## 2 Method
### Preprocessing Module for Dehazing Design
#### 2.2.1 Dark Channel Prior Dehazing  
Due to the scattering effect of particles, there is attenuation in the transmission of light between the target and the camera, resulting in atmospheric light scattering [28]. Therefore, researchers have proposed an atmospheric scattering model, which is represented by the following equation [29]:  
\[I(x)=J(x)t(x)+A(1-t(x)) \tag{3}\]  
In this equation, \(x\) represents pixel value, \(I(x)\) represents the hazy image, \(J(x)\) represents the dehazed recovered image, \(t(x)\) is the transmission map, and \(A\) denotes the atmospheric light value.  
Figure 4: Dehazing preprocessing operation flowchart.  
Among these values, only the hazy image \(I(x)\) is known, while \(t(x)\) and \(A\) are both unknown. Therefore, solving for the dehazed recovered image \(J(x)\) constitutes an ill-posed equation, requiring prior knowledge or assumptions to aid in the solution. In the Dark Channel Prior theory, [PERSON] et al. observed through extensive experiments that in most areas of an image, excluding the sky region, pixel values in at least one color channel are typically small, often close to zero. This is mathematically expressed as follows [30; 31]:  
\[J^{dark}=\min_{y\in\Omega(x)}\biggl{(}\min_{c\in\{r,g,b\}}J^{c}(y)\biggr{)}\approx 0 \tag{4}\]  
Therefore, the method can be simplified by extracting the minimum value from the R, G, and B channels to form a grayscale image of the same size as the original image. This grayscale image is then processed with a single minimum filter operation to obtain a dark channel image of the same size as the original image [31; 32]. Subsequently, in the dark channel image, the average value of the brightest points occupying 0.1% of the total pixel count of the image is selected as the atmospheric light value \(A\). The transmission rate \(t\) can be obtained from Equation (5):  
\[t(x)=1-\min_{y\in\Omega(x)}\biggl{(}\min_{c\in\{r,g,b\}}\frac{I^{c}(y)}{A^{c}} \biggr{)} \tag{5}\]  
However, in real-world scenarios, there are still tiny particles in the air that can create a sense of haze, resulting in a depth-of-field effect in captured images. Therefore, dehazing algorithms need to retain some sense of haze to avoid color distortion, making the dehazed images appear natural and realistic. By introducing a factor \(\omega\) between 0 and 1 to modify the estimated transmission rate \(t(x)\), haze can be preserved. In general, a value of 0.95 for the \(\omega\) factor is often chosen as it closely matches human visual perception. The modified expression is given by Equation (6) as follows:  
\[t(x)=1-\omega\min_{y\in\Omega(x)}\biggl{(}\min_{c\in\{r,g,b\}}\frac{I^{c}(y)}{ A^{c}}\biggr{)} \tag{6}\]  
If the transmission rate \(t(x)\) is too small, it can lead to overly bright values in \(J(x)\). In such cases, it is common to set a lower limit for \(t(x)\), denoted as \(t0=0.1\). When the value of \(t\) is less than \(t_{0}\), \(t\) is set to \(t_{0}\). Finally, the obtained transmission rate \(t(x)\) and the atmospheric light value \(A\) are substituted into Equation (6) to obtain the final formula for obtaining the clear image, as follows:  
\[J_{1}(x)=\frac{I(x)-A}{\max(t(x),t_{0})}+A \tag{7}\]