# Progressive Pruning of Light Dehaze Networks for Static Scenes
## 3 Methods
### Channel Importance Analysis  
Following the localized fine-tuning, we conduct an in-depth channel importance analysis to identify the most critical components of our network for the dehazing task. This analysis forms the foundation for our subsequent pruning efforts, ensuring that we can create a lightweight model without significant performance degradation.  
Our approach to assessing channel importance is based on the impact of each channel on the overall dehazing performance. We define the importance score \(I_{c}\) for a channel \(c\) as follows:  
\[I_{c}=\max(0,\text{PSNR}_{o}-\text{PSNR}_{p}+\text{SSIM}_{o}-\text{SSIM}_{p}) \tag{1}\]  
In Equation (1), \(I_{c}\) represents the importance score for channel \(c\). The terms \(PSNR_{o}\) and \(SSIM_{o}\) denote the Peak Signal-to-Noise Ratio and the Structural Similarity Index of the output from the original model, respectively. Correspondingly, \(PSNR_{p}\) and \(SSIM_{p}\) represent the same metrics but for the output when channel \(c\) is pruned from the model. The subscript \(o\) is used to indicate the original model, while \(p\) denotes the pruned model. This formulation allows us to quantify the impact of pruning a specific channel on the overall image quality, considering both the PSNR and SSIM metrics.  
This importance score considers both the PSNR and SSIM metrics, providing a comprehensive measure of how each channel contributes to the final image quality. A higher score indicates greater importance, as it suggests that pruning the channel results in a more significant degradation of the output image quality.  
To compute these scores, we employ the following methodology:  
1. For each channel \(c\) in a given layer: a. Create a copy of the original model. b. Prune channel \(c\) from the copied model. c. Process the test image through both the original and pruned models. d. Calculate the PSNR and SSIM for both outputs. e. Compute the importance score \(I_{c}\) using the formula above.  
2. Repeat its process for all channels in the layers of interest.  
Our analysis reveals interesting patterns in channel importance across different layers of the network. Some channels consistently show high importance scores across different test images, suggesting their critical role in the dehazing process. Conversely, other channels demonstrate lower importance, indicating potential candidates for pruning.  
To visualize these findings, we create importance distribution plots for each analyzed layer. These plots provide a clear picture of which channels are most crucial for maintaining dehazing performance within each layer of the network.  
Interestingly, our analysis reveals that the channels showing high importance often correspond to features that are unique to our static viewpoint scenario. For instance, channels that effectively capture the structural elements of buildings or the textural details of vegetation in the scene consistently rank high in importance. This observation underscores the value of our localized fine-tuning approach and informs our subsequent pruning strategy.  
By leveraging this channel importance analysis, we can make informed decisions about which channels to prune in our lightweighting process. This approach allows us to significantly reduce the model size while maintaining high dehazing performance,particularly for our specific fixed camera environment. The insights gained from this analysis not only guide our pruning strategy but also provide valuable understanding of how different parts of the network contribute to the dehazing process in our specific use case.