## 3 Our Approach
### Progressive Multi-Scale Dynamic Aggregation  
The LR images corresponding to each scale are fed into the multi-scale feature interaction (MSI) module to facilitate cross-scale feature interaction, thereby further enhancing and integrating the feature representations, as shown in Figure 3.  
The features of the second scale are upsampled once, and the features of the third scale are upsampled twice. These two features are then concatenated with the features from the first scale along the channel dimension. Afterward, a convolution operation is applied to reduce the number of channels to one-third, followed by a feature extraction module for further feature extraction. The features of the first scale are downsampled once, and the features of the third scale are upsampled once. These two features are concatenated along the channel dimension with the features from the second scale. Then, a convolution operation is applied to reduce the number of channels to one-third, followed by feature extraction through the feature extraction module. The features from the first scale are downsampled twice, and the features from the second scale are downsampled once. These two features are then concatenated along the channel dimension with the features from the third scale. Afterward, convolution is applied  
Figure 3: Multi-scale feature interaction. to compress the number of channels to one-third, followed by feature extraction using a feature extraction module. After feature interaction through the MSI module, the LR image features at three scales are input into the PDA, where progressive dynamic aggregation is performed multiple times at each scale to complete the super-resolution reconstruction. \[F_{Agg}=PDA(Conv([F_{LR};F_{Ref}]))+F_{LR}, \tag{9}\]  
The aligned low-resolution (LR) image features are concatenated with the reference (Ref) image features, which are subsequently fed into a convolutional layer. A dynamic decoupling filter, namely the channel-spatial attention (CSA) mechanism, is then employed to extract texture information across both spatial and channel domains. The structure of CSA is shown in the Figure 4.  
In the spatial domain, CSA extracts features through the spatial gate (SG) module and convolution. The SG module captures the local correlation between pixels and dynamically generates weights related to the texture, thereby enhancing the spatial feature representation of the image. Additionally, the convolution operation further refines the spatial domain features, ensuring that the texture details of local regions are fully preserved. In the channel domain, CSA utilizes the channel attention (CA) module to adaptively adjust the weight distribution of channel features. CA models the importance of different channels and dynamically optimizes the feature representation ability, enabling efficient processing and expression of multi-channel features. Following the channel-wise and spatial domain output operations, a filtering normalization process was implemented to standardize the feature representations. \[ \begin{split} N_{i}^{s}&=\alpha^{s}\frac{N_{i}^{s -}\mu(N_{i}^{s})}{\delta(N_{i}^{s})}+\beta^{s},\\ N_{k}^{c}&=\alpha^{c}\frac{N_{k}^{c}-\mu(N_{k}^{c })}{\delta(N_{k}^{c})}+\beta^{c},\end{split}  \tag{10}\]  
where \(N_{i}^{s}\) and \(N_{k}^{c}\) represent the spatial and channel filters before filter normalization, respectively. \(\mu(\cdot)\) and \(\delta(\cdot)\) are used to compute the mean and standard deviation of the filters, while \(\alpha^{s}\), \(\alpha^{c}\), \(\beta^{s}\), and \(\beta^{c}\) are learnable scaling and shift parameters, similar in function to the scale and shift parameters in batch normalization [31], used to control the normalized numerical range. The four parameters are defined as \(1\) during network initialization and updated through backpropagation training of the entire network.