# Multi-Scale Factor Image Super-Resolution Algorithm with Information Distillation Network
## 2 Materials and Methods
### Information Distillation Module  
In Figure 3, the information distillation block firstly uses four 3 \(\times\) 3 convolutions to progressively extract image features. After each convolution, a channel split operation is used to divide the feature maps into two parts. One of the parts flows into the next convolutional layer, and the other part is retained. Finally, the retained feature maps are concatenated to flow into the next IDB. Assuming that the input of the \(n\_th\) information distillation module is \(F\_in\), the process can be expressed as Formulas (1)-(4). \[F^{n}_{r\_1},F^{n}_{c\_1}=Split^{n}_{1}(C^{n}_{1}(F^{n}_{in})) \tag{1}\]  
\[F^{n}_{r\_2},F^{n}_{c\_2}=Split^{n}_{2}\big{(}C^{n}_{2}\big{(}F^{n}_{c\_1}} \big{)} \tag{2}\]  
\[F^{n}_{r\_3},F^{n}_{c\_3}=Split^{n}_{3}\big{(}C^{n}_{3}\big{(}F^{n}_{c\_2}} \big{)}\big{)} \tag{3}\]  
\[F^{n}_{r\_4}=C^{n}_{4}\big{(}F^{n}_{c\_3}}\big{)} \tag{4}\]  
Figure 2: Network architecture of multi-factor image super-resolution based on information distillation (IDMF-SR). (**a**) The blue box represents Conv-3; (**b**) The green box represents Conv-1. \(C_{1}^{n}\) represents the first convolutional layer of the _n_th_ information distillation module, \(C_{2}^{n}\), \(C_{3}^{n}\), \(C_{4}^{n}\), and so on. \(Split_{1}^{n}\) represents the first channel split layer of the _n_th_ information distillation module. \(F_{r,1}^{n}\) represents the first retained feature maps, and \(F_{c,1}^{n}\) represents the first coarse feature, which is fed into the next calculation unit. After each level of convolutional layer, the feature maps are divided into two parts. Two-thirds flow into the next level, and one-third are retained. Table 1 shows the hyperparameter in the information distillation module. We set 3 \(\times\) 3 as the kernel size in the convolutional layer. The output channels numbered 64, 48, and 16 are the convolutional layer. The number of the retained feature maps are 16, after four convolutional layers, the number of the output channels is also 64. The convolution kernel and stride follow the common operations in the SISR method. Next, we connect the previously retained feature maps \(F_{r}^{n}\), which can be expressed by Formula (5):  
\[F_{distilled}^{n}=Concat\big{(}F_{r_{1}}^{n},F_{r_{2}}^{n},F_{r_{3}}^{n},F_{r_{ 4}}^{n}\big{)} \tag{5}\]  
We discard the traditional channel attention mechanism and add contrast variables to the original channel attention. In low-level image tasks, such as image super-resolution reconstruction, the contrast-based channel attention mechanism can enhance image details, such as edges and textures. In Figure 4, the contrast is the sum of the standard deviation and the mean. Assuming that the input feature has \(C\) feature maps, the size of each feature map is \(H\times W\), and the input is expressed as \(X=[x_{1},x_{2},\ldots x_{c},\ldots x_{C}]\), and the contrast is calculated as Formula (6):  
\[Z_{c}=H_{GC}(x_{c})=\sqrt{\frac{1}{HW}\sum_{(i,j)\in x_{c}}{(x_{c}^{i,j}-\frac {1}{HW}\sum_{(i,j)\in x_{c}}{x_{c}^{i,j}})}^{2}}+\frac{1}{HW}\sum_{(i,j)\in x _{c}}{x_{c}^{i,j}} \tag{6}\] \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Layer** & **Number of Input\_Channel** & **Kernel\_Siz\&tride** & **Number of Output\_Channel** \\ \hline C\_1 & 64 & 3 & 1 & 64 \\ C\_2 & 48 & 3 & 1 & 64 \\ C\_3 & 48 & 3 & 1 & 64 \\ C\_4 & 48 & 3 & 1 & 16 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Convolutional parameter setting in the information distillation module. Figure 4: Contrast-based channel attention mechanism (S is sigmoid function). Figure 3: Information distillation module. Among them, \(H_{GC}(\bullet)\) represents the global contrast information measurement function of the feature map, \(\sqrt{\frac{1}{HW}\sum\limits_{(i,j)\in x_{c}}{(x_{c}^{ij}-\frac{1}{HW}\sum \limits_{(i,j)\in x_{c}}{x_{c}^{ij}})}^{2}}\) represents the standard deviation, and \(\frac{1}{HW}\sum\limits_{(i,j)\in x_{c}}{x_{c}^{ij}}\) represents the mean.