## 3 Methods
### Multi-Scale Channel Cross-Fusion Module
#### 3.5.1 Channel-Wise Cross-Fusion Transformer  
The CCT module involves three steps: multi-scale feature embedding, multi-head channel cross-attention, and multi-layer perceptron.  
The multi-scale feature embedding first downsamples the input feature map to obtain four different scales of output \(S_{i}\in R^{\frac{iW}{2^{i}}\times C_{i}},(i=1,2,3,4)\). Firstly, the input feature map is convolved with different kernel sizes and strides to adjust to blocks of the same size (e.g., \(14\times 14\)), which compresses spatial information while retaining channel information. Then, each feature vector is position-encoded to preserve the positional information of the feature map, resulting in tokens \(T_{i}\in R^{\frac{iW}{2^{i}}\times C_{i}}\), \((i=1,2,3,4)\). Finally, the tokens for the four scales are concatenated along the channel dimension to form \(T_{\Sigma}\).  
The multi-head channel cross-attention mechanism is used to weight and refine the semantic and detail features between inter-channel image blocks. To achieve this, as expressed in Equation (16), we derive \(Q_{i}\) and \(K,V\) using linear transformations on the five outputs \(T_{i}(i=1,2,3,4,\Sigma)\) embedded with multi-scale features.  
\[Q_{i}=T_{i}\times W_{qi},K=T_{\Sigma}\times W_{k},V=T_{\Sigma}\times W_{v} \tag{16}\]  
Let \(W\) be the weight matrix, where \(W_{qi}\in R^{N_{i}\times d}\), \(W_{k}\in R^{N_{\Sigma}\times d}\), \(W_{v}\in R^{N_{\Sigma}\times d}\) represents the feature channel dimension and, in our settings, \(N_{1}=64\), \(N_{2}=128\), \(N_{3}=256\), \(N_{4}=512\), \(N_{\Sigma}=960\) represents the sequence length (i.e., the patch numbers). Because the encoder has multiple scales of output, we expand \(Q_{i}\) and \(K\), \(V\) from (B, N, C) to (B, num_head, N, C) at dim = 1 to fuse the features, where num_head is set to 4. At this point, \(Q_{i}\in R^{N_{i}\times d}\), \(K\in R^{N_{\Sigma}\times d}\), \(V\in R^{N_{\Sigma}\times d}\). After computing the similarity matrix \(M\) using \(Q_{i}\) and \(K\), we perform a weighted sum with \(V\) to obtain \(CA_{i}\). The specific formula is as follows (17):  
\[CA_{i}=M_{i}V^{T}=\sigma[\psi(\frac{Q_{i}^{T}K}{\sqrt{C_{\Sigma}}})]V^{T}= \sigma[\psi(\frac{W_{Q_{i}}^{T}T_{i}T_{\Sigma}W_{K}}{\sqrt{C_{\Sigma}}})]W_{V} ^{T}T_{\Sigma}^{T} \tag{17}\]  
where \(\psi()\)represents the instance normalization function and \(\sigma()\) represents the Softmax normalization function. In order to facilitate gradient propagation, we take the mean over the num_head dimension and restore the dimensionality back to (B, N, C). Finally, we add the attention matrix to the original input, pass it through an MLP layer, and perform residual computation to obtain four output matrices \(O_{i}\in R^{C\times H\times W}(i=1,2,3,4)\). These \(O_{i}\) matrices are concatenated with the features from the decoder \(D_{i}\in R^{C\times H\times W}(i=1,2,3,4)\) and further enhanced by the CCA module for feature fusion, as shown in Equations (18) and (19):  
\[MCA_{i} =(CA_{i}{}^{1}+CA_{i}{}^{2}+\cdots+CA_{i}{}^{N})/N \tag{18}\] \[O_{i} =MCA_{i}+MLP(Q_{i}+MCA_{i}) \tag{19}\]Here, \(CA_{i}^{N}\) represents the output of the multi-head channel cross-attention mechanism, where \(N\) is the number of heads; \(O_{i}\) is the output of the CCT module, and \(Q_{i}\) is the query vector. In practice, we set \(N\) to 4.  
As shown in Figure 4, after passing through the multi-head channel cross-attention fusion mechanism, the feature map generates four different scale outputs. Each input feature is related to the other input features, which effectively reduces the problem of information loss during the transmission of images.