## 3 Results
### Homogeneous Cylindrical Phantom  
Examples of data reconstructed with (a) OSCG and (b) OSEM algorithm in xSPECT software for the homogeneous phantom are shown in Figure 6.  
Figure 4: A transaxial and coronal cross-section of the used phantoms: (**a**) cylindrical phantom, (**b**) NEMA/IEC NU2 phantom, and (**c**) Abdo-Man anthropomorphic phantom.  
Figure 5: Planar images obtained from the system calibration with the \({}^{57}\)Co point source.  
For the homogeneous phantom, the nominal (\(C_{bg}\)) and measured (\(c_{bg}\)) activity concentration in the phantom background at the time of the acquisition, the standard deviation of the activity concentration values (\(\sigma_{bg}\)) the recovery coefficient (\(RC_{ug}\)) and the coefficient of variation (COV) are reported in Table 3. The first two delineation methods (ROI1 and ROI2) provided an excellent agreement with the know activity concentration with a recovery coefficient (\(RC_{ug}\)) of 1.00 and 1.02, respectively. As expected, the third delineation method (ROI3) resulted in a lower \(RC_{ug}\), as the expansion of the ROI out of the physical volume provided lower activity values. It is worth noting that all three methods provided activity concentration values consistent with the accuracy stated by the manufacture (below 10%).  
Figure 7 compares activity concentration profiles obtained using different reconstruction algorithms. No substantial differences are reported between xSPECT with OSCG or OSEM when images are normalized to their maximum values, confirming that OSEM and OSCG differ only for a counts-to-Bq/mL rescaling factor. Therefore, xSPECT with the OSCG algorithm was used for image reconstruction in the NEMA phantom and in the 3D printed phantom.  
\begin{table}
\begin{tabular}{c c c c c c} \hline
**ROIs** & \(\begin{array}{c}C_{bg}\\ \textbf{(MBq/mL)}\end{array}\) & \(\begin{array}{c}c_{bg}\\ \textbf{(MBq/mL)}\end{array}\) & \(\begin{array}{c}\sigma_{bg}\\ \textbf{(MBq/mL)}\end{array}\) & \(RC_{ug}\) & \(\begin{array}{c}COV\textbf{(\%)}\end{array}\) \\ \hline ROI 1 & 0.030 (\(\pm\)5\%) & 0.0301 & 0.007 & 1.00 & 23\% \\ ROI 2 & 0.030 (\(\pm\)5\%) & 0.0305 & 0.007 & 1.02 & 22\% \\ ROI 3 & 0.030 (\(\pm\)5\%) & 0.0278 & 0.010 & 0.93 & 36\% \\ \hline \end{tabular}
\end{table}
Table 3: Calibration factors assessed for the homogeneous phantom. \(C_{bg}\) represents the known activity concentration in the phantom, \(c_{bg}\) is the measured activity, \(c_{bg}\) is the standard deviation of the activity concentration values, \(RC_{ug}\) is the recovery coefficient of the cylindrical phantom and \(COV\) is the coefficient of variation.  
Figure 6: Data reconstructed with (**a**) OSEM and (**b**) OSCG algorithm in xSPECT system for the homogeneous phantom.  
The analysis of AVHs of the homogeneous phantom for the three ROIs is reported in Figure 8. The activity concentration obtained considering the physical volume of the homogeneous phantom (blue line) clearly underestimates the known activity value in the phantom due to spill out effects. Activity underestimations are exacerbated when the phantom wall and cap are included in the ROI (ROI3, green line). Spill out effects are shown in Figure 7c, with activity concentration suddenly decreasing close to the phantom walls. ROL, including 80% of the phantom's volume, provided the best results with an agreement below 2% between measured activity concentration and known activity concentration value.  
Figure 7: (a) Profiles generated at a central slice of the homogeneous phantom reconstructed with the xSPECT software using OSEM algorithm (blue line) with respect to (**b**) OSCG algorithm (red line); (c) Activity profiles.