## 1 Introduction  
The issue of image color distortion caused by varying capture environments has been a pivotal research topic in the field of image enhancement. Prominent cases include various similar environmental conditions such as haze, dust, underwater scenarios, rainy weather, and snowfall. The color distortion stemming from environmental factors results in an overall degradation of image quality, thereby adversely affecting computer vision tasks reliant on image data, including applications like surveillance systems, autonomous driving, underwater exploration, and more [1]. Existing methods for enhancing color-distorted images often focus solely on addressing individual cases, such as haze removal, dust reduction, and underwater image enhancement. However, introducing an algorithm or allocation strategy that effectively harnesses the intrinsic relationships among different types of color-distorted images for multi-task learning (MTL) has the potential to tap into the untapped opportunities in this domain, leading to significant improvements in processing outcomes. In the current domain, the limitations of traditional algorithms mainly stem from their reliance on prior knowledge and parameters, rendering them unable to meet the demands of multi-task scenarios. The previously proposed RGB color balance algorithm [2] demonstrated a degree of effectiveness in enhancing dust and underwater images, yielding favorable results. Nevertheless, due to the absence of non-uniform RGB channel adjustments in haze images, its performance remains suboptimal for such cases. In recent years, deep learning has exhibited substantial competitiveness in the field of computer vision. Some algorithmic models address multi-task challenges by employing distinct pre-trained weights, as exemplified by [3; 4]. Other network models introduce gating mechanisms, enabling differentiated task handling across diverse network branches, thereby achieving improved results. However, the underlying principle of these approaches still hinges on accentuating the disparities between tasks to realize multi-task processing. This methodology fundamentally overlooks the inherent relationships among distinct types of images. Effective information exchange is lacking between different tasks, resulting in each task being influenced solely by other isolated tasks. This deficiency hampers the collaborative advancement of each task, leading to models of this nature often underperforming compared to models specifically tailored for individual tasks [3]. This study delves into a comprehensive exploration of haze, dust, and underwater images, all of which suffer color distortion due to environmental factors. Through the application of neural networks, we engage in feature exploration of these images with the aim of unearthing their intrinsic connections. Our focus lies in the deep-level features, where we design a strategy encompassing multi-task learning and knowledge allocation. Our main contributions in this paper are as follows:  
* In general, we have developed a multi-task learning and knowledge allocation strategy tailored for enhancing three categories of images: haze, dust, and underwater images. This strategy has been applied to our network model. By uncovering the interconnections and unique characteristics of these three image categories, we aim to mutually enhance the overall model performance and the enhancement effects for individual tasks. This approach also mitigates the performance degradation caused by the interplay between different tasks;
* We have introduced a novel approach called the Frequency Domain Similarity-Gated Selection Vision Transformer (FSGS-ViT) and a Mixed-Scale Frequency Domain Feed-forward Network (MDFN). In these methods, we have incorporated the Discrete Cosine Transform (DCT) operator for self-attention value decomposition and similarity calculation.