## 4 Phantom Measurements
### Results  
In Table 5, the CR achieved by the smallest (7 mm) sphere at 48 MLEM-equivalent updates in all the considered TOF and non-TOF configurations is shown. The highest CR is obtained on the TOF system with the lowest CTR (SIGNA scanner), the lowest one is found in non-TOF, in the HCR configuration, due to the high random fraction. As to BV, due to the difficulty in comparing noise levels among scanners with different sensitivities, only SIGNA results are reported. The BV at 48 updates is reported in Table 6. As predicted by theory, at a fixed update number, noise is higher in TOF than in non-TOF reconstructions, due to the faster high frequencies convergence. Table 7 shows the update numbers provided by the rule to match the D690 scanner TOF contrast at 48 updates, together with the corresponding CR. If only 32 updates are needed in the low CTR TOF condition, 128 updates are required in non-TOF for large objects (Double Configuration). Although the two scanners have different scatter fractions, spatial resolutions, and sensitivities, the rule appears able to provide comparable CR This confirms the independence of the rule from the acquisition statistics. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Reconstruction:** & **TOF** & **Non-TOF** \\ \hline SIGNA Single & 26.2 & 20.6 \\ SIGNA Double HCR & 23.5 & 18.6 \\ SIGNA Double LCR & 39.5 & 29.6 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Background variability [%] at 48 updates for the 1 pixel scale for the different SIGNA acquisitions. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Reconstruction:** & **TOF** & **Non-TOF** \\ \hline
**Acquisition:** & **CR [\%]** & **CR [\%]** \\ \hline D690 Single & \(36\pm 3\) & \(21\pm 1\) \\ D690 Double & \(30\pm 3\) & \(22\pm 2\) \\ SIGNA Single & \(42\pm 2\) & \(29\pm 1\) \\ SIGNA Double HCR & \(34\pm 1\) & \(17\pm 2\) \\ SIGNA Double LCR & \(33\pm 2\) & \(21\pm 1\) \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Contrast recovery at 48 updates for the 7 mm sphere for the different acquisitions. Data reported as mean \(\pm\) one standard error. In Figure 5 results for non-TOF reconstructions are shown. Again, in the third column, images at the update number provided by the rule to match the D690 48 update contrast are shown (96 update for the Single configuration, 128 updates for the Double configuration). \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Reconstruction:** & **TOF** & **Updates** & **Non-TOF** & **Updates** \\
**Acquisition:** & **CR [\%]** & **N** & **CR [\%]** & **N** \\ \hline D690 Single & \(36\pm 3\) & 48 & \(40\pm 4\) & 96 \\ D690 Double & \(30\pm 3\) & 48 & \(35\pm 3\) & 128 \\ SIGNA Single & \(36\pm 2\) & 32 & \(37\pm 2\) & 96 \\ SIGNA Double HCR & \(29\pm 1\) & 32 & \(28\pm 3\) & 128 \\ SIGNA Double LCR & \(30\pm 2\) & 32 & \(29\pm 2\) & 128 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Contrast recovery for the 7 mm sphere using the proposed CR matching rule. Figure 4: TOF Reconstructions of the phantoms in different conditions. **Upper:** Single acquisitions. **Lower:** Double acquisition, HCR only for SIGNA shown for clarity. **Left (a,d)**: D690 acquisitions, 48 updates. **Center (b,e)**: SIGNA acquisitions, 48 updates. **Right (c,f)**: SIGNA acquisitions, 32 updates according to the proposed rule. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Reconstruction:** & **TOF** & **Non-TOF** \\ \hline SIGNA Single & 18.6 & 37.5 \\ SIGNA Double HCR & 17.4 & 36.5 \\ SIGNA Double LCR & 28.5 & 64.5 \\ \hline \hline \end{tabular}
\end{table} 
Table 8: 1 pixel scale Background Variability [%] at the CR matching update numbers for the different acquisitions. It is evident, in this case, how the increase in the update number necessary to reach the TOF contrast inevitably leads to a noise augment, particularly in the Double configuration. In this configuration, the smallest sphere is barely visible at 48 updates (Figure 5e); a full recover is associated with a marked noise augment (Figure 5f). In Figure 6 reconstructions of the hot rods section are shown.