## 3 Results
### Head Dataset Results  
The results for all tissues using the head dataset are depicted in Tables 1-3; the results using only the bone voxels are detailed in Tables 4-6; the results using only the fat voxels are detailed in Tables 7-9; and the results using only the soft-tissue voxels are detailed in Tables 10-12. The best performing 2D network for the head dataset was the Residual-net. The results presented a MAE of 99.83 HU, a PSNR of 24.83 and a Pearson Coefficient of 0.931 in all tissues, and a MAE of 326.33 HU, a PSNR of 19.04 and a Pearson Coefficient of 0.826 in bone voxels. The ANOVA test revealed a statistically significant effect of the 2D architectures for MAE results (all tissues: \(F_{2,36}=91.1\), \(p<0.001\); bone: \(F_{2,36}=74.2\), \(p<0.001\)) and PSNR results (all tissues: \(F_{2,36}=99.3\), \(p<0.001\); bone: \(F_{2,36}=85.6\), \(p<0.001\)). A paired \(t\)-test was used to compare the Residual-net to the other networks reporting also statistically significant differences in the MAE and in the PSNR (Table 13). Using 2D convolutions, the Atrous-net and the U-net performed 5% and 18% worse than the residual-net, respectively. Moreover, the U-net network was clearly behind the other networks using 2D convolutions. Nevertheless, the U-net in 3D-16 obtained a MAE of 89.54 HU, a PSNR of 25.69 and a Pearson Coefficient of 0.943 in all tissues, and a MAE of 289.10 HU, a PSNR of 20.05 and a Pearson Coefficient of 0.861 in bone voxels, which were the best results for the head dataset. The ANOVA test also reported a statistically significant effect of the 3D networks for the MAE (all tissues: \(F_{2,36}=63.2,p<0.001\); bone \(F_{2,36}=189.8\), \(p<0.001\)) and the PSNR (all tissues: \(F_{2,36}=10.5\), \(p<0.001\); bone: \(F_{2,36}=83.1\), \(p<0.001\)). The post hoc paired \(t\)-test that is depicted in Table 14 also reported statistically significant differences in the MAE and PSNR after comparing each architecture. Summarizing, the results using 3D convolutions from the U-net were 17% and 10% better than those of the Atrous-net and Residual-net, respectively. Visual result examples of head pseudo-CTs are depicted in Figures 6 and 7. Table 15 shows the time needed to synthesize a whole head volume using the different architectures. \begin{table}
\begin{tabular}{c c c c} \hline \hline  & **MAE** & **PSNR** & **Pearson** \\ \hline
**2D** & \(117.21\)\(\pm\) 9.49 & 23.26 \(\pm\) 0.596 & 0.898 \(\pm\) 0.011 \\ \hline
**3D-32** & \(93.45\)\(\pm\) 7.96 & 25.40 \(\pm\) 0.675 & 0.939 \(\pm\) 0.010 \\ \hline
**3D-16 av** & \(90.06\)\(\pm\) 7.65 & **25.77 \(\pm\) 0.706** & **0.944 \(\pm\) 0.010** \\ \hline
**3D-16** & \(89.54\)\(\pm\) 7.79 & 25.69 \(\pm\) 0.703 & 0.943 \(\pm\) 0.009 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Head dataset with U-net. Mean Absolute Error, PSNR and Pearson coefficient on the head data set obtained using U-net with different convolutions and reconstructions. \begin{table}
\begin{tabular}{c c c c} \hline \hline  & **MAE** & **PSNR** & **Pearson** \\ \hline
**2D** & \(105.16\)\(\pm\) 8.92 & 24.51 \(\pm\) 0.615 & 0.924 \(\pm\) 0.009 \\ \hline
**3D-32** & \(110.89\)\(\pm\) 7.56 & 24.12 \(\pm\) 0.546 & 0.917 \(\pm\) 0.009 \\ \hline
**3D-16 av** & \(104.98\)\(\pm\) 7.28 & **25.77 \(\pm\) 0.706** & 0.926 \(\pm\) 0.009 \\ \hline
**3D-16** & \(104.03\)\(\pm\) 6.98 & 24.65 \(\pm\) 0.555 & **0.927 \(\pm\) 0.009** \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Head dataset with Atrous-Net. Mean Absolute Error, PSNR and Pearson coefficient on the head data set obtained using Atrous network with different convolutions and reconstructions.