## 3 Our Method
### Loss Function  
Effective image dehazing requires both structural restoration and precise color fidelity. To this end, we propose a novel dual-space loss function, optimizing reconstruction in both RGB and Lab color spaces. By leveraging RGB for structural consistency and Lab for perceptual color accuracy, our approach mitigates color distortions while preserving image integrity.  
To maintain structural consistency between the dehazed output and the ground truth, we employ an L1 reconstruction loss in the RGB domain. The first component of the loss function is the pixel-level reconstruction \(L1\) loss. During training, the model takes hazy images as input and outputs dehazed images after processing by the network. \(L1\) loss calculates the pixel-level differences between the dehazed image and the ground-truth (GT) image, guiding the network to optimize the image reconstruction by minimizing the absolute differences between the two images. Specifically, the \(L1\) loss is computed as the sum of the absolute pixel-wise differences between the two images. The primary goal of this loss function is to reduce reconstruction errors, making the dehazed image as close as possible to the real clear image, thereby enhancing the image details. \(L1\) can be expressed mathematically as follows:  
\[L1=\|I_{dehazed}-I_{GT}\|_{1} \tag{4}\]  
To further refine color correction, we introduce an \(L1\) loss in the Lab color space, specifically focusing on the a (red-green) and b (yellow-blue) chromatic channels. While pixel-level \(L1\) reconstruction loss enhances structural clarity, it remains insufficient for precise color restoration, particularly in maintaining color fidelity. In our approach, the a and b chromatic components of both the dehazed output and the ground truth are extracted, and the \(L1\) loss is computed between them. Given that the Lab color space inherently decouples luminance (L) from chromaticity (a, b), this loss formulation enables CCD-Net to more effectively restore natural colors and mitigate hue shifts introduced by atmospheric scattering. By incorporating this constraint, the loss function not only ensures accurate brightness restoration but also enhances color consistency, significantly reducing potential chromatic distortions in the dehazing process. \(L_{color}\) can be expressed mathematically as follows:  
\[L_{color}=\|\hat{X}_{AB}-I_{GT}^{ab}\|_{1} \tag{5}\]  
To comprehensively address both brightness restoration and color restoration, this paper combines the two loss components into a unified loss function. Specifically, the loss function is a weighted sum of the pixel-level \(L1\) loss and the \(L1\) loss in the Lab color space, with each component contributing equally to the total loss by setting the weight factor to 0.5. This weighted combination enables the model to optimize both the brightness restoration and color consistency during training, resulting in final outputs that are visually  
Figure 7: Illustration of CBAM.  
clear and color-accurate. The final objective function is a weighted combination of both loss components:  
\[L=L1\times 0.5+L_{color}\times 0.5 \tag{6}\]  
where \(L1\) denotes the pixel-based \(L1\) loss and \(L_{color}\) represents the L1 loss in the LAB color space.