# Multi-Scale Cross-Attention Fusion Network Based on Image Super-Resolution
## 3 Methods
### Integrating the Attention Enhancement Module  
Currently, most SR networks usually use standard convolutional connections and ultimately perform deep feature extraction. Adding an extra module enhances the feature learning capability and thus improves the network's overall performance. Therefore, we designed the Integrated Attention Enhancement Module (IAEM) according to this assumption. We continue with the attention mechanism, inspired by DANet [31], and optimize it. We treat the mapping of each deep feature extraction module as a specific response; different module responses correlate. The interdependence between module mappings is used to enhance the interdependent feature information mapping and the feature representation ability of modules, as shown in Figure 4.  
Different from the above CAM module, the input is the deep feature group \(F_{IFG}\in R^{N\times H\times W\times C}\) output from N multi-scale cross-attention modules, and the dimension is \(N\times H\times W\times C\). Through the change of dimension, the weight of feature information is re-learned to strengthen the attention of high-frequency information. Firstly, in this paper, the feature group is convolved by 3D convolution to strengthen the representation of local context features. Then, the sigmoid function is used to extract the feature information of the deep feature group and generate the corresponding attention map.  
According to the dimensions of the feature groups, we chose a 3D convolution with kernel size three and step size 1 to generate the attention maps of the three feature groups. Then, in this paper, we multiply it element-by-element with the original input depth-extracted feature layer and multiply it by the scale parameter \(C\) to generate the attention map B. Formally, the process is described as:  
\[F_{IAEM}^{CHW}=\mu(\sigma(f_{3 dconv}(F_{IFG}))\cdot F_{IFG}), \tag{11}\]  
where \(f_{3 dconv}\) represents the 3D convolution function, \(\sigma\) represents the softmax function, \(\cdot\) represents element-wise multiplication, and \(\mu\) learns weights starting from initialization 0.  
Secondly, this paper reshapes these deep extracted feature groups IFGs into a two-dimensional matrix of \(N\times HWC\). After that, the reshaped feature group is matrix multiplied with its transpose, and then, softmax is applied to obtain the attention map \(S\in R^{N\times N}\) that strengthens the correlation between modules. Formally, the process is described as follows:  
\[s_{ji}=\frac{\exp(IFGs_{i},IFGs_{j})}{\sum\limits_{i=1}^{N}\exp(IFGs_{i},IFGs_{ j})},i,j=1,2,\ldots,N, \tag{12}\]  
where \(s_{ji}\) represents the influence between the \(i\)-th module and the \(j\)-th module, the attention map of the depth extraction feature layer is obtained by multiplying the reshaped depth extraction feature set with the original feature set matrix and then multiplying the result with the scale parameter \(\lambda\). Finally, the two attention maps are summed element-wise to obtain the output \(F_{IAEM}\in H\times W\times NC\). Formally, the process is described as follows:  
\[F_{IAEM_{j}}=\lambda\sum\limits_{i=1}^{N}{(s_{ji}IFGs_{i})}+F_{CHW_{j}}^{IAEM}, \tag{13}\]  
Figure 4: Integration of the Attention Enhancement Module architecture.  
where \(\lambda\) learns the weights from the initialization of 0, and the final feature of each module represents a weighted sum of all the parts of the module that are related to the original quality and models the long-range semantic dependencies of the entire feature graph. Thus, integrating the attention enhancement modules by learning the interdependencies between the modules is a way to enhance and optimize the overall network's performance effectively.