## 4 Ingredients of the Experimental Study
### The HR Clean Images  
The experiments are performed on 100 HR clean images. More specifically, Table 2 gives the 10 ancestor categories \(c_{a}\), and the 10 corresponding target categories \(c_{t}\) used in the \((c_{a},c_{t})\)-target scenario whenever applicable (see Section 4.4). These categories (ancestor or target) are the same as those of [27,49], which were picked at random among the 1000 categories of ImageNet. For each ancestor category, we picked at random 10 clean ancestor images from the ImageNet validation scheme in the corresponding \(c_{a}\) category, provided that their size \(h\times w\) satisfies \(h\geq 224\) and \(w\geq 224\). This requirement ensures that these images \(\mathcal{A}_{a}^{\text{hr}}\) belong to the \(\mathcal{H}\) domain. These images are pictured in Figure A1 in Appendix A, while Table A1 gives their original sizes. Note that, out of the 100 HR clean images in Figure A1, 92 coincide with those used in [27,49] (which were picked at random in this article). We replaced the 8 remaining images used in [27,49] whose sizes did not fulfill the requirement. As a consequence, the images \(\mathcal{A}_{1}^{1}\) and \(\mathcal{A}_{1}^{10}\) in the category \(c_{a_{1}}\), \(\mathcal{A}_{3}^{3}\) in the category \(c_{a_{3}}\), \(\mathcal{A}_{5}^{1},\mathcal{A}_{5}^{2},\mathcal{A}_{5}^{2}\) in the category \(c_{a_{5}}\), and \(\mathcal{A}_{9}^{1},\mathcal{A}_{9}^{2}\) in the category \(c_{a_{9}}\) differ from those of [27,49]. \begin{table}
\begin{tabular}{l l c c c} \hline \hline \(\mathcal{C}_{k}\) & **Name of the CNN** & **Parameters** & **Top-1 Accuracy** & **Top-5 Accuracy** \\ \hline \(\mathcal{C}_{1}\) & DenseNet121 & 8M & 0.750 & 0.923 \\ \(\mathcal{C}_{2}\) & DenseNet169 & 14M & 0.762 & 0.932 \\ \(\mathcal{C}_{3}\) & DenseNet201 & 20M & 0.773 & 0.936 \\ \(\mathcal{C}_{4}\) & MobileNet & 4M & 0.704 & 0.895 \\ \(\mathcal{C}_{5}\) & NASNetMobile & 4M & 0.744 & 0.919 \\ \(\mathcal{C}_{6}\) & ResNet50 & 26M & 0.749 & 0.921 \\ \(\mathcal{C}_{7}\) & ResNet101 & 45M & 0.764 & 0.928 \\ \(\mathcal{C}_{8}\) & ResNet152 & 60M & 0.766 & 0.931 \\ \(\mathcal{C}_{9}\) & VGG16 & 138M & 0.713 & 0.901 \\ \(\mathcal{C}_{10}\) & VGG19 & 144M & 0.713 & 0.900 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: The 10 CNNs trained on ImageNet, their number of parameters (in millions), and their Top-1 and Top-5 accuracy. \begin{table}
\begin{tabular}{l c} \hline \hline \(\mathbf{p}\) & \(\mathbf{(c_{a_{p}},a_{p})}\) \\ \hline
1 & (abacus, 398) & (bannister, 421) \\
2 & (acorn, 988) & (rhinoceros beetle, 306) \\
3 & (baseball, 429) & (ladle, 618) \\
4 & (broom, 462) & (dingo, 273) \\
5 & (broom bear, 294) & (pirate, 724) \\
6 & (canoe, 472) & (saluki, 176) \\
7 & (hippopotamus, 344) & (trifle, 927) \\
8 & (llama, 355) & (agama, 42) \\
9 & (maraca, 641) & (conch, 112) \\
10 & (mountain bike, 671) & (strainer, 828) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: For \(1\leq p\leq 10\), the second column lists the ancestor category \(c_{a_{p}}\) and its ordinal \(1\leq a_{p}\leq 1000\) among the categories of ImageNet. _Mutatis mutandis_ in the third column with the target category \(c_{t_{p}}\) and ordinal \(t_{p}\). Although the images \(\mathcal{A}_{q}^{p}\) are picked from the ImageNet validation set in the categories \(c_{a_{q}}\), CNNs may not systematically classify all of them in the \"correct\" category \(c_{a_{q}}\) in the process of Steps 1 and 2 of Scheme (11). Indeed, Tables 15 and 16 in Appendix A show that this phenomenon occurs for all CNNs, whether one uses \(\rho=\) \"Lanczos\" (L) or \"Nearest\" (N). Table 3 summarizes these outcomes, where \(\mathcal{S}_{clean}^{c}(\rho)\) designates the set of \"correctly\" classified clean images \(\mathcal{A}_{q}^{p}\). Table 3 shows that the sets \(\mathcal{S}_{clean}^{c}(L)\) and \(\mathcal{S}_{clean}^{c}(N)\) usually differ. Tables 15 and 16 proves that this holds as well for \(\mathcal{C}=\mathcal{C}_{7},\mathcal{C}_{9},\mathcal{C}_{10}\) although both sets have the same number of elements.