## 2 Materials and Methods
### Noise Maps  
In order to assess local noise properties, as suggested by the AAPM Task Group 233 report [65], noise maps of CT images reconstructed by using FBP (N-FBP), ASiR (N-ASiR), and ASiR-V (N-ASiR-V) were obtained on a voxel-by-voxel basis computing the SD of each voxel value across the 40 repeated acquisitions. Then, maps of the percentage difference between noise of FBP-reconstructed images and noise of both ASiR-V-reconstructed (PDN-ASiR-V) and ASiR-reconstructed (PDN-ASiR) images were computed voxelwise. In particular, N-FBP as well as N-ASiR, N-ASiR-V, PDN-ASiR-V, and PDN-ASiR maps with different blending levels of reconstruction were obtained for the slice at the central level of both the CTP486 and CTP404 phantom modules.  
For CT imaging of the homogeneous CTP486 module, a summary noise level was estimated as the mean \(\pm\) SD value of N-FBP, N-ASiR, and N-ASiR-V maps within a central circular ROI of 1 cm diameter. Analogously, a summary percentage noise reduction of ASiR-V and ASiR with respect to FBP was estimated as the mean \(\pm\) SD value of PDN-ASiR-V and PDN-ASiR maps, respectively, within a central circular ROI of 1 cm diameter.  
For CT imaging of the CTP404 module, a summary noise value of each contrast object was estimated as the mean \(\pm\) SD value of N-FBP, N-ASiR, and N-ASiR-V maps within a circular ROI of 1 cm diameter placed in the center of the contrast object. Analogously, for each contrast object, a summary percentage noise reduction of ASiR-V and ASiR with respect to FBP was estimated as the mean \(\pm\) SD value of PDN-ASiR-V and PDN-ASiR maps, respectively, within a circular ROI of 1 cm diameter placed in the center of the contrast object.  
In order to assess the spatial nonuniformity degree of N-FBP, N-ASiR, and N-ASiR-V maps, the nonuniformity index (_NUI_) [67], as proposed by the AAPM Task Group 233 report [65], was employed. Specifically, for both the CTP486 and CTP404 modules, the entire inner part of the phantom (diameter, 15 cm) was divided into \(k\) = 249 ROIs (size, 8 mm \(\times\) 8 mm). Then, for each map (N-FBP, N-ASiR, and N-ASiR-V), the _NUI_ was calculated as:  
\[NUI=\frac{100}{<m>}\sqrt{\frac{1}{k-1}\sum_{i=1}^{k}\left(m_{i}-<m>\right)^{2}} \tag{1}\]  
where \(m_{i}\) and <\(m\)> are the average of the values of the considered map within the \(i\)-th ROI and the average of all \(m_{i}\) values, respectively.  
Furthermore, in order to characterize the spatial distribution of noise in CT imaging with ASiR and ASiR-V reconstruction algorithms, the histograms of N-ASiR and N-ASiR-V maps, as well as of N-FBP map, were computed for the entire inner part of the CTP486 module (diameter, 15 cm). Then, the histogram descriptors of median, interquartile range, kurtosis, and skewness were calculated.  
Image analysis was performed by using the MATLAB R2018a (MathWorks, Natick, MA, USA) software package.  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Material** & **CT Numbers (HU)** \\ \hline Air & \(-1046\): \(-986\) \\ PMP a & \(-220\): \(-172\) \\ LDPE b & \(-121\): \(-87\) \\ Polystyrene & \(-65\): \(-29\) \\ Acrylic & 92: 137 \\ Delrin & 344: 387 \\ Teflon & 941: 1060 \\ \hline \hline \end{tabular}  
* Polymethylpentene, b low-density polyethylene.  
\end{table}
Table 1: Nominal CT numbers of the Catphan-CTP404 contrast objects [66].