## 3 Results
### Reconstruction Results  
#### 3.2.1 Training with the Sinogram Domain Loss \(L_{sine}\)  
Figure 4 shows some test CT slices reconstructed by the four methods on the two datasets. The reconstructed images of the three machine-learning-based models are close and significantly better than those of linear interpolation. As the sparsity level \(s\) increases, the quality of all reconstructed CT images decreases significantly, and the linear interpolation method degrades the most significantly due to not using prior knowledge in the training set. Our network performs slightly better than the two baseline networks (SDS-net and Res-Unet) at higher sparse levels (\(s=8,15\)). As shown in the local zooms corresponding to \(s=8\) and \(15\), the proposed network is better in terms of edge preservation of CT images.  
Figure 3: CT samples from (a) the LIDC-IDR dataset and (b) the AAPM dataset.  
The average PSNR values (dB) in the sinogram domain on the two datasets are given in Table 1, and reflect the similarity between the estimated sinogram (\(\hat{\mathbf{Y}}\)) and the expected (full-view) sinogram (\(\mathbf{Y}\)). Consistent with the results of human visual inspections, the three deep-learning-based methods significantly outperform linear interpolation in sinogram domain prediction.  
The proposed interpolation network performs comparably to the two baseline networks on both datasets, though its computational complexity is significantly lower than those of the two baselines (a comparison of computational efficiency will be given in Section 3.3). On the LIDC-IDRI dataset, when \(s=2/4\), the reconstruction results of our network are 60.31 dB and 52.24 dB, which are only 0.2 dB lower than the optimal results. On the AAPM dataset, when \(s=2/4\), the reconstruction results of our network are 56.84 dB and 50.12 dB. The highest difference compared to the optimal result is also only 0.6 dB.  
Ours network demonstrates a slight advantage over the other deep-learning-based methods, particularly at higher levels of sparsity (\(s=8,15\)). On the LIDC-IDRI dataset, the advantages of our model are more significant. For \(s=8/15\), it outperforms the optimal baseline model by 2.2 bB and 1.81 dB, respectively. Meanwhile, our model also maintains this advantage with the AAPM dataset, with the reconstruction results being higher than the optimal baseline model by 0.4 dB and 1.21 dB.  
Tables 2 and 3 show the average PSNR (dB) and SSIM (%) in the CT image domain, and this reflects the similarity between the reconstructed CT images (\(\hat{\mathbf{X}}\)) and the expected (full-dose) CT images (\(\mathbf{X}\)). In the CT image domain, combining both PSNR and SSIM metrics, the proposed network still performs well. The trends in the PSNR in the CT image domain and in the sinogram domain are consistent with both the AAPM and LIDC-IDRI  
\begin{table}
\begin{tabular}{c l c c c} \hline \hline \multicolumn{2}{c}{**Sparse Levels**} & \multicolumn{1}{c}{**s = 2**} & \multicolumn{1}{c}{**s = 4**} & \multicolumn{1}{c}{**s = 8**} & \multicolumn{1}{c}{**s = 15**} \\ \hline \multirow{3}{*}{LIDC-IDRI} & Linear interp & 55.77 & 48.07 & 42.01 & 37.46 \\  & SDS-net & **60.57** & **52.76** & 45.04 & 39.23 \\  & Res-Unet & 58.74 & 51.52 & 44.82 & 39.94 \\  & ours & 60.31 & 52.54 & **47.26** & **41.75** \\ \hline \multirow{3}{*}{AAPM} & Linear interp & 51.93 & 45.35 & 40.14 & 35.57 \\  & SDS-net & **56.95** & **50.72** & 44.77 & 38.54 \\ \cline{1-1}  & Res-Unet & 56.05 & 48.74 & 43.19 & 37.69 \\ \cline{1-1}  & ours & 56.84 & 50.12 & **45.17** & **39.75** \\ \hline \hline \end{tabular}
\end{table}
Table 1: Averaged PSNR (dB) in the sinogram domain trained with \(l_{sine}\).  
Figure 4: Reconstructed CT images of the four methods from our own dataset (**a**) and the AAPM dataset (**b**).  
datasets. When the sparsity level rises, the SSIM of the reconstructed image decreases rapidly. When \(s=15\), the optimal reconstruction results in SSIM are also only 78.84% and 66.53%, requiring subsequent denoising in the image domain.