# Deep-Learning-Based Framework for PET Image Reconstruction from Sinogram Domain
## 4 Results
### Simulation Experiments
#### 4.1.4 Robustness and Runtime Analysis  
The Zubal thorax dataset was chosen to validate the robustness of the algorithm under different counting rates. The values of the evaluation parameters for reconstruction are shown in Figure 10. The three curves at the top of both the bias graph and the variance graph show the properties of MLEM, the three curves in the middle show the properties of TV, and the curves at the bottom show the properties of cGANs. The three solid curves at the bottom of the graph have the highest coincidence, which means that the cGAN method is the least affected by the count value. For the other two methods, as the count increases, both the variance and bias of the MLEM and TV methods decrease distinctly. Therefore, one can conclude that these two methods are significantly influenced by the \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Frame**} & \multirow{2}{*}{**Method**} & \multicolumn{4}{c}{**Bias**} & \multicolumn{4}{c}{**Variance**} \\ \cline{3-10}  & & **Total** & **ROI1** & **ROI2** & **ROI3** & **Total** & **ROI1** & **ROI2** & **ROI3** \\ \hline \multirow{3}{*}{3 rd} & MLEM & 0.1225 & 0.1739 & 0.0654 & 0.1284 & 0.0271 & 0.0510 & 0.0070 & 0.0233 \\ \cline{2-10}  & TV & 0.0611 & 0.0909 & 0.0503 & 0.0420 & 0.0110 & 0.0227 & 0.0040 & 0.0063 \\ \cline{2-10}  & **cGANs** & **0.0189** & **0.0112** & **0.0454** & **2.0**\(\times\)\(10^{-5}\) & **8.1**\(\times\)\(10^{-4}\) & **2.4**\(\times\)\(10^{-4}\) & **0.0022** & **7.8**\(\times\)\(10^{-8}\) \\ \hline \multirow{3}{*}{7 th} & MLEM & 0.1034 & 0.1335 & 0.0547 & 0.1221 & 0.0204 & 0.0356 & 0.0047 & 0.0210 \\ \cline{2-10}  & TV & 0.0407 & 0.0586 & 0.0189 & 0.0446 & 0.0086 & 0.0168 & 0.0014 & 0.0077 \\ \cline{2-10}  & **cGANs** & **0.0106** & **0.0066** & **0.0252** & **2.0**\(\times\)\(10^{-5}\) & **2.7**\(\times\)\(10^{-4}\) & **1.0**\(\times\)\(10^{-4}\) & **7.2**\(\times\)\(10^{-4}\) & **7.8**\(\times\)\(10^{-8}\) \\ \hline \multirow{3}{*}{12 th} & MLEM & 0.1049 & 0.1325 & 0.0573 & 0.1249 & 0.0208 & 0.0355 & 0.0055 & 0.0215 \\ \cline{2-10}  & TV & 0.0457 & 0.0631 & 0.0342 & 0.0399 & 0.0089 & 0.0173 & 0.0025 & 0.0065 \\ \cline{2-10}  & **cGANs** & **0.0042** & **0.0058** & **0.0068** & **1.0**\(\times\)\(10^{-5}\) & **6.7**\(\times\)\(10^{-5}\) & **8.9**\(\times\)\(10^{-5}\) & **1.1**\(\times\)\(10^{-4}\) & **3.9**\(\times\)\(10^{-8}\) \\ \hline \multirow{3}{*}{18 th} & MLEM & 0.1211 & 0.1545 & 0.0649 & 0.1439 & 0.0263 & 0.0444 & 0.0068 & 0.0277 \\ \cline{2-10}  & TV & 0.0531 & 0.0689 & 0.0320 & 0.0584 & 0.0109 & 0.0195 & 0.0031 & 0.0103 \\ \cline{2-10}  & **cGANs** & **0.0055** & **0.0067** & **0.0098** & **2.0**\(\times\)\(10^{-5}\) & **1.0**\(\times\)\(10^{-4}\) & **1.1**\(\times\)\(10^{-5}\) & **2.0**\(\times\)\(10^{-4}\) & **7.8**\(\times\)\(10^{-8}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Zubal thorax reconstruction evaluation results. Figure 9: Bias and variance of whole images for ROI1, ROI2, and ROI3 of the Zubal thorax phantom. count. This may be because both methods are based on a probabilistic statistical model; therefore, when the count increases, the probabilistic statistical characteristics of the data can be better guaranteed. Compared with the other two methods, the proposed framework has minimum variance and deviation and maximum stability. The Zubal head phantom is more complex than the Zubal thorax phantom. It was used to verify whether the proposed algorithm can predict the reconstructed images of the last six frames by training the first 12 frames. Figure 10: Bias and variance of three methods (MLEM, TV, and cGANs) of Zubal thorax phantom with different counts. The top three curves represent the results of the MLEM method, the middle curves represent results of the TV method, and the bottom curves correspond to the proposed method. With increasing counts, the bias and variance values of the MLEM and TV methods decrease, but there is a slight effect on the cGANs method. The concentration distribution of the first 12 frames is shown in Figure 11a.