# Multi-Input Attention Network for Dehazing of Remote Sensing Images
## 1 Introduction  
In recent years, the quality and quantity of satellite data have tremendously increased. However, the impact of haze has been a common issue with optical remote sensing data. Haze can severely interfere with the transmittance in all optical spectral bands, which impacts the reflected signal and hinders the observation of the underlying surface of the haze. This further results in huge data loss in both the spatial and temporal domains. Haze becomes serious interference for applications requiring time consistency (such as agricultural monitoring) and applications requiring observation of a scene at a specific time (such as disaster monitoring). Therefore, effective recovery from haze will greatly increase the usability of remote sensing data. Early studies on the dehazing problem of remote sensing images use different methods to eliminate the influence of haze [1; 2; 3; 4]. They use multi-source or multi-temporal images in the same area as auxiliary data, the complementary relationship between images, image fusion, pixel replacement, etc. All these methods have achieved good results. However, the need to obtain multiple sets of data from the same area as auxiliary data leads to poor applicability; especially for some remote sensing data with long collection interval, it will be more difficult to obtain available auxiliary data. Therefore, the single image dehazing method has attracted more and more attention. Some studies on single image dehazing use image enhancement methods, including processing the histogram of the image [5], and enhancing the contrast [6] and saturation [7] of the image. Additionally, some dehazing methods are based on homomorphic filtering [8] and the retinex color constancy theory [9]. Image enhancement lacks the hazy imaging mechanism, which could lead to a certain degree of distortion in the restored image. Researchers build an image dehazing methodbased on the Atmospheric Scattering Model (ASM). The most popular ASM model was proposed by [PERSON] and further improved by [PERSON] [10] and [PERSON] [6]. The model can usually be written as in Formula (1):  
\[I(x)=J(x)t(x)+A[1-t(x)] \tag{1}\]  
where \(I(x)\) is the image disturbed by haze; \(J(x)\) is the haze-free image that needs to be restored; \(t(x)\) is the transmittance of light passing through the atmospheric medium; \(x\) represents the image pixel; \(A\) represents the global constant: atmospheric light. To obtain the haze-free image \(J(x)\), we first need to obtain the transmittance \(t(x)\) and the global atmospheric light \(A\). However, using hazy images to estimate transmittance requires prior information. At present, studies on prior information are mainly based on statistical properties of hazy images, such as contrast prior [11], dark channel prior (DCP) [12], color attenuation prior [13], etc. However, this prior information will very likely become less applicable in images of different scenes, which affects the dehazing results. The development of deep learning brings new ideas to the dehazing research: convolutional neural network (CNN). Some earlier studies use neural networks to replace prior information to estimate the parameters of Formula (1) [14; 15; 16] and to obtain the dehazed image. Since the real transmittance value of the hazy image cannot be obtained, the training data can be achieved through simulated parameters, which could impact the accuracy of the estimated transmittance. Meanwhile, the transmittance model is a simplified expression for hazy imaging. The advantage of feature extraction capability of neural networks cannot be fully utilized. Some research uses end-to-end networks to directly explore the mapping relationship from hazy images to haze-free images and, finally, generate dehazed images [17; 18; 19; 20]. This research obtained prominent dehazing effects. However, there are limitations. First, the dataset used in the dehazing models is usually less disturbed by haze, which is relatively uniformly distributed.