This methodology, facilitated through foggy day image enhancement, endeavors to ameliorate image contrast while minimizing the impact of image noise, thereby effectuating the restoration of a lucid image devoid of fog [5,6]. The inherent advantage lies in the utilization of well-established image processing algorithms that target the enhancement of image contrast [7], thereby accentuating scene characteristics and pertinent information within the image. However, a drawback is discerned in the potential loss of certain information, leading to image distortion. Notwithstanding, this algorithmic approach boasts broad applicability. Representative algorithms within this category encompass the Retinex algorithm [8–12], histogram equalization algorithm [13–17], the partial differential equation algorithm [18,19], the wavelet transform algorithm, and analogous methods [20–23]. While these techniques often yield visually appealing images with relatively efficient computational times, their efficacy is constrained by the inability to comprehensively eradicate haze, given the absence of explicit degradation processes.

The methodology for enhancing images captured under foggy conditions encompasses a suite of techniques, including the Retinex algorithm, histogram equalization algorithm, partial differential equation algorithm, and wavelet transform algorithm. These methodologies are employed to enhance image contrast and reduce noise, thereby restoring clarity to fog-obscured images. Leveraging established image processing algorithms, these techniques aim to emphasize scene characteristics and essential information. Despite their widespread applicability and relatively efficient computational characteristics, a notable limitation resides in the potential loss of information, which can lead to image distortion. Furthermore, these techniques encounter challenges in completely mitigating haze due to the absence of explicit degradation modeling. The selection of a particular technique entails a trade-off between heightened contrast and the risk of distortion, necessitating careful consideration aligned with the specific demands of the application at hand.

This category of algorithms is predicated on the principles of atmospheric scattering theory, resolving the atmospheric scattering (Eq. (1)) by imbuing it with supplementary conditions to render it nonpathological [24,25]. These algorithms leverage diverse a priori information as auxiliary inputs to estimate the parameters λ, η, and β in Eq. (1). Subsequently, by harnessing image degradation, these algorithms enable the direct restoration of the fog-free map [26–28]. It is noteworthy that a common limitation shared by a priori algorithms is the circumstance-specific nature of their efficacy; optimal results in a priori estimation are attainable only under specific scenario conditions, thereby engendering variable performance across diverse scenarios. The atmospheric scattering equation is articulated as follows: (1)I(x)=J(x)t(x)+A[1−t(x)],t(x)=e−βd(x)where I(x) is the fogged image, J(x) is the reflected light from the observation target, the image after de-fogging, A and t(x) are the atmospheric light coefficient and the atmospheric transmittance, respectively, d(x) is the depth map of the scene and β is the atmospheric light scattering coefficient. It is evident from Eq. (1) that the fog-free image, denoted by J(x) can be recovered from the fogged image I(x) provided that accurate estimations of atmospheric transmittance ((t(x))) and atmospheric light (A) are obtained.

In tandem with the relentless evolution of deep learning theory, the Convolutional Neural Network (CNN) [46–49] has garnered widespread adoption and commendable success in diverse domains such as face recognition and image segmentation. CNN networks can efficiently learn complex feature representations from large amounts of image data to achieve excellent performance in visual tasks [50–53]. Image dehazing, a salient concern within the realm of image processing, has garnered considerable scholarly interest. Notably, data-driven dehazing techniques, rooted in deep learning paradigms, have demonstrated remarkable advancements when juxtaposed against conventional haze removal methods.

Deep learning defogging algorithms can be stratified into two overarching categories: estimated parameter methods and direct repair methods. The parameter estimation method employs deep convolutional neural networks to directly estimate key parameters such as t(x) and A, etc., subsequently facilitating image dehazing through the application of the atmospheric scattering model. Leveraging the learning capability inherent in deep neural networks, the direct inpainting method achieves an end-to-end process, directly deriving the haze-free image from the foggy image within the framework of data-driven conditions.

The quest to mitigate atmospheric haze in remote sensing images and enhance their quality has given rise to two principal categories of methods: traditional a priori knowledge-based approaches and deep learning-based methods.

Traditional a priori methods typically commence by estimating transmittance maps for atmospheric light and hazy images, followed by the application of classical atmospheric scattering models to reconstruct fog-free images. However, these methods heavily hinge on assumptions about the scene and haze properties, rendering their defogging performance susceptible to inaccuracies in these assumptions [81–83]. Additionally, these approaches are formulated based on diverse assumptions and models, constraining their universal applicability across various environmental conditions and atmospheric compositions.

In contrast, deep learning-based methods for de-fogging remote sensing images leverage advanced algorithms to learn the mapping between fogged and fog-free images. Utilizing extensive datasets containing paired foggy and clear images, these methods have demonstrated efficacy in alleviating haze in diverse remote sensing scenarios.

Deep learning-based image-defogging methods can be broadly categorized into two main groups. These categories are determined by the architectural design of the defogging networks, with commonly employed networks either operating independently of atmospheric scattering models or incorporating them. The former category includes encoder-decoder networks, GAN-based networks, attention-based networks, and transformer-based networks. Notably, these state-of-the-art networks demonstrate superior generalization capabilities and robustness compared to their early counterparts, making them the mainstream methods in the field. Despite their advancements, the complex architectures of these networks pose challenges. While they enhance performance, they also significantly increase network complexity, introducing challenges in terms of training, inference, and deployment [84,85]. Balancing performance improvement and complexity is an ongoing area of research in de-fogging networks, addressing the challenge this paper seeks to resolve. These methods contribute to reducing the defogging network’s reliance on specific datasets, endowing them with more robust generalization abilities.

Conventional neural networks (CNNs) demonstrate proficiency in learning multi-level image features but encounter difficulties in achieving pixel-level image classification. The introduction of Fully Convolutional Networks (FCN) represented a significant leap forward in image segmentation compared to traditional CNNs. FCN achieves end-to-end image segmentation by up-sampling the feature mapping from its final convolutional layer [86,87]. However, the relatively simplistic structure of FCN imposes limitations on its overall performance. Addressing this constraint, U-Net enhances image feature fusion by introducing an encoder-decoder structure based on FCN. The encoder module of U-Net utilizes convolution and down-sampling to extract shallow features from the image [88–91]. Simultaneously, the decoder module employs deconvolution and up-sampling to capture deep image features. U-Net further refines segmentation by incorporating skip connections between shallow and deep features, facilitating the extraction of finer image details.

Despite these advancements, an increase in the number of network layers often results in a performance decline due to the challenge of gradient vanishing. To tackle this issue, He et al. proposed the widely acclaimed Residual Network (ResNet). Res-Net adopts a novel approach by focusing on learning the residual representation between inputs and outputs rather than solely emphasizing feature mapping [92,93]. This architectural innovation has proven effective in mitigating the impact of gradient vanishing, leading to improved network performance, especially in tasks involving a large number of layers.

This paper predominantly employs a neural network model based on PyTorch, leveraging key building blocks to enhance the network’s performance. The ‘make dense’ class defines a dense connection block, fostering feature accumulation by linking input and output in the channel dimension. This design facilitates information transmission and gradient flow, mitigating the issue of vanishing gradients. The introduction of residual blocks, instantiated through the ‘ResidualBlock’ class, further bolsters gradient propagation. These blocks, connected via skips, enable direct gradient flow to shallow layers, alleviating vanishing gradient challenges in deep networks–a crucial aspect for effectively capturing complex image features.

The overall network structure follows a U-shaped encoding-decoding architecture. The encoding section captures image features, while the decoding portion progressively restores spatial resolution through up-sampling convolution. The ‘UpsampleConvLayer’ class handles the upsampling operation, with interpolation implemented using PyTorch’s ‘F.interpolate’ function. In the decoding phase, the ‘AttentionBlock’ class introduces an attention mechanism, enabling the model to focus on crucial feature areas during image reconstruction [98–101]. This inclusion enhances the network’s performance and generalization capabilities. Batch normalization and the Rectified Liner Units (RELU) activation function are integral components of the code, contributing to improved stability and faster convergence of the network. The entire model is instantiated on Compute Unified Device Architecture (CUDA) devices and leverages GPU acceleration, underscoring its commitment to efficient processing. In summary, this paper’s neural network model adeptly combines dense connections, residual blocks, multi-scale design, and attention mechanisms, creating an image-processing network with robust generalization capabilities. The U-Net architecture exhibits inherent limitations, particularly in spatial information loss during encoder down-sampling and insufficient connectivity between features from non-adjacent levels. To address these drawbacks, a straightforward approach involves resampling all features to a common scale and subsequently fusing them through bottleneck layers, incorporating connectivity and convolutional layers, similar to DenseNet [102]. However, the conventional splicing method for feature fusion proves less effective, primarily due to variations in scales and dimensions across features from different layers. In response to these challenges, we propose a novel Dense Feature Fusion with Attention (DFFA) module to efficiently compensate for missing information and leverage features from non-adjacent layers [103,104]. The DFFA module is designed to enhance features at the current level through an error feedback mechanism, specifically implemented in the encoder.

As depicted in the architecture, a DFFA module is strategically introduced before the residual group in the encoder for effective feature extraction and fusion. This module not only addresses the limitations of the U-Net architecture but also leverages an error feedback mechanism to enhance the features at each level, ensuring improved information compensation and connectivity across non-adjacent layers [105,106]. The utilization of the DFFA module represents a significant enhancement to the overall network, contributing to the efficiency and efficacy of feature extraction and fusion processes.

Following the extraction of local dense features utilizing a series of Dense Blocks, the introduction of DFFA aims to encapsulate hierarchical features from a global standpoint. The DFFA is structured around two principal constituents: global feature fusion (GFF) and global residual learning, as referenced in [107,108]. Within this framework, global feature fusion entails the derivation of the global feature (FGF) by amalgamating features originating from all Dense Blocks. (4)FGF=HGFF([F1⋯,FD])where [F1,⋯,FD] is the stitching of the feature maps generated by the Dense Block, and HGFF represents the composite function of the 1 × 1 and 3 × 3 convolutions.

The feature mappings are then obtained through global residual learning, followed by Eq. (5), and scaling is then performed (5)FDF=FLF+FGFwhere FLF denotes shallow feature mapping. Our proposed residual dense block makes full use of all other layers before global feature fusion. The Residual Group produces multi-level local dense features, which are further adaptively fused to form FGF. After global residual learning, dense features are obtained as FDF.

 Attention gates [109,110] are akin to a human visual attention mechanism that automatically focuses on the target region. They learn to suppress irrelevant feature responses in the feature map while highlighting salient feature information crucial for a particular task. From the pseudo-code flow in Algorithm 1, it is evident that the inputs of the Attention gate are two feature maps (g,x) These correspond to the feature map of the decoder part and the feature map of the encoder part of the layer above it. The specific steps are given as follows: firstly, g and x are operated in parallel, and g′ is calculated by means Wg of g and x′ is then derived by means Wx of. Subsequently, the operation g+x is thus performed to obtain σ1. Then σ2 is calculated through the Rulu operation on σ1, ζ1 is calculated by means ψ of σ2, ζ2 is calculated through means of ζ1, and α is then derived by means of. Finally, multiply α by x to get the fusion feature. A typical architecture of an attention-gating unit is shown in Fig. 6.

The loss function of a network plays a crucial role in determining the training efficiency and effectiveness of the network. The mean square error (MSE) loss function is commonly used for image-defogging tasks. However, defogged images obtained using the MSE loss often exhibit blurriness, leading to a mismatch in visual quality. The L1 loss function, being less sensitive to outliers than the MSE loss, has been found to achieve better performance [111].

To address the blurriness issue and enhance the visual quality of defogged images, we introduce the Structural Similarity Index Metric (SSIM) loss. The total loss function is defined as follows: (6)loss=λ1×SmoothL1_LOSS+λ2×SSIM_losswhere λ1=λ2=0.5, the first L1 smoothing error is based on the MSE, which addresses the zero non-smoothing problem. It is employed to measure the loss between the residual images obtained by URA-Net and the actual residual images. This smoothing mean square error is defined as: (7)SmoothL1(x)={0.5x2if|x|<1|x|−0.5otherwise

SSIM is proposed to assess the structural similarity between two images by extracting structural information, which can be defined as follows [112,113]: (8)SSIM(Ide,Igt)=2μIdeμIgt+C1μ2Ide+μ2Igt+C12σIdeIgt+C2σ2Ide+σ2Igt+C2 where μIde and μIgt are the mean of the defogged and clear images, respectively. σ2Ide and σ2Igt are the variance of the defogged and clear images, respectively. σIdeIgt is the covariance of the defogged and clear images; and C1 and C2 are constants. Correspondingly, the SSIM loss can be expressed as: (9)LS=1−SSIM(Ide,Igt)

For hazy images with ground truth, we use the reference image as the ground truth, and the defogging effect can be quantitatively assessed by calculating the statistical values of the image before and after defogging. The metrics mean square error (PSNR) and structural similarity index (SSIM) are employed. PSNR, which stands for peak signal-to-noise ratio, indicates the quality of the images. The higher the PSNR value, the lower the distortion between the two images and the higher the quality. SSIM, or structural similarity index, measures how similar the two images are; the closer SSIM is to 1, the more similar the images are in terms of structure.

For hazy images without ground truth, we introduce BRISQUE (Blind/Referenceless Image Spatial Quality Evaluator) [123], NIQE (Natural Image Quality Evaluator) [124], and PIQE (Perception-based Image Quality Evaluator) [125] as performance evaluation metrics. BRISQUE is an image quality assessment metric based on the analysis of local image features. The NIQE algorithm employs features that are more sensitive to regions with higher contrast in images, without relying on any subjective assessment scores. PIQE is a perception-based image quality assessment algorithm that frames the problem of image quality evaluation as simulating human visual perception. Additionally, all three evaluation metrics exhibit the characteristic that lower values indicate better image quality.

Table 1 presents the results of a comprehensive quantitative comparison of the SateHaze1k and RICE datasets. The proposed URA-Net model demonstrates a noteworthy improvement over other mainstream state-of-the-art methods listed in the table. The performance gains are particularly evident across various metrics. Notably, URA-Net outperforms the second-place method by a margin of 0.1 in terms of SSIM on the dense haze dataset, showcasing a substantial advantage over CNN-based methods. On the RICE dataset, URA-Net exhibits a remarkable improvement, surpassing GCA-Net by more than 2.0 and 8.5 dB over SRD. This compelling performance differential underscores the efficiency and accuracy of our proposed method in handling diverse types of haze distributions. The results affirm URA-Net’s robustness and effectiveness in comparison to contemporary approaches.

In Table 1, quantitative evaluations on the benchmark dehazing datasets. Red texts and blue texts indicate the best and the second-best performance, respectively. ↑ and ↓ mean the better methods should achieve higher/lower scores of this metric.

Table 2 presents the results of a comprehensive quantitative comparison on the Real-World dataset. Red texts and blue texts indicate the best and the second-best performance respectively. For quantitative comparison, three well-known no-reference (BRISQUE, NIQE and PIQE) image quality assessment indicators are adopted for evaluations. All these metrics are evaluated on 350 real-world hazy images selected from the Goole and public datasets. The BRISQUE, NIQE, and PIQE metrics are used to assess the overall quality of the restored images, with lower values indicating better results. As observed, URA-Net achieves two first and third places in these three indicators, respectively, showing that the haze-free images restored by our method are of high quality.

Figs. 7–10 depict the denoising outcomes obtained from RICE-1 and SateHaze1k images, respectively, following resizing to a 512 × 512 dimension to enhance detail visibility. While DCP and Aod-Net effectively eliminate the translucent cloud layer, they concurrently induce a perceptible darkening across the resultant images. Although GCA-Net exhibits improved fidelity in restoring original colors, its efficacy in deblurring remains wanting, particularly discernible in scenarios where denoising performance falls short. In contrast, OTM-AAL showcases superior deblurring capabilities, albeit at the expense of noticeable image distortion, overexposure in bright regions, and inadequate de-fogging performance. HALP demonstrates enhanced image clarity; however, it comes at the cost of conspicuous exposure effects.

The proposed URA-Net method addresses these inherent shortcomings by assimilating DCP’s superior deblurring capabilities while ameliorating the issue of darkened imagery. URA-Net further enhances cloud shadow and dark area details, resulting in a more lucid depiction. In comparison, our algorithm surpasses existing methodologies by furnishing images endowed with sharper structures and details closely approximating ground truth. The perceptual evaluation of results underscores the superior performance and enriched visualization achieved by our proposed URA-Net method.

We qualitatively evaluate URA-Net with other dehazing approaches on several real-world hazy images from the Goole-net. Fig. 11 exhibits 4 real-world hazy samples and the corresponding restored results by different dehazing algorithms. As can be seen from the figure, DCP suffers from color distortion (e.g., sky component), which leads to inaccurate color reconstruction. For HALP, AOD, and GCA, the details of objects are relatively blurred in real foggy conditions, probably because these methods do not accurately estimate the fog component when dealing with complex real scenes. OTM-AAL and SRD produce bright effects but have poor and limited de-fogging capabilities. Our method generates better perceptual results in terms of brightness, colorfulness, and haze residue compared to other methods.