set and the same epoch as AR-GAN and maintained the training strategy and parameters consistent with original text. The FBP algorithm selects Ram-Lak as the filter function and nearest neighbor interpolation as the interpolation function. Since the literature has not come to a consensus on the data-driven parameters of the setting method, we tuned the SART-TV hyperparameters manually to obtain the best average performance. We finally set 15 iterations for each image, and in each epoch, we took 15 steps of TV with the factors \(\alpha=0.06\) and \(\alpha_{s}=0.997\), where \(\alpha\) denotes the maximum step size for the steepest descent of TV minimization, and \(\alpha_{s}\) is the decreasing proportion of \(\alpha\) after each calculation.  
Figure 4: Averaged PSNR, SSIM, and RMSE Indicator values versus the number of epochs for SI-GAN and AR-GAN based on the \([0^{\circ},90^{\circ}]\) projection data reconstruction training from lung data.