## 3 Proposed Method
### Knowledge Allocation Strategy  
As a multi-task and knowledge allocation system, a well-designed knowledge allocation strategy is crucial for achieving effective multi-task learning after the completion of the backbone feature extraction phase. In our study, we employed a mixed dataset training approach, combining dust images, haze images, and underwater images into a comprehensive dataset. The purpose of this approach is to solely rely on the network itself to differentiate between the features of the three categories and shared features. Through this strategy, we aim to perform multi-task learning within a unified framework, allowing the network to fully leverage the acquired knowledge and better address the challenges of multiple tasks. Such a knowledge allocation strategy enhances the model's generalization capabilities and enables more efficient utilization of existing data resources.  
To effectively distinguish between the features extracted by the backbone feature extraction and classify them into the three distinct categories and shared features, we employed four independent parallel Mixed-Scale Knowledge Selection Modules (MKSM) for knowledge selection. Subsequently, knowledge allocation was performed using the approach provided by [43], where the features belonging to each of the three categorieswere allocated to their respective Enhancement Modules (EB), while the shared features were allocated to each Enhancement Module. Through this approach, we were able to enhance the enhancement effects for the three categories of images.  
Firstly, the backbone features were individually fed into the MKSM for the following knowledge selection process:  
\[X_{S}=\text{MKSM}_{S}(X_{B}) \tag{17}\]  
\[X_{H}=\text{MKSM}_{H}(X_{B}) \tag{18}\]  
\[X_{W}=\text{MKSM}_{W}(X_{B}) \tag{19}\]  
\[X_{F}=\text{MKSM}_{F}(X_{B}) \tag{20}\]  
where \(X_{B}\) represents the backbone features, \(X_{S}\) represents the independent features required for dust image enhancement, \(X_{H}\) represents the independent features required for haze image enhancement, \(X_{W}\) represents the independent features required for underwater image enhancement, and \(X_{F}\) represents the shared features. The knowledge allocation strategy is carried out as follows:  
\[R_{S}=EB_{S}(X_{S},X_{F}) \tag{21}\]  
\[R_{H}=EB_{H}(X_{H},X_{F}) \tag{22}\]  
\[R_{W}=EB_{W}(X_{W},X_{F}) \tag{23}\]  
\[R_{F}=EB_{F}(X_{S},X_{H},X_{W}) \tag{24}\]  
where \(EB\) represents the respective enhancement modules, \(R\) represents the results after enhancing the three types of images, and \(R_{F}\) represents the recognition results of the three types of images. The structure of \(EB\) is illustrated in Figure 1 as shown.  
The above constitutes the fundamental principle of the entire multi-task knowledge allocation. By utilizing the knowledge selection capability of MKSM, an adaptive multi-task processing is achieved, effectively leveraging the variations and connections among different tasks. This approach facilitates the collaborative enhancement of task performance through the interplay of relationships between different tasks, ultimately leading to a balanced performance across tasks.