## 2 Materials and Methods
### Channel Distillation Module  
Current methods for enhancing underwater images employ multi-scale feature fusion techniques, which involve extracting and merging feature information from intermediate layers of neural networks. These methods typically utilize feature extraction modules based on residual blocks [33] and dense blocks [34] to extract features from convolutionally generated multiscale feature maps. These features are then fused together using operations like channel splicing and dense joining to generate enhanced underwater images [21; 22; 23]. However, these feature extraction branches and fusion modules significantly increase computational demands and impact the real-time performance of the algorithm. To address this issue, we leverage the knowledge distillation framework to transfer middle layer feature information from the teacher model to the student model through a loss function. This approach effectively improves the model's performance without increasing the number of parameters or computational requirements of the student network.  
In this study, we employ the channel distillation [35] to effectively enhance the texture details of underwater images by extracting and transferring middle layer feature information from the teacher model. Initially, a \(1\times 1\) convolution is utilized to address the discrepancy in the number of channels between the \(G_{T}^{M}\) and the \(G_{S}\) feature maps. This expansion of channels in the student generator ensures compatibility. Subsequently, we utilize global average pooling (GAP) to compute the importance of each channel's feature map, which reflects the attention information associated with that channel. We regard the attention information of each channel's feature map as knowledge. The \(G_{T}^{M}\) and the \(G_{S}\) independently calculate the attention information of each channel from their respective feature maps. The \(G_{T}^{M}\) then guides the \(G_{S}\) to learn the attention information of each channel and transfers this knowledge to the \(G_{S}\). Through this process, the \(G_{S}\) can acquire the teacher's attention information for each channel, resulting in an enhancement of its performance. Consequently, the texture information of the underwater image is further improved. Notably, the Channel Distillation (CD) module only utilizes computational resources during the training process of the framework, and there is no need to invoke this module when utilizing the student model. Figure 3 provides a detailed depiction of the CD module architecture.  
In Figure 3, we use GAP to compute the importance of each channel's feature map, which represents the attention information of each channel [35; 36]. The weight of each channel is defined as follows:  
\[w_{c}=\frac{1}{H\times W}\sum_{i=1}^{H}\sum_{h=1}^{W}\mu_{c}(i,j) \tag{1}\]  
where \(w_{c}\) denotes the weight of the \(cth\) channel. \(H\), \(W\) are the spatial dimensions of the feature map and \(\mu_{c}(i,j)\) is the activation work. When calculating the channel distillation (CD) loss, due to the inconsistency of the number of \(G_{S}\) and \(G_{T}^{M}\) channels, it is necessary to upgrade the dimensionality by using \(1\times 1\) convolution first, and then perform channel distillation. The CD loss is defined as follows:  
\[\mathcal{L}_{\text{CD}}(G_{T}^{M},G_{S})=\frac{\sum_{i=1}^{f}\sum_{j=1}^{c} \left(w_{t_{M}}^{ij}-w_{s}^{ij}\right)^{2}}{f\times c} \tag{2}\]  
where \(w^{ij}\) denotes the attention weight of the \(jth\) channel of the \(ith\) feature map of the model, \(f\) denotes the number of feature maps, and \(c\) represents the number of channels.