## 2 Related Works
### ResNeSt-Split Attention Network  
CNN has a strong ability to learn signal features. However, with the deepening of the network, the CNN gradient will disappear [22]. In 2015, [PERSON] et al. [23] proposed ResNet residual neural network. Using the residual block structure combined with \"Shortcut Connections\", the previous residual block can flow into the following block without obstruction. Thus, the problem of gradient disappearance caused by the network being too deep is avoided. Residual neural network (ResNet) used in this paper adds multiple split-attention (SA) block modules based on the ResNet. Moreover, residual split-attention networks (ResNeSt) combine the multipath structure with the channel attention mechanism, expressing the channel attention as a feature map group and weighting different branch feature channels to generate the final feature map (see Figure 2).  
Firstly, the input feature map was divided into \(K\) branches, and each branch was subdivided into \(R\) subgroups. Hence, the total number of feature maps was \(G=K\times R\). Secondly, \(1\times 1,3\times 3\) convolution operation was carried out for each subgroup, and different weights were assigned to each subgroup through the SA module before it was finally aggregated. The feature map outputs obtained via aggregation and the residual module were combined linearly. Figure 3 shows the SA module.  
Figure 3: Split-attention module.  
Figure 2: ResNeSt structure.  
In the SA module, the combined feature \(\hat{U}^{k}\) of the \(k\)-th branch was obtained by element-wise summation and fusion of \(R\) subgroups:  
\[\hat{U}^{k}=\sum_{j=R(k-1)+1}^{Rk}U_{j},j\in 1,2,\cdots,SK;k\in 1,2,\cdots,K \tag{1}\]  
where \(U_{j}\) represents the \(j\)-th input feature in the SA module (the output feature after \(3\times 3\) convolution shown in Figure 3).  
\[\hat{U}^{k}\in\mathbb{R}^{H\times W\times\frac{C}{K}},k\in 1,2,\cdots,K \tag{2}\]  
where \(H\), \(W\), and \(C/K\) represent the length, width, and the number of channels of each output feature map, respectively.  
The global information obtained by global pooling of the fused feature maps was calculated next:  
\[r_{c}^{k}=\frac{1}{H\times W}\sum_{i=1}^{H}\sum_{j=1}^{W}\hat{U}_{c}^{k}(i,j) \tag{3}\]  
where \(r_{c}^{k}\) represents the \(c\)-th channel value of the \(1\times 1\times C/K\) feature map of \(\hat{U}^{k}\) following the global pooling. Further, \(\hat{U}_{c}^{k}(i,j)\) represents the value at pixel (\(i\),\(j\)) in the \(c\)-th channel of \(\hat{U}^{k}\).  
Next, \(r^{k}\) adaptively calculates the weight of each subgroup through the fully connected layer:  
\[a_{i}^{k}(c)=\begin{cases}\frac{\exp(G_{i}^{r}(r^{k}))}{\sum_{j=0}^{K}\exp(G_{ i}^{r}(r^{k}))}R>1\\ \frac{1}{1+\exp\left(-G_{i}^{r}(r^{k})\right)}R=1\end{cases} \tag{4}\]  
where \(a_{i}^{k}(c)\) is the weight of the \(i\)-th subgroup and \(G_{i}^{r}\) is the weight function composed of two fully connected layers and a ReLU activation function.  
Therefore, the final weighted fusion feature \(V^{k}\in\mathbb{R}^{H\times W\times C}\) is generated by multiplying the original feature of each subgroup with the weight of each channel. The output of the \(c\)-th channel is as follows:  
\[V_{r}^{k}=\sum_{i=1}^{R}a_{i}^{k}(c)U_{R(k-1)+i},i\in 1,2,\cdots,R \tag{5}\]  
where \(V_{c}^{k}\) represents the weighted fusion features of the \(c\)-th channel of each branch and \(U_{S(k-1)+i}\) represents features of the \(S(k-1)+i\)-th subgroup.