## 2 Materials and Methods
### Methodology  
#### 2.2.1 Context-Based ResU-Net  
The latest research results indicate that the quality of SR increases as more convolution layers or deeper neural networks are assigned [6; 8; 9]. Most recent deep learning-based SR neural networks adopt this trend by maintaining the size of the input image until the output stage. The enlargement function to create HR is applied to the final stage [8; 11; 12]. The existing methodology was applied to our datasets with unsatisfactory results. It is speculated that different imaging geometry between aerial and space-borne sensors may lead to unsatisfactory results even with similar research methods. Because the aerial orthoimage contains more context information than the space-borne Sentinel-2 image, we determined that it would be critical to arrange context-preserving and deep and dense neural networks in the initial stage. The proposed architecture of the context-based ResU-Net for our study is depicted in Figure 5.  
In our study, the residual U-Net proposed by [PERSON] et al. [17] was modified to maintain the context information and build deep neural networks. Batch normalization (BN) and ReLU activation functions are included in most of the steps. BN helps to solve gradient vanishing/exploding and overfitting caused by the deep neural network; it also improves accuracy [6; 11]. The ReLU is used to remove the values below zero [6]. The encoder's role is to make the input image compact, and the decoder recovers the information to generate the final image. There is a path connecting the encoder and the decoder, and all convolution layers have a filter size of 3 \(\times\) 3. The encoding path has three  
Figure 4: Example of training sets (Input: [B2 B3 B4 B8]: 10 m, [B5 B6 B7 B8A B11 B12]: 20 m, and [B1 B9]: 60 m, output: aerial orthoimages 2\(\times\) for 5.0 m, 4\(\times\) for 2.5 m). conv-depth blocks. Each block's stride was set to 2 instead of using downsampling layers to reduce the feature map's size in half. The decoding path has three conv-depth blocks to correspond to the encoder, and the size is increased through upsampling layers. End of the decoding path, a convolution layer is inserted to make feature dimensions as 3 with ReLU activation function for generating desired resolution similar to that of aerial orthoimage. There are three major differences between the existing Residual U-Net and our network. First, the conv-depth block was included to reduce computation resources. It is known that depth-wise separable convolution (DepthConv) maintains performance while reducing the number of parameters [18]. As shown in Table 2, if a convolution layer is used instead of a DepthConv layer in our architecture, the number of parameters to be learned becomes larger. In addition, the difference in the number of parameters increased as the size of the feature dimensions increased. Moreover, we had encountered that the validation loss was jagged when only the convolution layer was used. On the contrary, the loss converges evenly with a lower value when using the DepthConv layer, as shown in Figure 6. When only the convolution layer was used, the loss at epoch 1 was 45,328.06, but the value was too large to be displayed on the graph, so only the corresponding value was clipped. \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Feature Dimensions**} & \multirow{2}{*}{**Compositions**} & \multicolumn{2}{c}{**Number of Parameters**} \\ \cline{3-4}  & & **Trainable Parameters** & **Total Parameters** \\ \hline \multirow{2}{*}{\(f_{a}\)} & Using convolutional layer only & 4,718,035 & 4,725,331 \\ \cline{2-4}  & Using DepthConv layer & 3,159,955 & 3,167,251 \\ \hline \multirow{2}{*}{\(f_{b}\)} & Using convolutional layer only & 18,845,091 & 18,859,683 \\ \cline{2-4}  & Using DepthConv layer & 12,595,491 & 12,610,083 \\ \hline \multirow{2}{*}{\(f_{c}\)} & Using convolutional layer only & 75,326,275 & 75,355,459 \\ \cline{2-4}  & Using DepthConv layer & 50,293,315 & 50,322,499 \\ \hline \hline \end{tabular}
\end{table}