## 2 Materials and Methods  
The torso NEMA phantom (Figure 1) containing six spheres (0.52, 1.15, 2.57, 5.58, 11.49, and 26.52 mL or cm\({}^{3}\)) was filled with \({}^{18}\)F solutions to yield three different contrasts between the hot spheres and the colder uniform background (2:1 and 4:1). The activity ratio between spheres and background are shown in Table 1. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Attributes** & **2:1 (kBq/mL)** & **4:1 (kBq/mL)** \\ \hline Sphere & 1668.52 & 2775.43 \\ Background & 838.59 & 697.24 \\ Measured Ratio & 1.99:1 & 3.98:1 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Activity concentration of the spheres and background for different contrasts. The phantom data were acquired on the TrueV PET-CT scanner (Siemens, Malvern, PA, USA) in 3D mode with a 21.6 cm axial FOV (field of view). The total acquisition duration was 120 min. Images were reconstructed into 109 image planes or slices with a \(256\times 256\times 109\) matrix. The voxel dimensions were 2.67 \(\times\) 2.67 \(\times\) 2.00 mm\({}^{3}\). OSEM (ordered subset expectation maximization) algorithm was used for 3D image reconstruction with four iterations and 21 subsets. For creating different levels of noise, the entire 120 min scans were divided into five different scan durations (900, 1200, 2000, 4000, and 7200 s (15, 20, 33.3, 66.6 and 120 min)). To create five different overlapping measurements or realizations, the frame start time of each duration was shifted before reconstruction. The procedure is only carried out for the first four durations. Decay correction and a 4-mm FWHM (full width at half maximum) Gaussian filter were applied on all the images once the reconstructions were completed. The details of the full reconstruction can be found in [32]. In a separate scan, data were acquired by replacing the six spheres with two separate spheres with volumes of 8.18 and 18.82 mL, corresponding to 25 and 33 mm diameter, respectively (Figure 1). Each of these spheres also contained another smaller sphere of volume 1.15 mL (13 mm diameter) within it to create two separate compartments. The wall thickness kept at 2 mm. When these two compartments were filled with different levels of activity, they represented a tumor which has a deprived core and a hot rim. 3D printing technology was utilized to create the two hot rim tumors. The background and inner spheres were filled with 564 kBq/mL and the outer rims of the spheres were filled with 2564.5 kBq/mL activity to create a contrast of 4:1 between the hot rim and inner core and background. Three different delineation methods were implemented to segment both homogeneous and heterogeneous spheres from their background. The first one is termed as true volume of interest (VOI\({}_{\text{true}}\)) and serves as a reference volume. It was estimated using the exact  
Figure 1: (**a**) Torso NEMA phantom for PET with six fillable spheres and a cold insert in the middle; (**b**) the diameter of each of the six spheres; (**c**) CAD drawing of the lead with the heterogeneous insert; and (**d**) CAD drawing showing the two spheres to create a hot rim and cold core. The diameter of the inner sphere is 13 mm. The outer sphere diameters are 25 and 33 mm for two separate inserts. known position of each individual sphere and the calculated boundaries from the known diameter. A 40% fixed threshold method was considered as a second delineation method. In this method, a VOI is determined by voxels having 40% (I40T) of the maximum intensity (Imax) within a roughly delineated VOI and noted as VOI40T [33]  
\[\text{I}_{\text{40T}}=0.4\times\text{I}_{\text{max}} \tag{1}\]  
Voxels having activity more than I40T were included in the VOI40T. The third and final volume of interest (VOIA) was estimated using an adaptive threshold-based method.