## 3 Proposed Method
### TRA Module  
Due to the difficulty in obtaining paired images under various adverse weather conditions and normal conditions at the same construction site, this study addressed this challenge by artificially synthesizing construction site images with fog, rain, and snow. The influence of rain and snow was also considered. Raindrops and snowflakes scatter and absorb light, thereby reducing image quality. These extensions enhanced the mathematical model, making it more inclusive when considering the image formation process under various weather conditions. Specifically, in the image restoration module, the parameters obtained from the estimation part were utilized to generate the final restored image through element-wise addition and multiplication layers. This process can be regarded as achieving high-quality image dehazing, deraining, and desnowing through joint learning based on the modeling parameters of fog, rain, and snow. Below is the specific design of the dehazing, deraining, and desnowing filters. The formation of blurry images in foggy weather can be expressed as follows:  
\[I_{1}(x,\lambda)=e^{-\beta(\lambda)}d(x)K(x,\lambda)+A(1-e^{-\beta(\lambda)}d(x)) \tag{1}\]  
where \(I_{1}(x,\lambda)\) represents the foggy image, \(x\) is the position of pixels in the image, \(\lambda\) is the wavelength of light, \(K(x,\lambda)\) denotes the scene radiance (clean image), \(A\) is the global atmospheric light, and \(e^{-\beta(\lambda)}d(x)\) is the medium transmission map, where \(\beta(\lambda)\) represents the atmospheric scattering coefficient and \(d(x)\) is the scene depth. To restore the clean image \(K(x,\lambda)\), it was crucial to obtain the atmospheric light \(A\) and the transmission map \(e^{-\beta(\lambda)}d(x)\). To do this, we first computed the dark channel map of the foggy image \(I_{1}(x,\lambda)\) and selected the brightest 1000 pixels. We estimated \(A\) by averaging the corresponding positions of these 1000 pixels in the foggy image \(I_{1}(x,\lambda)\). Furthermore, we introduced a parameter \(\varepsilon_{1}\) to control the degree of defogging. The defogging filter is expressed as follows:  
\[K(x,\lambda)=\frac{I_{1}(x,\lambda)-A}{\max(e^{-\beta(\lambda)}d(x),\varepsilon _{1})} \tag{2}\]  
Considering the impact of raindrops on images, we can represent the blurred rainy image as follows:  
\[I_{2}(x,\lambda)=(1-M(x))G(x,\lambda)+Q(x,\lambda) \tag{3}\]  
where \(I_{2}(x,\lambda)\) is the rainy image, \(G(x,\lambda)\) denotes the scene radiance (clean image), and \(M(x)\) is the binary mask for raindrops, based on the scattering and reflection effects of raindrops and used to mark the positions and intensities of raindrops. \(Q(x,\lambda)\) represents the blurred image formed by the light reflected from raindrops. To restore the clear image \(G(x,\lambda)\), we needed to estimate the effect of raindrops and remove their influence. Firstly, we computed the dark channel map of the rainy image \(I_{2}(x,\lambda)\) and selected the brightest pixel. Then, by averaging the corresponding pixels in the rainy image \(I_{2}(x,\lambda)\), we could estimate the light reflected by raindrops \(Q(x,\lambda)\). We introduced a parameter \(\varepsilon_{2}\) to control the degree of deraining, similar to the design of the defogging filter. The final deraining filter can be expressed as follows:  
\[G(x,\lambda)=I_{2}(x,\lambda)-\varepsilon_{2}Q(x,\lambda) \tag{4}\]  
By adjusting the parameter \(\varepsilon_{2}\), we could effectively mitigate the impact of raindrops and restore a clearer image. For the desnowing filter design, the snowy image model can be represented as follows:  
\[I_{3}(x,\lambda)=(1-z)S(x)+H(x,\lambda) \tag{5}\]where \(I_{3}(x,\lambda)\) is the snowy image, \(H(x,\lambda)\) represents the scene radiance (clean image), and \(z\) is the binary mask for snowflakes, based on the reflection effects of snowflakes and used to form spots on the image. \(S(x)\) denotes the blurred image formed by the light reflected from snowflakes.