## 1 Introduction  
Airplanes flying at high altitude may come into contact with water vapor in the air which causes icing, causing loss of control or reduced performance. This seriously affects flight safety. To study aircraft tcing, researchers conduct such scenarios in wind tunnels. An icing wind tunnel provides low temperatures, low pressures, high wind speeds, and cloud and fog conditions, and is a facility specifically designed to simulate and study aircraft surface icing phenomena and their behavior. In the icing wind tunnel test section, there are suspended water droplets with a certain liquid water content. When light passes through these water droplets, the resulting image becomes blurred and the quality deteriorates due to scattering and attenuation, seriously affecting the observation of the icing. Compared with traditional hazy images and those captured in natural environments, images captured in icing wind tunnels generally have a higher concentration of fog. The liquid water content (LWC) is usually around 1.0 g/m\({}^{3}\). In contrast, the LWC of hazy images captured in natural environments is typically around 0.5 g/m\({}^{3}\). Moreover, when performing dehazing on images captured in icing wind tunnels, it is crucial to preserve the structural and edge information of the ice on the wings to facilitate subsequent ice detection work by researchers. Therefore, to improve the quality of monitoring images in the icing wind tunnel test and help researchers obtain more information, image dehazing technology can be applied. This technology can address problems such as color distortion, decreased contrast, and loss of edge and texture information in images, which are common in icing wind tunnel tests. Overall, this approach has practical and significant importance for advancing wind tunnel icing experiments. The purpose of this work is to explore the problem of image dehazing in wind tunnel experiments, in which the icing wind tunnel environment has a high fog density. In dehazing algorithms, an atmospheric scattering model [1] is commonly used to describe the relationship between hazy and haze-free images:  
\[I=J(x)t(x)+A(1-t(x)) \tag{1}\]  
where \(J(x)\) represents the haze-free image, \(I(x)\) represents the collected hazy image, \(t(x)\) represents the transmittance map, and \(A\) represents the atmospheric illumination value. When the atmospheric illumination value is fixed, the transmittance map \(t(x)\) can be described as  
\[t(x)=e^{-\beta t(x)} \tag{2}\]  
where \(\beta\) is the atmospheric scattering coefficient, and \(d(x)\) represents the distance from the object to the visual sensor, that is, the depth of the scene. The essence of image defogging is the process of restoring the foggy image to the fogless image infinitely. After \(I(x)\) is given, in order to find \(J(x)\) for the reverse solution, we usually focus on finding the value of both \(t(x)\) and \(A\). Image dehazing is a highly ill-posed problem. Image dehazing algorithms can generally be divided into those based on prior knowledge and those based on learning. Prior knowledge-based dehazing algorithms can be further divided into physical model-based algorithms and non-physical model-based algorithms. Physical model dehazing algorithms are based on the atmospheric scattering model, and use prior knowledge to obtain relevant parameters such as transmission rate and atmospheric illumination value, and then use Equation (1) to obtain a dehazed image, such as the DCP [2] and CAP [3] algorithms. DCP assumes that in outdoor images without haze, most local regions contain some pixels with very low intensity in at least one color channel. Thus, the transmission rate can be estimated using the dark channel prior. This algorithm has low complexity, but it has limitations, such as being affected when processing scenes similar to the sky. CAP establishes a linear model of the depth of the hazy scene, and then restores the haze-free image through the atmospheric model.