## 4 Discussion  
By comparing the 3D reconstructions of the simulated phantoms with the activity maps used in the simulation, as shown in Figure 4, we can see how both show the same distribution of activity. In order to validate the results obtained, a manual check was performed on all the generated phantoms to confirm that the voxelized images and their reconstructions were similar and that the radiotracer was found in the same regions for all the cases. Qualitatively, it was observed that for all the images, the voxelized phantoms and the reconstructed images were identical in all cases. Due to the nature of the PET acquisition simulation, the reconstructed images were of lower quality than the voxelized images. Figure 5 shows that the NEMA, Jaczaczk, and Derenzo reconstructed images showed good agreement with the original voxelized images because the intensities in the regions of interest were similar. In the case of the Shepp-Logan line profile, the line profiles were quite different; this was due to the more complex geometry of the Shepp-Logan phantom; the acquisition was more computationally expensive, which means we had lower total coincidence for the same simulation time compared with the NEMA, Jaczaczk, and Derenzo cases, resulting in a worse line profile. Nonetheless, the region of maximum intensity showed fairly good agreement in the voxelized and reconstructed phantoms. The acquisition times should be longer for the Shepp-Logan-like phantoms to address this issue. From the information provided from the line profiles, we can confirm that the reconstruction obtained from the simulated data in GATE was successful, as the direct comparison of the voxelized image and the reconstruction was consistent. In regards to the quantitative metrics employed, from the SSIM, it can be interpreted that the voxelized and reconstructed images were similar in the NEMA, Jaczaczk, and Derenzo cases. The SSIM result for the Shepp-Logan phantom was lower than the other three due to the lower coincidence counts, as we have already discussed. A longer acquisition time is required to obtain similar results. In general, the values are high enough to confirm the agreement between the voxelized and reconstructed images. The values of the SSIM indicate that for the generated phantoms, the voxelized and reconstructed images were in agreement. Finally, from the FID, it can be interpreted that in the NEMA and Derenzo cases, the voxelized images and the reconstructions were quite similar, as the FID score value was close to zero. For the Jaczaczk and Shepp-Logan cases, the FID score was also relatively low. However, it indicated that the reconstructions of these phantoms were not as good as \begin{table}
\begin{tabular}{c c} \hline
**Phantom** & **Mean SSIM** \\ \hline NEMA & 0.851 \\ \hline [PERSON] & 0.934 \\ \hline [PERSON] & 0.879 \\ \hline Shepp–Logan & 0.487 \\ \hline \end{tabular}
\end{table} 
Table 6: Mean Structural Similarity Index for each type of phantom. \begin{table}
\begin{tabular}{c c} \hline
**Phantom** & **FID Score** \\ \hline NEMA & 0.056 \\ \hline [PERSON] & 0.484 \\ \hline [PERSON] & 0.061 \\ \hline Shepp–Logan & 0.529 \\ \hline \end{tabular}
\end{table} 
Table 7: Fréchet Inception Distance for each type of phantom. in the other cases. Nonetheless, considering that the results were below the value where they would be considered similar and of high quality, it can be stated that this metric is also in accordance with the results obtained so far. In order to thoroughly validate the results obtained with the pipeline, the ideal criterion would be to compare the simulated dataset with data from real PET scans. Unfortunately, due to limitations in the availability of PET scans and the impossibility of obtaining data from clinical sources due to data privacy concerns, the data, at this time, could not be compared against real data. In order to validate the results, several phantoms would need to be built to test them properly.