# Multi-Scale Cross-Attention Fusion Network Based on Image Super-Resolution
## 3 Methods
### Network Framework  
We proposed a multi-scale cross-attention fusion network architecture, as shown in Figure 1, which consists of a shallow feature extraction module (SFM), a deep feature extraction module (DFM), and a feature reconstruction module (FRM).  
First, the SFM extracts shallow feature information \(F_{0}\in R^{C\times H\times W}\), including edges and corners, through a single \(3\times 3\) convolution function \(f_{sf}(\cdot)\), given an input LR image \(I_{LR}\in R^{C\times H\times W}\).  
\[F_{0}=f_{SFM}(I_{LR}), \tag{1}\]  
At the same time, \(F_{0}\) is also the input to the Deep Feature Extraction Module (DFM). Inside the DFM, the \(F_{0}\) is used as the input of the M multi-scale trans-attention modules and an optimized, Integrated Attention Enhancement Module (IEAM) in order to extract and fuse image feature information. The function of this process is called \(f_{DFM}\). In addition, global skip and dense connections are introduced to make the central part of the network focus on high-frequency information, which can be formally expressed as follows:  
\[\begin{array}{l}F_{R}=f_{DFM}(F_{0})=F_{0}+f_{IAEM}(Concat[F_{1},F_{2},\dots,F_{i},\dots,F_{M}]),\\ F_{i}=f_{MTM}^{i}(F_{i-1}),\end{array} \tag{2}\]  
\(f_{MTM}^{i}\) denotes the mapping of the \(i\)-th multi-scale trans-attentive module, and \([\cdot]\) denotes concatenation. \(F_{i}\) denotes the output of the \(i\)-th MTM, and its input is a concatenation of the outputs of the previous \(i-1\) MTM modules. _Concat_ denotes the connectivity operator, and \(f_{IAEM}\) denotes the mapping in which the module learns feature information from the outputs of the M MTMs, enhancing the feature information for high-frequency information. The IAEM module is designed to enhance the feature layers that are highly informative in their contribution and suppress the feature layers that contain redundant information. Finally, the feature reconstruction module generates a high-resolution image \(I_{SR}\in R^{C\times H\times H\times W}\) according to the feature information \(F_{R}\), which is upsampled to the required size by sub-pixel convolution:  
\[I_{SR}=f_{PixelShuffle}(F_{R}), \tag{3}\]  
where \(f_{PixelShuffle}\) denotes sub-pixel convolution, which aggregates low-resolution feature information to reconstruct the image.  
Currently, loss functions such as \(L_{1}\), \(L_{2}\), perceptual loss, and adversarial loss are commonly used to train SR models. In this paper, we choose loss \(L_{1}\) to reduce computational complexity. In a given training set, \(\big{\{}I_{LR}^{i},I_{SR}^{i}\big{\}}_{i=1}^{N}\), N images, and corresponding images, \(L_{1}\) loss is defined as:  
\[L(\Theta)=\frac{1}{N}\sum_{i=1}^{n}\left(f_{MCFN}(I_{LR}^{i})-I_{HR}^{i} \right)_{1}=\frac{1}{n}\sum_{i=1}^{n}\left(I_{SR}^{i}-I_{HR}^{i}\right)_{1}, \tag{4}\]  
Figure 1: Framework of the multi-scale cross-attention fusion network.  
where \(f_{M\text{CFN}}\) and \(\Theta\) denote the proposed functional mapping and its learning parameters, respectively. The configuration of each module will be shown in detail next.