## 3 Results
### Qualitative Experimental Results for Lung Data  
The full experimental results of lung CT data reconstruction are shown in Figure 7. The reconstruction results of SART-TV and FBP methods become significantly worse as the projection data decreases, especially in the upper left and lower right corners, where the structure and texture have become completely blurred for the \([0^{\circ},\ 90^{\circ}]\) projection data. Both Tomo-GAN and SIN are methods based on unsupervised deep learning hybrid-domain artifact removal. Compared with SART-TV and FBP methods, the reconstruction results are significantly improved, but when the projection angle is only \([0^{\circ},\ 90^{\circ}]\); they too cannot effectively suppress artifacts and textures, and cannot effectively restore the profile information, as shown in the area corresponding to the red arrows in Figure 7. In contrast, the method proposed in this paper, through joint optimization of projection domain and image domain, played a significant role in suppressing artifacts, and the important structure  
Figure 5: SI-GAN inpainting results with 90\({}^{\circ}\) limited-angle data (one case per row). (**a**) The ground truth of sinogram; (**b**) the output of SI-GAN with (**c**) as input; (**c**) the original 90\({}^{\circ}\) limited-angle data; (**d**) the ground truth of reconstruction image; (**e**) FBP reconstruction for (**b**); (**f**) FBP reconstruction for (**c**).  
and texture information of the area corresponding to the red arrows is effectively restored and preserved.  
The absolute difference image can further compare the reconstruction results of each method. The results are shown in Figure 8. The smaller difference corresponds to a better reconstruction. The results of these three cases of projection angles all show that the reconstruction quality of the method in this paper works better. Comparing the reconstruction results of \([0^{\circ},\ 150^{\circ}]\) and \([0^{\circ},\ 90^{\circ}]\), it can be found that the reconstruction quality degrades when less projection data are used.  
Figure 6: Artifact-removed results of AR-GAN. **(a)** FBP reconstruction for 90\({}^{\circ}\) limited-angle data; **(b)** FBP reconstruction for the output of SI-GAN; **(c)** Output of AR-GAN with **(a)** as input; **(d)** Output of AR-GAN with **(b)** as input; **(e)** Ground truth of reconstruction image. The red line is a hand-drawn outer profile of **(e)**. (Best viewed with zoom-in).  
Figure 7: Experimental results on lung CT data. The first, second, and third rows are the results of reconstruction from \([0^{\circ},\ 150^{\circ}]\), \([0^{\circ},\ 120^{\circ}]\), and \([0^{\circ},\ 90^{\circ}]\) projection data. The first column is the full-angle reconstructed reference image, and the images in the subsequent columns are SIAR-GAN, Tomo-GAN, SIN, SART-TV and FBP reconstruction results. (Best viewed with zoom-in).  
In order to compare the texture and structural details of the reconstruction results of each method more clearly, we selected the red framed area in Figure 7 to zoom in, as shown in Figure 9. Consistent with the results of the above analysis, the SART-TV and FBP methods exhibited a considerable number of artifacts and only the outline can be distinguished, while the textural details were completely blurred. In the area indicated by the red arrow in Figure 9, part of the structure and contours were not restored correctly, and the textural details were also lost when Tomo-GAN and SIN methods had only a limited angle of \([0^{\circ},\ 90^{\circ}]\). In contrast, the SIAR-GAN method not only restored the complete structure, but also retained more textural details. Although there are still some imperfections compared with the reference image, SIAR-GAN produced high quality images that are superior to the other methods according to quantitative evaluation results by the RMSE, PSNR, and SSIM indicators.