## 4 Experiments
### Datasets and Experimental Settings  
**Datasets.** For dust images, due to the lack of publicly available standard datasets in the academic community, other related studies often rely on synthetic datasets. To address this issue, we collected and curated a real dust image dataset named \"D-Sand.\" This dataset consists of high-quality dust images that exhibit strong dust effects. The \"D-Sand\" dataset consists of a total of 900 high-quality dust images, primarily collected through a combination of web scraping and manual photography. The manually captured images were taken in the northwestern regions of China, including locations such as Dunhuang and Lanzhou. The dataset encompasses diverse content, featuring natural landscapes (mountains, sand dunes), urban scenes (buildings, roads, vehicles), and human subjects.  
For haze images, we utilized multiple datasets, including \"RESIDE\" [45], \"O-Haze\" [46], \"Dense-Haze\" [47], and \"NTIRE 2020\" [48] datasets. In the underwater image domain, we selected the \"SUIM\" [49], \"UIEB\" [50], and \"RUIE\" [51] datasets. To ensure a sufficient and balanced number of samples for different categories in the mixed dataset, we ensured that each class of images contained 10,000 images in the training set. To address the scarcity of data, we excluded test images, split the remaining images into non-overlapping image blocks, and applied appropriate image augmentation techniques to generate 10,000 training images. Therefore, the mixed dataset contains a total of 30,000 pairs of training images. Additionally, we employed collected paired datasets for network pretraining to enhance the effectiveness of subsequent unsupervised training.  
**Training details.** We employed the same loss function as in [52] to constrain the network. The image size was fixed at 256 \(\times\) 256. During the training process, we utilized 3 NVIDIA A100 GPUs in conjunction with the FSDP training mode proposed by Facebook.  
We employed the Adam optimizer for local parameter updates [10] and used default parameters to accelerate training efficiency. The initial learning rate was set to \(1\times 10^{-4}\), and after 100 K iterations, we employed a cosine annealing strategy to gradually reduce the learning rate. The minimum value of the learning rate was set to \(1\times 10^{-6}\).  
**Comparison methods.** To validate the effectiveness of our method, we conducted comprehensive comparisons with both traditional and learning-based approaches. In the realm of traditional methods, techniques like DCP [6], RCP, MSRCR, RGHS, ACE, and Park [53] have maintained a certain status in the field of image enhancement due to their good results and simple processing pipelines. In our experiments, we evaluated these traditional methods on the three types of images based on their respective application domains.  
For learning-based methods, we selected TBNN [16], USDR-Net [54] for sandstorm image enhancement comparison, TBNN [16], DehazeC [55], FSAD [15] for haze image enhancement comparison, and FUnIEGAN [56], UWNet [37], NU'2 NET [57], and PUIE-NET [58] for underwater image enhancement comparison. For models that did not provide pre-trained parameters, we retrained the models with the provided code. For models with existing pre-trained parameters, we performed fair comparisons using their online code and parameters.  
**Evaluation metrics.** We employed PSNR and SSIM as the evaluation metrics for the aforementioned benchmarks. Following prior research practices, we computed the PSNR and SSIM metrics for the Y channel of the YCbCr color space. For images without paired ground truth values, we utilized non-reference metrics such as e-score, r-score, UIQM, and UCIQE algorithms.