## 4 Discussion  
After the network architecture is determined, the loss function has a great effect on the results. In this work, the weighted sums of MSE and MS-SSIM are adopted as the loss function, as shown in Equation (16), where \(\omega_{1}\) and \(\omega_{2}\) represent the weight of MSE and MS-SSIM. \(\omega_{1}\) of 1 and \(\omega_{2}\) of 0.2 are adopted in the experiments. To discuss the influence of the weight values on the image quality and to validate that the best weight values are adopted, the experiments are repeated with different \(\omega_{1}\) and \(\omega_{2}\). Considering the experimental datasets as examples, the network is trained with several commonly used loss functions (i.e., Loss1, Loss2, Loss3, Loss4, Loss5, and Loss6), as presented in Table 7.  
\[loss=\omega_{1}MSE(\alpha,\hat{\alpha})+\omega_{2}(1-MS\_SSIM(\alpha,\hat{ \alpha})) \tag{16}\]  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Efficiency** & **DD-Net** & **DLFBP** & **HD-Net** & **DDPC-Net** \\ \hline Parameters (million) & 1.46 & 2.04 & 5.91 & 4.48 \\ Runtime (s) & 0.22 & 0.29 & 0.61 & 0.52 \\ \hline \hline \end{tabular}
\end{table}
Table 6: The efficiency of the used methods with experimental datasets.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Weight** & **Loss1** & **Loss2** & **Loss3** & **Loss4** & **Loss5** & **Loss6** \\ \hline \(\omega_{1}\) & 1 & 1 & 1 & 1 & 1 & 0 \\ \(\omega_{2}\) & 0 & 0.1 & 0.2 & 0.5 & 1 & 1 \\ \hline \hline \end{tabular}
\end{table}
Table 7: The weight values of loss functions used in this work.  
Figure 8: The _rell_ curves of the average values of FSIM and IW-SSIM of the experimental testing datasets.  
Figure 9 shows one of the results of the experimental testing datasets with 60 views, and the ROI is indicated with a dashed square, which is enlarged and shown for better visualization. It can be observed that Loss2 and Loss3 help to obtain high-quality results, and the result with Loss3 has a relatively clearer structure. Table 8 lists the FSIM and IW-SSIM values of the images in Figure 9. These values provide evidence that the network trained with Loss3 outperforms those trained with other loss functions mentioned.  
Table 9 lists the average FSIM and MS-SSIM values of the results with different loss functions. Figure 10 presents the _rel1_ of the average values of FSIM and IW-SIIM. Furthermore, regarding the number of the sampling view, DDPC-Net with Loss3 enables the best performance in imaging. It also indicates that the CNNs with a combination of several losses may outperform that with a single loss of the applic  
Figure 9: The reconstructed images of one of the results of the experimental testing datasets with different loss functions. This sinogram has 60 sampling views, and the reconstructed images are obtained by DDPC-Net with loss functions as presented in Table 7.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Evaluation** & **Loss1** & **Loss2** & **Loss3** & **Loss4** & **Loss5** & **Loss6** \\ \hline FSIM & 0.9301 & 0.9348 & 0.9509 & 0.9340 & 0.9339 & 0.9270 \\ IW-SSIM & 0.9531 & 0.9573 & 0.9676 & 0.9558 & 0.9535 & 0.9458 \\ \hline \hline \end{tabular}
\end{table}
Table 8: The weight values of loss functions used in this work.