# Dual Attention Fusion Enhancement Network for Lightweight Remote-Sensing Image Super-Resolution
## 3 Methods
### Channel-Spatial Lattice Block (CSLB)  
Lattice structures [16; 46; 49] enable high-speed parallel processing, making them highly suitable for lightweight models that require fast execution speeds. To achieve more efficient feature extraction, we designed the CSLB, which incorporates a dual-branch architecture inspired by lattice structures. As shown in Figure 5a, the input features \(x\in\mathbb{R}^{C\times H\times W}\) are first split into two equal parts along the channel dimension: \(P_{\text{i-1}}(x)\in\mathbb{R}^{C/2\times H\times W}\) and \(Q_{\text{i-1}}(x)\in\mathbb{R}^{C/2\times H\times W}\). This can be expressed as follows:  
\[P_{i-1}(x),Q_{i-1}(x)=\text{Split}(x) \tag{14}\]  
where \(x\) represents the input to the CSLB, and \(P_{\text{i-1}}(x)\) and \(Q_{\text{i-1}}(x)\) denotes the inputs of the upper and lower branches, respectively. This design allows each branch to process only half of the input signal, enabling faster parallel processing and reduced complexity. Specifically, our CSLB is divided into two operational stages. In the first stage, \(Q_{\text{i-1}}(x)\) is fed into three GRSBs for stepwise feature extraction and refinement. Considering the feature misalignment between the two branches, simple operations like addition, multiplication, or concatenation are not sufficiently convincing. Therefore, we designed the CSAIM to calculate attention weights for the two branches from both the spatial and channel dimensions, which consist of two components: Spatial Attention Interaction (SAI) and Channel Attention Interaction (CAI). These weights are then used to perform a \(1\times 1\) convolution fusion with the other branch to obtain \(P_{\text{i-2}}(x)\) and \(Q_{\text{i-2}}(x)\). This process can be expressed as follows:  
\[P_{i-2}(x)=\text{Conv}_{1\times 1}(\text{Concat}(P_{i-1}(x),F_{C-1}(f(Q_{i-1}(x))))) \tag{15}\]  
Figure 5: **(a)** The Channel-Spatial Lattice Block (CSLB), where the Channel-Spatial Attention Interaction Module (CSAIM) includes the Spatial Attention Interaction (SAI) and the Channel Attention Interaction (CAI). ‘Split’ represents the channel separation operation. **(b)** The Spatial Attention Interaction (SAI). **(c)** The Channel Attention Interaction (CAI). \[Q_{i-2}(x)=\text{Conv}_{1\times 1}(\text{Concat}(F_{S-I}(P_{i-1}(x)),f(Q_{i-1}(x)))) \tag{16}\]  
where \(f(\cdot)\) denotes three GRSB operations, \(F_{C-I}(\cdot)\) and \(F_{S-I}(\cdot)\) denote channel attention and spatial attention operations. In the second stage, \(P_{i-2}(x)\) is fed into three GRSBs for stepwise feature extraction and refinement. Similar to the first stage, we perform weighted cross-combination from the spatial and channel dimensions for the two branches. This process can be expressed as follows:  
\[P_{i-3}(x)=\text{Conv}_{1\times 1}(\text{Concat}(f(P_{i-2}(x)),F_{C-I}(Q_{i-2}(x) ))) \tag{17}\]  
\[Q_{i-3}(x)=\text{Conv}_{1\times 1}(\text{Concat}(F_{S-I}(f(P_{i-2}(x))),Q_{i-2} (x))) \tag{18}\]  
where \(P_{i-3}(x)\) and \(Q_{i-3}(x)\) denote the upper and lower branch features obtained from the second stage, respectively. Subsequently, we fuse \(P_{i-3}(x)\) and \(Q_{i-3}(x)\) using a \(1\times 1\) convolution. Here, we provide a detailed description of the calculation of weight coefficients. For the SAI, as shown in Figure 5b, given a set of feature maps, they are directly passed through a nonlinear function, \(\text{Conv1}\rightarrow\text{ReLU}\rightarrow\text{Conv1}\), where the reduction ratios for pointwise convolution are 8 and C/8, with C representing the number of channels in the feature maps. Finally, a sigmoid function is used to generate combination coefficients, which range from 0 to 1. For the CAI, as shown in Figure 5c, given a set of feature maps, we first obtain the average value of each feature map through GAP. The resulting feature vectors are then passed through a nonlinear function, \(\text{Conv1}\rightarrow\text{ReLU}\rightarrow\text{Conv1}\), where the reduction and expansion ratios for pointwise convolution are set to 8.