1. Introduction

Figure 1. The comparison between our scheme and the traditional encryption distribution method. The encrypted remote sensing image is presented in garbled code, which is easy for attackers to pay attention to. In our scheme, the remote sensing image is hidden in the ordinary image in an invisible form, which can be more effective and secure distribution. .

Figure 1. The comparison between our scheme and the traditional encryption distribution method. The encrypted remote sensing image is presented in garbled code, which is easy for attackers to pay attention to. In our scheme, the remote sensing image is hidden in the ordinary image in an invisible form, which can be more effective and secure distribution. .

2. Related Work

3. Proposed Scheme

3.1. overview

As show in Figure 1, DIH4RSID workflow can be described as follows. Firstly, Alice(RSI owner) extracts feature maps through preparing network, and then hide that into a nature image (cover) by embedding network, which outputs a stego (also called the hidden image ). The stego could transmitted through public channels to Bob (receiver) , who decoded information through extracting network to reconstruct RSI. During the embedding process, discriminating network acts as a attacker to improve the indistinguish ability between cover and stego.

Figure 2. DIH4RSID Flowchart.

Figure 2. DIH4RSID Flowchart.

The secure distribution schema for RSI based on information hiding must satisfy there properties: 1) To avoid attracting the attention of attackers, embedding process should have minimal visual impact on cover, 2)In order to enhance the practicality of the algorithm, the semantics of the extracted remote sensing images should be preserved and 3) To improve the security of the model, it is important to restrict the success rate of detecting algorithms to a minimal level. Considering above mentioned three requirements, We have adopted three unique designs based on traditional encoder-decoder network, namely the preprocessing network based on Inception structure, PAM, and semantic loss.

3.2. Preprocessing network

RSI feature large scale variations in objects, rich details, complex structures, and ambiguous distinctions between subjects and backgrounds. The model proposed by Balujia and others employs a single-scale convolutional kernel to extract the spatial distribution features of image targets, which does not sufficiently delve frequency structures and spatial characteristics. To address this issue, we integrate the Inception structure into the design of the preprocessing network, as depicted in Figure 3. The Inception structure employs three distinct sizes of convolutional kernels and one max pooling in parallel to obtain spatial features at different scale receptive fields. In the parallel branches, dimensions are firstly adjusted through a $1\times 1$ convolution, then subjected to convolution kernels of varying scales and pooling operations. Finally, the extracted multi-scale spatial features are fused through Concat operations, enhancing the network’s ability to capture a more complete description of target spatial structural features at different depth levels.

Figure 3. Preparing network architecture.

Figure 3. Preparing network architecture.

3.3. Parallel Attention Mechanism

In the realm of deep learning, the attention mechanism trains networks to concentrate on salient features while disregarding those that are irrelevant. For CNN-based information hiding schemes that directly produce stegoes, the secret information is ingrained through integration with the cover features. Given that the value of these features varies with respect to information hiding, applying an attention mechanism could enhance the system’s performance. Given that the perceptual signals of primary targets in RSI are typically concentrated in certain areas [25], spatial attention mechanisms are highly appropriate for our endeavor. They enable the model to concentrate on areas of the image that are most significant. However, calculating weights between features at all positions will bring significant computational effort. Consequently, drawing inspiration from the Coordinate Attention (CA) and Efficient Channel Attention (ECA) mechanisms, we design the PAM to effectively grasp the inter-channel relationships and extensive spatial dependencies, incorporating precise positional details. The detailed structure of PAM is shown in Figure 4.

Firstly, the horizontal average pooling, vertical average pooling, horizontal max pooling and vertical max pooling are performed for each channel of the input feature map denoted as $F(h,w,c)$ respectively, as are formulated by equations (1)-(4).

$$F_{hap}\left(h,c\right)=\frac{1}{W}{\sum }_{i=1}^{w}F\left(h,i,c\right)$$

(1)

$$F_{vap}\left(w,c\right)=\frac{1}{h}{\sum }_{i=1}^{h}F\left(i,w,c\right)$$

(2)

$$F_{hmp}\left(h,c\right)=\underset{0\le i<w}{max}F\left(h,i,c\right)$$

(3)

$$F_{vmp}\left(w,c\right)=\underset{0\le i<h}{max}F\left(i,w,c\right)$$

(4)

Subsequently, to prevent the reduction in channel dimensionality during cross-channel interactions, we employ Conv2D with a flexible kernel size. This is designed to produce attention weights across both spatial dimensions. Additionally, we incorporate two distinct types of pooling strategies. These processes collectively can be expressed as Equation (5) - (6).

$${\widehat{F}}_{AP}\left(h,w,c\right)=\mathrm{Conv}2\mathrm{D}\left(F_{vap}\times F_{hap},kernal\right)$$

(5)

$${\widehat{F}}_{MP}\left(h,w,c\right)=\mathrm{Conv}2\mathrm{D}\left(F_{hmp}\times F_{vmp},kernal\right)$$

(6)

$$kernal={\left|\frac{{\log }_2\left(c\right)}{\gamma }+\frac{b}{\gamma }\right|}_{\mathrm{odd}}$$

(7)

According to ECA, the kernal of Conv2d is computed by (7), where ${\left|\right|}_{odd}$ denotes as the nearest odd number, b and $\gamma$ are set 1 and 2.

Figure 4. Detailed structure of PAM.

Figure 4. Detailed structure of PAM.

Finally, to determine the weight of the coordinate attention, we combine the adaptive pooling feature, ${\widehat{F}}_{AP}$ and ${\widehat{F}}_{MP}$ are combined using the operation of matrix multiplication. This procedure can be mathematically represented as formula (8).

$${Weight}_{pam}\left(h,w,c\right)=\mathrm{sigmoid}\left({\widehat{F}}_{AP}+{\widehat{F}}_{MP}\right)$$

(8)

3.4. Embedding Network

We use a network structure similar to Dense Connection Architecture (DCA) as the backbone of the embedding network. There are several reasons why such architecture is suitable for DIH4RSID: (1) DCA reduces the problem of gradient disappearance by means of cross-layer connection, so that information will not be lost during transmission. This is important for DIH4RSID because remote sensing images typically have large sizes and complex backgrounds that require the network to be able to efficiently transmit and utilize feature information. (2) DCA can better utilize and enhance features in the transmission process by including the features of all previous layers in the input of each layer. This is also very beneficial for DIH4RSID, because the features of RSI are often complex, and the network needs to be able to extract and transmit these features effectively. (3) DCA combines features of previous layers to form richer description and discrimination of features. This enables the network to use the feature information more effectively, thus improving the hiding effect and extraction quality of DIH4RSID. (4) Reducing the number of parameters: DCA reduces the number of parameters in the model by reducing the number of connections, thus reducing the complexity and calculation cost of the model. This is also important for DIH4RSID because RSI is usually very large and requires low model complexity and computational cost to achieve effective classification.

To maintain stealthiness, it is crucial for the stego image to bear a close resemblance to the cover image. Moreover, to ensure the integrity of the recovered image, it should be nearly identical to the RSI. Nevertheless, the process involving various convolutional and activation layers can unavoidably lead to a loss of information from input images like cover images and RSI, which is detrimental to both hiding and revealing capabilities. To mitigate this issue, the introduction of both global and local skip connections is proposed, as are shown in Figure 5. The global skip connection facilitates the direct transmission of original image data to the uppermost layer, aiding in the enhancement of edge and texture detail synthesis, which in turn boosts both concealment and retrieval efficiency. On the other hand, the local skip connection allows for the unimpeded flow of RSI within the embedding network, ensuring that its details and semantic content are effectively incorporated into the stego. This incorporation aids the follow-up extraction network in precisely restoring the RSI. The embedding procedure is defined by a specific equation.

$$Stego=EN\left(C,PN(RSI,{\theta }_{PN}),{\theta }_{EN}\right)$$

(9)

Figure 5. Embedding network architecture.

Figure 5. Embedding network architecture.

3.5. Revealing Network

RSI extraction is an inverse process of embedding. The revealing Network (RN) adopts a structure similar to the embedded network and still extracts depth features with dense connections, hoping to recover the RSI with high accuracy. Unlike the embedding process, the revealing process does not consider the effect of RSI feature integration, so the modules of global skip connection and local skip connection used in the embedded network are not used in the RN.

$$\widehat{RSI}=RN\left(Stego,{\theta }_{RN}\right)$$

(10)

Figure 6. Detailed structure of revealing network.

Figure 6. Detailed structure of revealing network.

3.8. Training Process

When training is complete and the model is deployed to a real-world application scenario, the stego will be disseminated through public channels. In theory, a completely secure distribution system requires stegos and cover to follow the same distribution. In fact, it is difficult to achieve exactly the same distribution in practical applications, generally using some way to measure the distance between the two distributions, the smaller the distance, the better the hiding effect. Therefore, minimizing the distance between the two distributions becomes our optimization goal for generating the stego. Under the guidance of this idea, the original GAN proposed by Goodfellow et al. [28] can optimize the generated distribution on the basis of the KL divergence. Subsequent researchers are dedicated to enhancing GAN by developing appropriate network architectures and introducing novel loss functions to mitigate its numerous shortcomings. Among them, Arjovsky et al. [29] discovered that the Wasserstein distance offers benefits over both $KL$ and $JS$ distances, leading to the introduction of Wasserstein-GAN (WGAN) to achieve more stable training processes. In the original version of WGAN, the 1-Lipschitz constraint was imposed via weight clipping, but this approach had several drawbacks, such as potentially leading to gradient vanishing or exploding, as well as limiting the capacity of the model. To overcome these limitations, WGAN-GP (Wasserstein GAN with Gradient Penalty) [30] was proposed. Building on the foundation of WGAN, WGAN-GP introduces a gradient penalty to more effectively enforce the 1-Lipschitz constraint, resulting in several advantages: improved training stability, elimination of problems associated with weight clipping, enhanced sample quality during training, and simplified fine-tuning. As a result, we utilize WGAN-GP to more accurately align the generator’s output distribution, which similarly facilitates the achievement of a stable training regimen. For our task, the Wasserstein-1 distance between the cover distribution $P_{cover}$ and the stego distribution $Q_{stego}$ is denoted by the following equation(17).

$$W(P_{cover},Q_{stego})=\underset{\gamma \in \Pi (P_{cover},Q_{stego})}{inf}{\int }_{\mathcal{X}\times \mathcal{Y}}\parallel x-y\parallel d\gamma (x,y).$$

(17)

Algorithm 1: Training DIH4RSID. We use default values of $\lambda =10,n_{\mathrm{DN}}=5,\alpha =$$0.0001,{\beta }_1=0,{\beta }_2=0.9.$

In equation (17), $W(P_{cover},Q_{stego})$ represents the Wasserstein-1 distance between probability distributions of Cover and Stego. $\Pi (P_{cover}$, $Q_{stego}$) represents the collection of all combined distributions $\gamma$ that transport $P_{cover}$ to $Q_{stego}$, where each $\gamma$ must satisfy the marginal distributions to be consistent with $P_{cover}$ and $Q_{stego}$. $\parallel x-y\parallel$ represents the Euclidean distance between two points $x\in Cover$ and $y\in Stego$ in space, and the integral calculates the expected cost of moving from x to y over all possible transport plans $\gamma$. Based on the aforementioned principles, our training process is outlined in Algorithm 1. The $(PN,EN,RN)$ and $DN$ are trained alternately until the number of iterations reaches the maximum value., where $(PN,EN,RN)$ jointly learn to minimize ${\mathcal{L}}_{PN,EN,RN}$ while $DN$ aims to minimize${\mathcal{L}}_{DN}$. Note that $DN$ is iterated 5 times once $(PN,EN,RN)$ is iterated. Within this framework, the generator is capable of receiving dependable gradients that consistently enhance the embedding’s effectiveness.

4. Experiments Result and Analysis

4.2. Visual Quality Test

The main purpose of this scheme is to hide RSI through natural images to achieve efficient and secure distribution. One of the most basic requirements is that the hidden image is not visually detectable by the attack, because if the attack finds the image suspicious, it will steal stego or block the distribution channel. Therefore, the first experiment we did after the program was trained was to test the visual effects of stego. In addition, we also tested the visual quality of the RSI extracted from stego, aiming to test the hidden performance of the scheme from the perspective of visual quality. Figure 1 shows the 6 randomly selected image pairs in our experimental results, which are Cover, RSI, Stego from left to right, the extracted RSI and the residual between Cover and Stego. Intuitively, the stego generated by the scheme and the extracted RSI have good visual effects. Subjective evaluation is not very accurate, and we have made some objective evaluation, mainly using PSNR [33] and SSIM [34] two general visual quality evaluation criteria. Table 1 shows the results of objective evaluation. It is generally believed that PSNR reaches 37db and SSIM reaches 0.85, which means that the evaluation object has better visual quality, that is, no visual anomaly can be detected compared with the reference object.

Figure 7. Visual performance display.

Figure 7. Visual performance display.

Table 2. Objective evaluation of embedding and revealing effects.

Table 2. Objective evaluation of embedding and revealing effects.

The test pairs	Embedding	Revealing
	PSNR/SSIM	PSNR/SSIM
Row#1	46.8db/0.97	38.7db/0.86
Row#2	47.1db/0.98	39.3db/0.84
Row#3	46.9db/0.96	39.2db/0.86
Row#4	46.8db/0.97	38.6db/0.88
Row#5	47.2db/0.98	38.8db/0.86
Row#6	46.9db/0.96	39.1db/0.85

* PSNR and SSIM can be calculated by equation 18 and 19 respectively.

$$PSNR=10·{log}_{10}\left(\frac{MA{X}^2}{MSE}\right)$$

(18)

In Equation (18), $MAX$ is the maximum possible pixel value of the two images involved in the calculation and $MSE$ represents the Mean Squared Error.

$$SSIM(x,y)=\frac{(2u_x{u}_y+C_1)}{(u_x^2+u_y^2+C_1)}·\frac{(2{\delta }_{xy}+C_2)}{({\delta }_x^2+{\delta }_y^2+C_2)}$$

(19)

In Equation (19), $u_x$ and $u_y$ represent the average values of images, ${\delta }_{xy}$ represents covariance between images, ${\delta }_x$ and ${\delta }_y$ represent the variances of images, $C_1$ and $C_2$ are two constants which are used to prevent unstable results.

4.3. Semantic Retention Capability Test

In image classification, three standard evaluation metrics are commonly utilized: overall accuracy, average accuracy, and the confusion matrix. Overall classification accuracy (OCA) is measured by the proportion of correctly classified samples across all classes relative to the total sample count. Average classification accuracy (ACA) calculates the mean classification accuracy for each class, independent of the class sample size. The confusion matrix, an insightful layout, serves to dissect the classification performance, detailing each correct or mistaken prediction by class through an accumulative tabulation of tested samples.

Figure 8. Embedding network architecture.

Figure 8. Embedding network architecture.

It is important to note that in the case of the NWPU-RESISC45 dataset, each class contains an identical number of images. Consequently, the overall accuracy coincides with the average accuracy. As a result, in our study, we only employ overall accuracy and the confusion matrix to gauge the effectiveness of various classification methodologies.

Furthermore, to ensure the dependability of the overall accuracy and confusion matrix metrics, we conducted ten iterations of the experimental process for each training-testing split. The outcomes are then presented as a mean and standard deviation, providing a robust and trustworthy statistical analysis of the classification results.

Table 3. Overall Accuracy of three kinds of method based on CNN and their fine-tuned variants under the training ratios of 70% and 80%.

Table 3. Overall Accuracy of three kinds of method based on CNN and their fine-tuned variants under the training ratios of 70% and 80%.

Method based on CNN	70% training ratio	80% training ratio
	Native/extracted	Native/extracted
AlexNet	91.5±0.18/91.3±0.17	92.7±0.12/92.6±0.11
VGGNet16	90.5±0.19/90.6±0.15	92.6±0.20/92.6±0.19
GoolgeLeNet	91.8±0.13/92.1±0.12	92.3±0.13/92.2±0.15
Fine-tuned AlexNet	97.5±0.18/97.2±0.16	98.7±0.10/98.5±0.11
Fine-tuned VGGNet16	97.6±0.18/96.9±0.19	98.9±0.09/98.3±0.08
Fine-tuned GoolgeLeNet	97.3±0.18/97.5±0.17	98.7±0.12/98.4±0.13

5. Discussion

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