# Dual Attention Fusion Enhancement Network for Lightweight Remote-Sensing Image Super-Resolution
## 3 Methods  
### Network Architecture  
In the paper, we propose an innovative network called DAFEN specifically for lightweight RSISR. The network architecture is illustrated in Figure 2, consisting of three integrated components: shallow feature extraction \(\mathcal{H}_{\text{fe}}\), feature refinement and fusion \(\mathcal{H}_{\text{rf}}\), and reconstruction \(\mathcal{H}_{\text{re}}^{s}\). Assume \(I_{\text{LR}}\in\mathbb{R}^{3\times H\times W}\) and \(I_{\text{SR}}\in\mathbb{R}^{3\times sH\times sW}\) are the input and output of DAFEN, where \(\text{H}\times\text{W}\) represents the spatial dimensions, and \(s\) is the upscaling factor. The process of the three integrated components can be expressed as follows:  
\[F_{0}=\mathcal{H}_{\text{fe}}(I_{\text{LR}}) \tag{1}\]  
\[F_{d}=\mathcal{H}_{\text{rf}}(F_{0}) \tag{2}\]  
\[I_{\text{SR}}=\mathcal{H}_{\text{re}}^{s}(F_{d})+\mathcal{H}_{\text{bicubic}} ^{s}(I_{\text{LR}}) \tag{3}\]  
where \(F_{0}\) and \(F_{d}\) denote the feature representations of \(\mathcal{H}_{\text{fe}}\) and \(\mathcal{H}_{\text{rf}}\). We utilize two 3 \(\times\) 3 convolutions to implement \(\mathcal{H}_{\text{fe}}\), which are used to extract the initial representations of the \(I_{\text{LR}}\) content. Similarly, \(\mathcal{H}_{\text{re}}^{s}\) is implemented through two 3 \(\times\) 3 convolutions combined with a pixel shuffle layer. It is noteworthy that \(\mathcal{H}_{\text{bicubic}}^{s}\) represents the bicubic interpolation function with an upscaling factor of \(s\). This function effectively conveys substantial information, compensating for the significant details of low-level features.  
To develop a lightweight network for RSISR, we meticulously design the feature refinement and fusion module \(\mathcal{H}_{\text{rf}}\). This section consists of four Dual Attention Fusion Enhancement Blocks (DAFEBs) and one Forward Fusion Enhancement Module (FFEM). After obtaining the coarse features \(F_{0}\) through shallow feature extraction \(\mathcal{H}_{\text{fe}}\), the four DAFEBs sequentially extract intermediate features. Here, we have  
\[F_{i}=\mathcal{H}_{\text{DAFEB}}^{i}(F_{i-1}),\ i=1,2,3,4 \tag{4}\]  
where \(\mathcal{H}_{\text{DAFEB}}^{i}(\cdot)\) denotes the \(i^{th}\) DAFEB function and \(F_{i}\) represents the intermediate features extracted by the \(i^{th}\) DAFEB. In order to more efficiently integrate these intermediate features containing multi-level information, we feed \(F_{i}\) (\(i=1,2,3,4\)) into FFEM for fusion and enhancement operations, as follows:  
\[T_{d}=\mathcal{H}_{\text{FFEM}}(F_{1},F_{2},F_{3},F_{4}) \tag{5}\]  
where \(T_{d}\) represents the features that have been integrated and enhanced by the FFEM, and \(\mathcal{H}_{\text{FFEM}}(\cdot)\) denotes the FFEM function.  
We employ the \(L_{1}\) loss function to train the aforementioned network. \(\{I_{\text{LR}}^{i},\ I_{\text{HR}}^{i}\}_{i=1}^{N}\) is used to denote the training set composed of N pairs of low-resolution (LR) and high-resolution (HR) images. The loss is defined as follows:  
\[L_{1}(\theta)=\frac{1}{N}\sum_{i=1}^{N}\|I_{\text{SR}}^{i}-I_{\text{HR}}^{i}\| _{1} \tag{6}\]  
where \(\theta\) denotes the parameter sets of our proposed DAFEN. \(I_{\text{SR}}^{i}\) and \(I_{\text{HR}}^{i}\) represent the \(i^{th}\) SR image reconstructed by the DAFEN and the corresponding HR image, respectively.