Remote Sensing Image Dehazing via Dual-View Knowledge Transfer

Abstract

Remote-sensing image dehazing (RSID) is crucial for applications such as military surveillance and disaster assessment. However, current methods often rely on complex network architectures, compromising computational efficiency and scalability. Furthermore, the scarcity of annotated remote-sensing-dehazing datasets hinders model development. To address these issues, a Dual-View Knowledge Transfer (DVKT) framework is proposed to generate a lightweight and efficient student network by distilling knowledge from a pre-trained teacher network on natural image dehazing datasets. The DVKT framework includes two novel knowledge-transfer modules: Intra-layer Transfer (Intra-KT) and Inter-layer Knowledge Transfer (Inter-KT) modules. Specifically, the Intra-KT module is designed to correct the learning bias of the student network by distilling and transferring knowledge from a well-trained teacher network. The Inter-KT module is devised to distill and transfer knowledge about cross-layer correlations. This enables the student network to learn hierarchical and cross-layer dehazing knowledge from the teacher network, thereby extracting compact and effective features. Evaluation results on benchmark datasets demonstrate that the proposed DVKT framework achieves superior performance for RSID. In particular, the distilled model achieves a significant speedup with less than 6% of the parameters and computational cost of the original model, while maintaining a state-of-the-art dehazing performance.

1. Introduction

Remote-sensing image dehazing (RSID), as a critical technique in remote-sensing image processing, aims to eliminate the blurring and degradation caused by atmospheric media [1]. With the widespread application of remote-sensing technology in meteorological monitoring, environmental assessment, and other fields, clear remote-sensing images are crucial for the accuracy and timeliness of information extraction. RSID technology not only enhances image quality but also plays a key role in meteorological monitoring [2], disaster response [3], and military surveillance [4].

In recent years, image-dehazing techniques have been extensively studied, and many dehazing methods have been proposed [5,6]. Currently, these dehazing methods can be categorized into two types [7]: prior-based dehazing methods and learning-based dehazing methods. Prior-based dehazing methods relies on manually extracting statistical differences between haze-degraded images and clear images to establish empirical priors [8,9,10]. The most classical prior-based image-dehazing methods recover the clear image based on the atmospheric scattering model (ASM). For instance, He et al. [11] raised the dark channel prior (DCP) method to estimate the transmission map for image dehazing. To reduce the model complexity, He et al. [12] proposed a guided filtering method for image dehazing subsequently. In addition, Zhu et al. [13] proposed the color attenuation prior (CAP) method to recover depth information so as to conduct image dehazing. Fattal [14] noticed that RGB values follow a color line prior (CLP) within each local patch in an image, and estimated the transmission map based on CLP. Although these prior-based methods are easy to implement, they rely on scene-specific prior assumptions, and when these assumptions are not met, the dehazing results may be unsatisfactory [15].

With the advancement of deep learning, learning-based dehazing methods have been widely explored [16,17,18], which mainly include atmospheric scattering model (ASM)-learning methods and end-to-end learning methods. ASM-learning methods achieve image dehazing by designing suitable deep neural networks to estimate the haze parameters in the ASM. For example, Chi et al. [19] incorporated prior knowledge into a gradient-guided Swin Transformer [20] for haze parameter estimation. To avoid explicitly collecting paired training data, Shyam and Yoo [21] proposed an adversarial auto-augmentation approach by combining extended atmospheric scattering model. End-to-end learning methods achieve effective image dehazing by directly learning the underlying mapping relationship between haze-degraded images and clear images [22]. For example, Qin et al. [23] developed a feature fusion attention network, named FFA-Net, for end-to-end image dehazing. Guo et al. [24] proposed a feature modulation module for effectively integrating Transformer and CNN features. Despite the notable achievements of current learning-based approaches, most of them are designed for dehazing natural scenes [25,26]. Compared to images in natural scenes, remote-sensing images are typically larger, more complex, and exhibit variable and irregular haze intensity distributions. Therefore, the application of existing end-to-end dehazing methods for haze-degraded remote-sensing images may not be ideal [27].

Recently, researchers have explored numerous methods specifically tailored for RSID [28], achieving significant results. For example, Li and Chen [29] designed a two-stage coarse-to-fine dehazing network FCTF-Net for gradually refining dehazing result. Song et al. [30] introduced a detail-compensated split attention to capture global and local regional dependencies for RSID. Zhang and Wang [31] proposed a dynamic collaborative reasoning learning framework for RSID. Zhang et al. [32] developed a frequency-oriented FOTformer for recovering haze-free images. Zheng et al. [33] achieved unsupervised RSID by introducing an enhanced attention-guided GAN network. Yu et al. [34] designed a hierarchical sliced interactive multi-layer collaborative decoding network (HSMD-Net) to achieve image restoration by realizing cross-layer global and local information interaction. In general, most state-of-the-art methods employ heavy backbone networks (e.g., Transformer models [28]) to obtain better performance. However, due to the demanding computational cost and slow running speed, these models are highly inefficient. Therefore, a fundamental question is how to obtain efficient RSID models rather than relying on heavy backbone networks. Furthermore, in comparison to dehazing tasks within natural scenes, there exists a significant scarcity of RSID datasets that incorporate unambiguously labeled images, resulting in suboptimal performance. Although a large number of lightweight techniques, such as quantization [35] and pruning [36], have been explored, there is still no good way to solve the problem of scarcity of RSID datasets. Fortunately, the emergence of knowledge distillation technology provides an alternative for addressing these issues.

As a result, this study proposes a Dual-View Knowledge Transfer (DVKT) framework for simultaneously distilling hierarchical features and cross-layer correlation knowledge. The framework encompasses two innovative modules: Intra-layer Knowledge Transfer (Intra-KT) and Inter-layer Knowledge Transfer (Inter-KT). Specifically, the Intra-KT module leverages representative features extracted from a well-trained teacher network to sequentially guide the corresponding features of the student network. This mechanism progressively corrects the learning bias of the student, enabling its features to exhibit similar visual and semantic patterns to those of the teacher. In contrast, the Inter-KT module calculates the relationships between features of the teacher network layer-by-layer and utilizes this knowledge to aid the student network in modulating its hierarchical features, thereby enabling the student to learn the solution process of the teacher. Based on the proposed DVKT framework, the distilled student network can effectively acquire compact and knowledge-rich features, resulting in high-quality haze-free remote-sensing images. With less than 6% of the parameters of the teacher model, the distilled model achieves nearly an 8-fold speedup while maintaining competitive dehazing performance.

In summary, the main contributions and novelty of this work are three-fold:

• A Dual-View Knowledge Transfer (DVKT) framework is proposed for effective RSID: to the extent of our knowledge, the proposed DVKT framework is the first work to concentrate on transferring shared knowledge from natural scene dehazing models to RSID models and learning remote-sensing scene-specific knowledge for lightweight models.
• Two complementary knowledge transfer modules, Intra-KT and Inter-KT, are integrated to comprehensively transfer the structured knowledge from well-trained natural scene-dehazing models to lightweight RSID models.
• Extensive experiments on benchmark datasets demonstrate the effectiveness of the proposed DVKT framework. In particular, the proposed DVKT framework achieves satisfactory dehazing results while significantly improving processing speed.

2. Materials and Methods

This study proposes a Dual-View Knowledge Transfer (DVKT) framework to address the efficiency and limited labeled data issues in RSID. As depicted in Figure 1, the framework aims to effectively transfer hierarchical and cross-layer knowledge from a well-trained teacher network to a student network based on multiple Intra-KT and Inter-KT modules. The teacher network in the proposed DVKT framework adopts our earlier SCSNet [37]. Differently, the SCSNet used in this study is pre-trained on the natural-scene-dehazing dataset RESIDE [38], instead of limited labeled remote-sensing images. The student network is 1/n-SCSNet, where the number of channels in its convolutional layers (except the last layer) is 1/n of the teacher network. Compared to the complex SCSNet, the 1/n-SCSNet model has only 1/n² of the parameters and computational cost of SCSNet, but its performance degrades slightly.

2.1. Feature Extraction

It is typical for teacher networks to be pre-trained on standard benchmark datasets, and the knowledge they have acquired can be represented explicitly as parameters or implicitly embedded in features. Building on previous research [39], knowledge transfer is conducted at the feature level, using the features of a pre-trained teacher network to guide the learning of a student network’s features hierarchically.

As illustrated in Figure 1, any given hazy image $\mathbf{I}$ is simultaneously fed into SCSNet and 1/n-SCSNet for feature learning. For the sake of simplicity, the features produced by the i-th block of SCSNet are uniformly represented as ${\mathbf{t}}_i$, while the features of the corresponding layer in 1/n-SCSNet are denoted as ${\mathbf{s}}_i$. Note that ${\mathbf{t}}_i$ and ${\mathbf{s}}_i$ have the same resolution, but the number of channels of ${\mathbf{s}}_i$ is 1/n of that of ${\mathbf{t}}_i$. To reduce the computational cost during training, only some representative features are distilled:

$$\mathbf{T}=\left\{{\mathbf{t}}_1,{\mathbf{t}}_2,\cdots ,{\mathbf{t}}_8\right\},$$

(1)

$$\mathbf{S}=\left\{{\mathbf{s}}_1,{\mathbf{s}}_2,\cdots ,{\mathbf{s}}_8\right\},$$

(2)

where $\mathbf{T}$ and $\mathbf{S}$ represent the feature sets to be distilled from SCSNet and 1/n-SCSNet, respectively.

2.2. Intra-Layer Knowledge Transfer

As discussed in the previous section, the learned features ${\mathbf{t}}_i$ implicitly inherently encompass the knowledge acquired by SCSNet. To enhance the efficiency of the student network 1/n-SCSNet, a simple yet powerful Intra-KT module is designed, which enables the sequential transfer of hierarchical knowledge from SCSNet to 1/n-SCSNet. Specifically, ${\mathbf{s}}_i$ is responsible for learning the semantic patterns of ${\mathbf{t}}_i$ and optimizing the parameters of 1/n-SCSNet by enhancing their distributional similarity.

Concretely, the Intra-KT module consists of two steps: channel reduction and knowledge transfer. Since the number of channels of features ${\mathbf{s}}_i$ and ${\mathbf{t}}_i$ is different, it is not suitable to directly calculate their similarity. To address this issue, a set of embedded features $\mathbf{E}=\left\{{\mathbf{e}}_1,{\mathbf{e}}_2,\cdots ,{\mathbf{e}}_8\right\}$ is generated by inputting each feature ${\mathbf{s}}_i$ into a 1 × 1 convolutional layer for channel reduction, which can be expressed as follows:

$${\mathbf{e}}_i={\mathbf{s}}_i\ast {\mathbf{k}}_{1\times 1},$$

(3)

where ${\mathbf{k}}_{1\times 1}$ denotes the to-be-learned parameters in the 1 × 1 convolutional layer. The output ${\mathbf{e}}_i$ is the embedded feature of ${\mathbf{s}}_i$, and it has the same channel number with ${\mathbf{t}}_i$.

The second step entails a similarity calculation and knowledge transfer. Given that the Euclidean distance is excessively strict and may result in mere rote memorization, a relatively relaxed metric, cosine similarity, is employed to quantify the similarity between two features. In particular, the similarity between ${\mathbf{t}}_i$ and ${\mathbf{e}}_i$ at position $\left(x,y\right)$ is calculated as follows:

$${\mathbf{s}\mathbf{i}\mathbf{m}}_i\left(x,y\right)=\mathrm{c}\mathrm{o}\mathrm{s}\left({\mathbf{t}}_i\left(x,y\right),{\mathbf{e}}_i\left(x,y\right)\right)={\sum }_{c=1}^C{\displaystyle \frac{{\mathbf{t}}_i\left(x,y,c\right)·\mathbf{e}\left(x,y,c\right)}{\left|{\mathbf{t}}_i\left(x,y\right)\right|·\left|{\mathbf{e}}_i\left(x,y\right)\right|}},$$

(4)

where $C$ denotes the channel number ${\mathbf{t}}_i$, and ${\mathbf{t}}_i\left(x,y,c\right)$ indicates the response value at position $\left(x,y\right)$ of the c-th channel in ${\mathbf{t}}_i$. $\left|·\right|$ denotes the length of a vector. Therefore,

$${\mathbf{L}}_{\mathrm{i}\mathrm{n}\mathrm{t}\mathrm{r}\mathrm{a}}={\sum }_{x=1}^{H_i}{\sum }_{y=1}^{W_i}{\mathbf{1}-\mathbf{s}\mathbf{i}\mathbf{m}}_i\left(x,y\right),$$

(5)

where $H_i$ and $W_i$ denote the spatial size of ${\mathbf{t}}_i$. By minimizing this loss, the parameters in 1/n-SCSNet can be effectively optimized. In comparison to computationally expensive pair-wise distillation that can only be performed on low-resolution high-level features, our Intra-KT is more efficient to transfer implicit knowledge embedded in each layer.

2.3. Inter-Layer Knowledge Transfer

To regularize the student network learning flow of the solution process (FSP) of the teacher network, an Inter-KT module is designed. This module calculates the pair-wise feature relationship within the teacher network layer by layer to regulate features from the student network. A detailed description of the Inter-KT module is as follows:

The Inter-KT module evaluates the feature interdependencies between pairs within the teacher network on a layer-by-layer basis, aiming to govern both the prolonged and immediate development of feature attributes in the student network. Below is an elaborative explanation of the Inter-KT module’s functionality.

Firstly, the FSP matrices need to be generated layer by layer. For any two general features ${\mathbf{X}}_1$ and ${\mathbf{X}}_2$, their FSP matrix $\mathrm{F}\left({\mathbf{X}}_1,{\mathbf{X}}_2\right)\in {\mathbb{R}}^{m\times n}$ can be calculated through channel-wise inner product:

$$\mathrm{F}\left({\mathbf{X}}_1,{\mathbf{X}}_2\right)={\sum }_{x=1}^h{\sum }_{y=1}^w{\displaystyle \frac{{\mathbf{X}}_1\left(x,y\right)·{\mathbf{X}}_2\left(x,y\right)}{h·w}},$$

(6)

It is worth noting that the FSP matrix is computed on features with the same resolution. However, the features in $\mathbf{T}$ have different resolutions. To address this issue, the resolution of all features in $\mathbf{T}$ is adjusted to that of ${\mathbf{t}}_4$ through max pooling so as to simultaneously reduce the computational cost. The adjusted features of ${\mathbf{t}}_i$ are denoted as $\mathrm{R}\left({\mathbf{t}}_i\right)$. Similarly, corresponding resolution adjustment is applied to features in feature set $\mathbf{E}$, so as to align them with the resolution of ${\mathbf{t}}_i$.

In this study, the FSP matrices of adjacent features are calculated in order to grasp the evolution of features. In particular, an FSP matrix $\mathrm{F}\left(\mathrm{R}\left({\mathbf{t}}_i\right),\mathrm{R}\left({\mathbf{t}}_{i+1}\right)\right)$ is generated for $\left({\mathbf{t}}_i,{\mathbf{t}}_{i+1}\right)$ in the teacher network. Similarly, the FSP matrix $\mathrm{F}\left(\mathrm{R}\left({\mathbf{e}}_i\right),\mathrm{R}\left({\mathbf{e}}_{i+1}\right)\right)$ is also calculated for $\left({\mathbf{e}}_i,{\mathbf{e}}_{i+1}\right)$ of in the student network. Finally, the computation of the loss function for Inter-RT can be carried out using the following:

$${\mathbf{L}}_{\mathrm{i}\mathrm{n}\mathrm{t}\mathrm{e}\mathrm{r}}={\sum }_{i=1}^7{‖\mathrm{F}\left(\mathrm{R}\left({\mathbf{t}}_i\right),\mathrm{R}\left({\mathbf{t}}_{i+1}\right)\right)-\mathrm{F}\left(\mathrm{R}\left({\mathbf{e}}_i\right),\mathrm{R}\left({\mathbf{e}}_{i+1}\right)\right)‖}^2,$$

(7)

By reducing the gap among these FSP matrices, the knowledge in the teacher network SCSNet can be effectively transferred into the student network 1/n-SCSNet.

2.4. Loss Function

At the output level, the smooth ${\mathbf{L}}_1$ loss is employed to train the proposed DVKT framework. The smooth ${\mathbf{L}}_1$ loss guarantees proximity between the reconstructed haze-free image and the ground truth, demonstrating superior performance over ${\mathbf{L}}_2$ loss and the traditional ${\mathbf{L}}_1$ loss in numerous low-level visual tasks. Let $\mathbf{I}$ denote the input haze-degraded image, ${\mathbf{O}}_{\mathrm{t}}$ denote the reconstructed haze-free image obtained by the teacher network, ${\mathbf{O}}_{\mathrm{s}}$ denote the reconstructed haze-free image obtained by the student network, and ${\mathbf{I}}_{\mathrm{g}\mathrm{t}}$ denote the ground truth clear image. The formula for the smooth ${\mathbf{L}}_1$ loss can be articulated as follows:

$${\mathbf{L}}_{\mathrm{S}\mathrm{L}1}={\displaystyle \frac{1}{K}}{\sum }_{k=1}^K{\sum }_{l=1}^3{\mathrm{s}\mathrm{m}\mathrm{o}\mathrm{o}\mathrm{t}\mathrm{h}}_{L1}\left({\mathbf{O}}_{\mathrm{s}}^{\mathrm{l}}\left(k\right)-{\mathbf{I}}_{\mathrm{g}\mathrm{t}}^{\mathrm{l}}\left(k\right)\right)+{\displaystyle \frac{1}{K}}{\sum }_{k=1}^K{\sum }_{l=1}^3{\mathrm{s}\mathrm{m}\mathrm{o}\mathrm{o}\mathrm{t}\mathrm{h}}_{L1}\left({\mathbf{O}}_{\mathrm{s}}^{\mathrm{l}}\left(k\right)-{\mathbf{O}}_{\mathrm{t}}^{\mathrm{l}}\left(k\right)\right),$$

(8)

where

$${\mathrm{s}\mathrm{m}\mathrm{o}\mathrm{o}\mathrm{t}\mathrm{h}}_{L1}\left(r\right)=\left\{\begin{array}{cc}0.5r^2,& if\left|r\right|<1\\ \left|r\right|-0.5,& \mathrm{o}\mathrm{t}\mathrm{h}\mathrm{e}\mathrm{r}\mathrm{w}\mathrm{i}\mathrm{s}\mathrm{e}\end{array}\right.,$$

(9)

where $K$ is the total number of pixels within the image, and l denotes the l-th color channel.

Ultimately, the optimization of parameters within the 1/n-SCSNet is achieved through the minimization of the overall loss function:

$${\mathbf{L}}_{\mathrm{t}\mathrm{o}\mathrm{t}\mathrm{a}\mathrm{l}}={{\lambda }_1·\mathbf{L}}_{\mathrm{i}\mathrm{n}\mathrm{t}\mathrm{r}\mathrm{a}}+{\lambda }_2·{\mathbf{L}}_{\mathrm{i}\mathrm{n}\mathrm{t}\mathrm{e}\mathrm{r}}+{{\lambda }_3·\mathbf{L}}_{\mathrm{S}\mathrm{L}1},$$

(10)

where ${\lambda }_1$, ${\lambda }_2$, and ${\lambda }_3$ represent the respective weights assigned to the various loss components.

3. Results and Discussion

To illustrate the efficacy of the proposed DVKT framework, four public datasets are applied for evaluation. Furthermore, the experimental setup, comparison with the state of the art, and some ablation studies are given successively.

3.1. Datasets

Extensive experiments were conducted on four public remote-sensing-image-dehazing datasets: SateHaze1k [40], RS-Haze [28], RSID [19], RRSD300 [41].

• SateHaze1k: The SateHaze1k dataset [40] consists of 1200 image pairs, divided into three sub-datasets with different haze densities. The SateHaze1k-thin sub-dataset contains images with thin haze, the SateHaze1k-moderate sub-dataset contains images with moderate haze, and the SateHaze1k-thick sub-dataset contains images with thick haze. The images in each sub-dataset are split among three categories: 320 for training, 35 for validation, and 45 for testing.
• RS-Haze: The RS-Haze dataset [28] is a comprehensive and challenging dataset designed for image dehazing tasks, featuring 51,300 image pairs. Among these, 51,030 pairs are designated for training purposes, while the remaining 270 pairs are reserved for testing. It encompasses various scenarios and levels of haze density, such as urban landscapes, forests, beaches, and mountain regions.
• RSID: The RSID dataset [19] comprises 1000 image pairs, with each pair consisting of a hazy image and a corresponding haze-free image. In line with prior research [41], 900 of these pairs are randomly chosen for the training set, while the rest are utilized for testing.
• RRSD300: The RRSD300 dataset [41] comprises 300 real-world hazy images collected from DIOR dataset [42] and Microsoft Bing. This dataset is used to verify the generalization of various models.

3.2. Experimental Details and Evaluation Criteria

(1) Experimental Details: The proposed DVKT framework is implemented with PyTorch 1.13, and the experiments are conducted on a PC with NVIDIA RTX 3090 GPU (NVIDIA, Santa Clara, CA, USA). To augment the training dataset, random rotations of 90°, 180°, and 270°, as well as horizontal flipping are applied. The inputs to the DVKT framework are with the spatial size of 256 × 256. For the training process, a batch size of 32 was used, and the number of epochs was set to 20. The DVKT framework was optimized using the Adam optimizer. The initial learning rate configured at 1.0 × 10⁻⁴, with a cosine annealing strategy employed to progressively reduce it to 0. To address the high cost associated with tuning weight coefficients, a multi-task learning approach based on equal variance and uncertainty [43] was implemented to determine the optimal weight coefficients ${\lambda }_1$, ${\lambda }_2$, and ${\lambda }_3$. Empirically, the hyperparameter n in 1/n-SCSNet was set to 5.

(2) Evaluation Criteria: To assess the performance of the proposed DVKT framework, the Peak Signal-to-Noise Ratio (PSNR), the Structural Similarity Index Measure (SSIM), and the Learned Perceptual Image Patch Similarity (LPIPS) are used as quantitative metrics. Higher PSNR and SSIM or lower LPIPS values signify superior quality in the restored images. They can be expressed as follows:

$$\mathrm{P}\mathrm{S}\mathrm{N}\mathrm{R}=20·\mathrm{l}\mathrm{o}\mathrm{g}\left({\displaystyle \frac{{MAX}_I}{\sqrt{MSE}}}\right),$$

(11)

$$\mathrm{S}\mathrm{S}\mathrm{I}\mathrm{M}\left({\mathbf{I}}_{\mathrm{g}\mathrm{t}},{\mathbf{O}}_{\mathrm{s}}\right)={\displaystyle \frac{\left(2{\mu }_{gt}{\mu }_s{+c}_1\right)\left(2{\sigma }_{gts}{+c}_2\right)}{\left({{\mu }_{gt}}^2+{{\mu }_s}^2+c_1\right)\left({{\sigma }_{gt}}^2+{{\sigma }_s}^2+c_2\right)}},$$

(12)

$$\mathrm{L}\mathrm{P}\mathrm{I}\mathrm{P}\mathrm{S}\left({\mathbf{I}}_{\mathrm{g}\mathrm{t}},{\mathbf{O}}_{\mathrm{s}}\right)={\sum }_i{\displaystyle \frac{1}{H_i{W}_i}}{\sum }_{h,w}{‖w_i·\left(I_{hw}^i-O_{hw}^i\right)‖}_2^2,$$

(13)

where ${MAX}_I$ denotes the maximum pixel value of ${\mathbf{I}}_{\mathrm{g}\mathrm{t}}$, and MSE represents the mean squared error between the corresponding pixels of ${\mathbf{I}}_{\mathrm{g}\mathrm{t}}$ and the reconstructed haze-free image ${\mathbf{O}}_{\mathrm{s}}$. ${\mu }_{gt}$ and ${\mu }_s$ are the means of ${\mathbf{I}}_{\mathrm{g}\mathrm{t}}$ and ${\mathbf{O}}_{\mathrm{s}}$, respectively. ${\sigma }_{gt}$ and ${\sigma }_s$ mean the standard deviations of ${\mathbf{I}}_{\mathrm{g}\mathrm{t}}$ and ${\mathbf{O}}_{\mathrm{s}}$, respectively. ${\sigma }_{gts}$ is the covariance between ${\mathbf{I}}_{\mathrm{g}\mathrm{t}}$ and ${\mathbf{O}}_{\mathrm{s}}$. $w_i$ means the weight for each image channel. $c_1$ and $c_2$ are constants introduced to maintain stability in the computation.

Furthermore, to evaluate the model size and computational cost, Params and floating-point operations (FLOPs) are adopted:

$$\mathrm{P}\mathrm{a}\mathrm{r}\mathrm{a}\mathrm{m}\mathrm{s}=\left(K_h·K_w·C_{in}+1\right)·C_{out},$$

(14)

$$\mathrm{F}\mathrm{L}\mathrm{O}\mathrm{P}\mathrm{S}=2HW\left(K_h·K_w·C_{in}+1\right)·C_{out},$$

(15)

where $C_{in}$ represents the channel number for the input feature, $K_h$ and $K_w$ denote the kernel size, and $C_{out}$ signifies the channel number for the output feature. H and W correspond to the height and width of the feature map. In this study, the units of Params and FLOPs are millions (M) and billions (G), respectively. Furthermore, the model’s inference time, measured in seconds, is determined by averaging the processing times of 100 haze-degraded images. During the experiments, all comparative methods utilize input images with a spatial dimension of 256 × 256.

3.3. Comparison with Other Image Dehazing Methods

This section reports comprehensive quantitative and qualitative comparisons against state-of-the-art methods on the adopted datasets. The compared methods are categorized into two primary groups: (1) those developed for natural image dehazing, encompassing techniques like DCP [11], CEP [44], SLP [45], AOD-Net [46], MOF [47], FFA-Net [23], Light-DehazeNet [48], Restormer [49], DehazeFormer [28], and Trinity-Net [19]; and (2) methods tailored specifically for dehazing remote-sensing images, such as FCTF-Net [29], DCRD-Net [50], and SCSNet [37]. To guarantee a fair assessment, the officially released code for each method was utilized, and a consistent data division strategy was applied during training.

3.3.1. Quantitative Evaluations

(1) Performance Comparison: The quantitative comparison results on the SateHaze1k dataset are summarized in

Table 1. Qualitative comparison results on the SateHaze1k dataset.

Methods	Thin Haze			Moderate Haze			Thick Haze			Mixed Haze
	PSNR	SSIM	LPIPS	PSNR	SSIM	LPIPS	PSNR	SSIM	LPIPS	PSNR	SSIM	LPIPS
DCP [11]	19.1183	0.8518	0.1451	19.8384	0.8812	0.1198	16.7930	0.7701	0.2103	18.5833	0.8344	0.1602
CEP [44]	13.5997	0.7222	0.3201	14.2122	0.7270	0.2294	16.0824	0.7762	0.2097	14.6950	0.7512	0.2703
MOF [47]	15.3891	0.7291	0.3002	14.7418	0.6256	0.3301	16.2495	0.6767	0.3303	15.5146	0.6859	0.3108
AOD-Net [46]	19.0548	0.7777	0.1903	19.4211	0.7015	0.2401	16.4672	0.7123	0.2702	17.4859	0.6332	0.3382
Light-DehazeNet [48]	18.4868	0.8658	0.1299	18.3918	0.8825	0.1002	16.7662	0.7697	0.2253	17.8132	0.8352	0.1499
FFA-Net [23]	20.1410	0.8582	0.1149	22.5586	0.9132	0.0657	19.1255	0.7976	0.1992	21.2873	0.8663	0.0998
Restormer [49]	20.9829	0.8686	0.1049	23.1574	0.9036	0.0598	19.6984	0.7739	0.2137	20.7892	0.8379	0.1479
DehazeFormer [28]	21.9274	0.8843	0.0918	24.4407	0.9268	0.0579	20.2133	0.8049	0.1635	22.0066	0.8659	0.1099
SLP [45]	16.4162	0.7428	0.2762	18.6182	0.7830	0.1837	16.5071	0.7659	0.2250	17.2483	0.7706	0.1852
Trinity-Net [19]	19.3708	0.7816	0.1761	19.6918	0.7062	0.2252	17.1281	0.7723	0.2116	17.6508	0.7864	0.1940
DCRD-Net [50]	20.8473	0.8767	0.0978	23.3119	0.9225	0.0589	19.7250	0.8121	0.1378	21.7468	0.8812	0.0849
FCTF-Net [29]	18.3262	0.8369	0.1362	20.9057	0.8553	0.1295	17.2551	0.6922	0.2897	19.5883	0.8434	0.1498
SCSNet (Teacher Network) [37]	26.1460	0.9415	0.0583	28.3501	0.9566	0.0398	24.6542	0.9015	0.0649	25.1759	0.9223	0.0519
DVKT	24.7284	0.9183	0.0618	27.0462	0.9417	0.0579	23.3136	0.8862	0.0919	23.9271	0.9105	0.0609

The bold font highlights our proposed method.

. As indicated, traditional prior-driven dehazing methods such as DCP, CEP, MOF, and SLP exhibit lower PSNR and SSIM values, suggesting they struggle with the complexities of remote-sensing image dehazing, thus delivering subpar performance. Similarly, AOD-Net and Light-DehazeNet show rather mediocre results when applied to remote-sensing imagery, possibly due to the limitations of early lightweight neural networks in capturing the intricate mappings between hazy and clear images. Conversely, data-driven approaches like FFA-Net, Restormer, Trinity-Net, and DehazeFormer demonstrate higher PSNR and SSIM scores, highlighting their potential in enhancing remote-sensing image dehazing. Models such as DCRD-Net, FCTF-Net, and SCSNet, which are specifically crafted for remote-sensing dehazing tasks, are also included in the comparison. It can be observed that both DCRD-Net and SCSNet achieve very good dehazing performance, and SCSNet performs best among all comparison methods. In contrast, FCTF-Net performs generally, which may be due to its relatively complex network structure, while the data volume in the SateHaze1k dataset is limited, leading to model overfitting. It is worth noting that, except for the teacher network SCSNet used in this study, the proposed DVKT framework delivers a state-of-the-art dehazing performance. Additionally, our DVKT framework matches the dehazing performance of the teacher network, SCSNet, but with a reduced number of parameters and faster inference times.

Table 2. Qualitative results on the RS-Haze and RSID datasets.

Methods	RS-Haze			RSID
	PSNR	SSIM	LPIPS	PSNR	SSIM	LPIPS
DCP [11]	18.1003	0.6704	0.2801	17.3256	0.7927	0.1699
CEP [44]	15.9097	0.5772	0.3502	14.2375	0.7034	0.2192
MOF [47]	16.1608	0.5628	0.3603	12.9052	0.6485	0.2901
AOD-Net [46]	23.9677	0.7207	0.1902	18.7037	0.7424	0.1781
Light-DehazeNet [48]	25.5965	0.8209	0.1203	17.9279	0.8414	0.1099
FFA-Net [23]	29.1932	0.8846	0.0898	21.2876	0.9042	0.0749
Restormer [49]	25.6700	0.7563	0.2001	11.7240	0.5971	0.3203
DehazeFormer [28]	29.3419	0.8730	0.0798	22.6859	0.9118	0.0649
SLP [45]	17.3805	0.6527	0.2882	16.7260	0.7751	0.1735
Trinity-Net [19]	29.7082	0.8973	0.0714	23.5273	0.9207	0.0562
DCRD-Net [50]	29.6780	0.8878	0.0749	22.1643	0.8926	0.0898
FCTF-Net [29]	29.6240	0.8958	0.0698	20.2556	0.8397	0.1203
SCSNet (Teacher Network) [37]	32.2504	0.9271	0.0499	25.3821	0.9585	0.0398
DVKT	31.4227	0.9135	0.0541	24.1082	0.9426	0.0449

The bold font highlights our proposed method.

illustrates the quantitative comparison results across the RS-Haze and RSID datasets. As indicated, the proposed method demonstrates notable advantages over other compared approaches. Specifically, aside from the teacher network SCSNet utilized in this study, the DVKT framework shows superior dehazing performance. On the RS-Haze dataset, it achieves PSNR and SSIM values of 31.4227 dB and 0.9135, respectively. For the RSID dataset, the PSNR and SSIM values are 24.1082 dB and 0.9426, respectively.

(2) Efficiency Comparison: One of the core objectives of this work is to enhance the efficiency of RSID models. To substantiate the effectiveness of the proposed DVKT framework in dehazing tasks, an exhaustive comparison of inference efficiency is conducted with the existing RSID models.

Table 3. Comparison of inference efficiency on the Satehaze1k dataset.

Methods	Params	FLOPS	Time	PSNR	SSIM	LPIPS
DCP [11]	—	—	0.2604	18.5833	0.8344	0.1602
AOD-Net [46]	0.01	0.15	0.0452	17.4859	0.6332	0.2498
Light-DehazeNet [48]	0.03	1.97	0.0571	17.8132	0.8352	0.1199
FFA-Net [23]	4.45	287.53	0.4465	21.2873	0.8663	0.0898
Restormer [49]	26.13	141.17	0.3157	20.7892	0.8379	0.0749
DehazeFormer [28]	9.68	89.85	0.2438	22.0066	0.8659	0.0599
Trinity-Net [19]	9.82	90.17	0.2615	17.6508	0.7864	0.1940
DCRD-Net [50]	0.04	14.92	0.1827	21.7468	0.8812	0.0549
FCTF-Net [29]	0.16	10.04	0.1574	19.5883	0.8434	0.1098
SCSNet (Teacher Network) [37]	1.53	10.79	0.1713	25.1759	0.9223	0.0419
DVKT	0.06	0.44	0.0225	23.9271	0.9105	0.0509

The bold font highlights our proposed method.

details the model sizes and inference efficiencies of various models. Concretely, it lists the model parameters (Params), FLOPs, and the average time required to process 100 haze-degraded images (inference time). As observed, while FFA-Net, Restormer, Trinity-Net, and DehazeFormer deliver superior dehazing outcomes, they come with larger Params and FLOPs, which can constrain their practical deployment. On the other hand, AOD-Net and Light-DehazeNet boast smaller parameter sizes, albeit at the expense of considerable performance loss. When compared to FCTF-Net and DCRD-Net, both designed specifically for RSID, the proposed DVKT framework exhibits the lowest computational cost and inference time, underscoring its advantage. Notably, the proposed DVKT framework achieves almost identical PSNR and SSIM values to the teacher model SCSNet but with reduced computational requirements and faster inference times.

3.3.2. Qualitative Evaluations

Figure 2 showcases the qualitative results of various methods applied to the SateHaze1k-thin dataset. The dehazed images from DCP and FCTF-Net display noticeable color distortions. A significant amount of haze persists in the images processed by AOD-Net and Light-DehazeNet. Methods such as FCTF-Net and Light-DehazeNet achieve some level of dehazing; however, compared to the ground truth images, there is still a minor presence of haze in the restored images. Similarly, DehazeFormer, SLP, Trinity-Net, and DCRD-Net manage to remove some haze, but the overall restoration still leaves a slight haze residue compared to the ground truth. The dehazed images produced by the teacher model SCSNet and our DVKT framework are more closely aligned with the ground truth images, achieving a higher level of detail recovery. It is important to note that our DVKT framework boasts a smaller model size and higher inference efficiency.

Figure 3 displays the visual results of multiple methods on the SateHaze1k-moderate test set. Under moderate haze conditions, crucial information in remote sensing images can become obscured. Apart from SCSNet and the proposed DVKT framework, other dehazing methods result in images with some residual haze. DCP, AOD-Net, SLP, and Light-DehazeNet show significant color distortion. While DCRD-Net and Trinity-Net achieve a certain level of dehazing, there remain noticeable differences when compared to the ground truth image. In contrast, both the teacher model SCSNet and the proposed DVKT framework produce visually more pleasing results, with enhanced color fidelity and better preservation of texture details.

Figure 4 illustrates the qualitative results of different methods when applied to the SateHaze1k-thick test set. This particular set includes remote-sensing images heavily affected by dense haze, causing a significant loss of texture detail information. Methods such as DCP, AOD-Net, Light-DehazeNet, SLP, and FCTF-Net show evident color distortions. Although DehazeFormer, Trinity-Net, and DCRD-Net achieve good dehazing effects, the texture details in the images produced by these methods do not match the ground truth images as closely. In contrast, both the teacher model SCSNet and the proposed DVKT framework effectively preserve the overall structure, local details, and color accuracy of the ground truth images, resulting in visually pleasing and realistic dehazed images.

Figure 5 showcases the visual results of various methods on the RS-Haze test set. While several methods demonstrate varying degrees of success, some exhibit notable shortcomings. For instance, SLP- and DCP-restored images often suffer from color distortion and residual haze. AOD-Net, DehazeFormer, Trinity-Net, DCRD-Net, and FCTF-Net frequently over-dehaze, leading to a loss of fine details. Light-DehazeNet, on the other hand, struggles with color distortion and detail preservation. In contrast, both SCSNet and the proposed DVKT framework effectively restore texture details and enhance image quality, aligning more closely with the ground truth.

Figure 6 presents the visual comparison of various methods on the RSID test set. Obviously, SLP and DCP-restored images suffer from severe color distortion. The images restored by AOD-Net and Light-DehazeNet suffer from a significant loss of texture details and exhibit notable color distortions. DehazeFormer, Trinity-Net, DCRD-Net, and FCTF-Net can avoid color distortions to some extent, but the generated images still have some haze that cannot be removed. In contrast, both SCSNet and the proposed DVKT framework effectively preserve color fidelity and texture details, producing visually superior results.

To further demonstrate the generalization capability of the proposed method, we conducted performance verification on the RRSD300 dataset. Since the RRSD300 dataset only contains real-world hazy images without corresponding ground truth images, all models are trained on SateHaze1k dataset and trained on the RRSD300 dataset. The visualization results are shown in Figure 7. It can be observed that the dehazing results obtained by DCP and SLP exhibit significant color distortion. AOD-Net and DCRD-Net introduce some artifacts, resulting in poorer dehazing outcomes. Light-DehazeNet’s dehazing results lose considerable detail information. Although FCTF-Net is a dehazing method tailored for remote-sensing images, it also suffers from color distortion. In contrast, the adopted teacher network SCSNet and the proposed DVKT framework achieve better dehazing results, indicating the good generalization and practicality of the proposed DVKT framework method.

3.4. Ablation Study

This study focuses on RSID and optimizes the dehazing model by reducing the number of channels in each layer. Typically, for models with the same network architecture, their size and computational cost are positively correlated with dehazing performance. To investigate this further, a study was conducted to evaluate the impact of different Channel Preservation Rates (CPRs) on the dehazing performance of the model. As shown in

Table 4. Ablation study about channel preservation rates (CPR) on SateHaze1k dataset.

CPR	Params	FLOPS	PSNR	SSIM	LPIPS
1	1.53	10.79	25.1759	0.9223	0.0386
1/2	0.39	2.71	24.6717	0.9184	0.0407
1/3	0.18	1.20	24.3804	0.9162	0.0424
1/4	0.10	0.68	24.1163	0.9140	0.0441
1/5	0.06	0.44	23.9271	0.9105	0.0509

, a detailed performance comparison of dehazing models trained with different CPRs was presented. The original teacher model has 1.53 M Params. For further optimization, the experiments were conducted by compressing the model using CPRs of 1/2, 1/3, 1/4, and 1/5. Significant degradation in dehazing performance is not observed when the parameter count is decreased to 0.06 M. Specifically, when CPR was set to 1/5, the PSNR and SSIM reached 23.9271 and 0.9105, respectively, which were nearly comparable to those of the original model (25.1759 and 0.9223). At this time, the Params and FLOPs of the student model are 0.06 M and 0.44 G, respectively, which is a significant optimization compared to the 1.53 M parameters and 10.79 GFLOPs of the teacher model. Overall, our method demonstrates a strong knowledge distillation capability in the field of dehazing and can generate an efficient model that is easy to deploy and apply on edge computing devices and smart terminals.

Additionally, ablation experiments were conducted to evaluate the effects of different knowledge transfer settings, and the results are presented in

Table 5. Ablation study about different transfer settings on SateHaze1k dataset.

Transfer Settings	PSNR	SSIM	LPIPS
W/T Transfer	19.8206	0.8625	0.1357
Only Intra-KT	22.3718	0.9051	0.0521
Only Inter-KT	21.5281	0.8937	0.0768
Intra-KT + Inter-KT	23.9271	0.9105	0.0509

. When no transfer strategy was employed and 1/5-SCSNet was trained directly, the performance was moderate. The incorporation of the Intra-KT strategy led to a significant enhancement in model performance, with PSNR and SSIM metrics increasing to 22.3718 dB and 0.9051, respectively. This indicates that intra-layer knowledge transfer can effectively transfer knowledge from the teacher network to the student network. When only the Inter-KT transfer strategy was used, the model’s PSNR, SSIM, and LPIPS metrics were 21.5281 dB, 0.8937, and 0.0768, respectively. Compared to the results without any transfer strategy, this also showed substantial improvement, suggesting that the proposed Inter-KT transfer module can effectively transfer cross-layer knowledge from the teacher network to the student network. The optimal dehazing performance was achieved when both Intra-KT and Inter-KT were combined. This is because the two proposed transfer modules facilitate knowledge transfer from complementary perspectives, demonstrating the superiority of the proposed approach.

3.5. Discussion

In this study, we have presented a comprehensive evaluation of the proposed Dual-View Knowledge Transfer (DVKT) framework for RSID. Our results demonstrate the efficacy of the DVKT approach in improving both the performance and efficiency of RSID models.

Firstly, the quantitative and qualitative evaluations on benchmark datasets (SateHaze1k, RS-Haze, and RSID) confirm that the DVKT framework almost achieves a state-of-the-art dehazing performance, comparable to heavy backbone models like SCSNet, while requiring significantly fewer parameters and computational resources. This highlights the effectiveness of our knowledge distillation approach in transferring structured knowledge from a well-trained teacher network to a lightweight student network.

Secondly, the ablation study investigating the impact of different channel preservation rates further validates the robustness of our framework. By progressively reducing the number of channels, we show that the DVKT framework can maintain high dehazing quality even with extremely compressed models. This finding underscores the practicality of our method for deployment on edge devices and mobile platforms with limited computational resources.

Finally, the proposed DVKT framework addresses two critical issues in remote-sensing image dehazing: lack of labeled data and high computational costs. By leveraging the abundance of natural-image-dehazing datasets and transferring knowledge from a pre-trained teacher model, we overcome the data scarcity challenge. Additionally, the lightweight student model generated through DVKT achieves significant speedups compared to heavy backbone networks, demonstrating its potential to enable real-time dehazing for various remote-sensing applications.

4. Conclusions

In summary, this study proposes an innovative Dual-View Knowledge Transfer (DVKT) framework to tackle the challenges of efficiency and dataset scarcity in RSID. The framework includes two innovative modules: Intra-layer Knowledge Transfer (Intra-KT) and Inter-layer Knowledge Transfer (Inter-KT), which can successfully distill hierarchical features and cross-layer correlations from a pre-trained teacher network to a lightweight student network. Specifically, the Intra-KT module can correct the learning bias of the student network by the guidance of representative features from a well-trained teacher network. The Inter-KT module can extract compact and effective features for RSID by distilling and transferring knowledge about cross-layer correlations. Comprehensive evaluations confirm that the proposed DVKT framework successfully compresses RSID models, yielding dual enhancements in both dehazing performance and efficiency.

While the proposed DVKT framework exhibits promising results, it currently relies on a pre-trained teacher model trained on natural-image-dehazing datasets. This may introduce a domain gap between the teacher and student networks, limiting the optimal performance for remote-sensing images. Future work could explore domain adaptation techniques to better bridge this gap.