## 3 Results  
RCs and CoVs obtained from PET/CT reconstructed images of P1 and P2 are reported, respectively, in Figure 1A,B as functions of matrix size. For P1, RC values are not affected by changes in matrix size. Data linear regression shows a slope m equal to 1.25 \(\times\) 10\({}^{-3}\) (\(\chi^{2}\) = 8.25 \(\times\) 10\({}^{-6}\)). Conversely, CoV grows increasing the matrix size with a variation of 21%. For P2, the RC values show an approximately constant trend by changing the matrix size with a maximum variation of 10% observed for the 10 mm sphere while CoV decreases increasing the matrix size with a maximum variation of 34% observed for the 10 mm sphere. The RC and CoV values obtained from PET/CT reconstructed images of P1 and P2 are reported in Figure 2A,B, respectively, as functions of EI. For P1 and P2, the RC values are not affected by changes in EI. The data linear regression shows a mean slope m equal to 3.44 \(\times\) 10\({}^{-5}\) (\(\pm\) 2.00 \(\times\) 10\({}^{-4}\)). Similarly, CoV grows, increasing the EI both for P1 (variation of 123%) and P2 (maximum variation of 23%). In order to obtain reconstructed images suitable for both phantoms, a 256 \(\times\) 256 matrix was selected, and the number of EIs was fixed to 21, since an increase in iterations results in higher image noise. The 256 \(\times\) 256 matrix (corresponding to 3.18 mm \(\times\) 3.18 mm pixel) was also selected considering the 90Y-PET spatial resolution for the mCT scanner (\(\sim\)3 mm). In Figures 3 and 4, images of experimental 90Y-PET/CT and mathematical uniform IEC NEMA Torso phantoms and IEC NEMA Phantom used for the dosimetric approach in the Gaussian filter analysis are reported. Figure 1: RC (**A**) and CoV (**B**) values for cylindrical phantom (black) and IEC NEMA Body phantom as functions of pixel dimension (inverse of matrix size). Figure 3: Experimental 90Y\(-\)PET/CT and mathematical uniform IEC NEMA Torso phantoms. Figure 2: RC (**A**) and CoV (**B**) values for cylindrical phantom (black) and IEC NEMA Body phantom as functions of EI. iDVHref and iDVHexp for the P3 liver compartment are shown in Figure 5A for different Gaussian filters. Similarly, iDVHref and iDVHsexp for the 37 mm sphere in P2 are shown in Figure 5B for different Gaussian filters. For the P3 liver compartment, the mean absorbed doses show an approximately constant value of 51 Gy [50.4-53.1 Gy] increasing the Gaussian filter amplitude while standard deviations decrease from 17.7 Gy to 13.0 Gy, with a more uniform absorbed dose map with high filters. Conversely, for the P2 37 mm sphere, the mean absorbed dose values for each iDVHexp decrease from 172.2 Gy to 133.8 Gy increasing the Gaussian filter magnitude while standard deviations remain at approximately 41 Gy [40.2-41.3 Gy]. Varying the Gaussian filter magnitudes RMSE values for the liver compartment remain approximately constant [0.156-0.163] while for 37 mm sphere grows [0.377-0.744], as reported in Figure 6.  
dDVHref and dDVHsexp for the liver compartment in P3 are shown in Figure 7A for different Gaussian filters. Similarly, dDVHref and dDVHsexp for the 37 mm sphere in P2 are shown in Figure 7B for different Gaussian filters. dDVHsexp for the P3 liver compartment shows Gaussian-like shapes (R2 = 0.9854) with approximately constant mean absorbed dose values [50.7-52.6 Gy] increasing the Gaussian filter magnitude. Standard deviations decrease increasing the Gaussian filter magnitude from 15.9 Gy (FWHM = 37.6 Gy) to 11.9 Gy (FWHM = 28.1 Gy) with a more uniform absorbed dose map with high filters. Conversely, the 37 mm sphere mean absorbed dose values for each dDVHexp decrease  
Figure 4: Experimental 90Y\(-\)PET/CT and mathematical uniform IEC NEMA Phantom. Figure 5: Integral Dose-Volume Histograms (iDVHs) for whole liver compartment (**A**) and for the 37 mm sphere (**B**), obtained with different Gaussian filters. Mean absorbed doses and respective standard deviations are also reported.