Remote sensing image robust watermarking method based on improved reversible neural network

Abstract

The invention discloses a remote sensing image robust watermarking method based on an improved reversible neural network, and relates to the technical field of digital image copyright protection, and the method comprises the steps: collecting an original remote sensing image and a binary watermark sequence, and carrying out the preprocessing, and forming a training sample; inputting the training sample into the watermark model; applying randomly selected noise attack to the watermark image through a noise layer to generate a disturbed watermark image; inputting the disturbed watermark image into the watermark model, and executing a reverse extraction path to obtain extracted watermark information; calculating a multi-target loss function, wherein the multi-target loss function is based on the original remote sensing image, the binary watermark sequence, the watermark image and the extracted watermark information; and training the model until convergence. Through a robust lifting mechanism and an improved reversible neural network structure, the method shows extremely high stability to various complex noise attacks, and has good generalization ability and environmental adaptability.

Description

Technical Field

[0001] This invention belongs to the field of digital image copyright protection technology, and in particular relates to a robust watermarking method for remote sensing images based on an improved reversible neural network. Background Technology

[0002] Traditional methods typically embed watermarks into the transform domain of images, such as the Discrete Cosine Transform (DCT), Discrete Fourier Transform (DFT), and Discrete Wavelet Transform (DWT) domains, to improve robustness. For example, some methods resist JPEG compression by modifying DCT coefficients; improve geometric robustness by utilizing the stability of DFT coefficient amplitudes under geometric transformations; or leverage the multi-resolution characteristics of DWT to balance perceptual quality and robustness. However, these traditional methods have inherent drawbacks: they generally rely on hand-designed features and shallow transform rules, and their robustness strategies are usually designed for specific types of attacks (such as JPEG compression or rotation). When faced with diverse or unknown complex noise combinations, these methods are poorly adaptable and struggle to guarantee reliable watermark extraction. Furthermore, hand-designed embedding rules are difficult to adapt to the rich and complex semantic structure of remote sensing images, easily introducing distortion in key regions or failing to find the optimal embedding location.

[0003] In recent years, deep learning-based methods, especially encoder-decoder architectures (such as HiDDeN and MBRS), have demonstrated stronger adaptability by automatically learning robust features through end-to-end training and differentiable noise layers. Some studies have improved performance by refining training strategies or introducing attention mechanisms. However, these methods suffer from the following key drawbacks: their encoder and decoder are structurally asymmetric and separate architectures, which can easily lead to insufficient structural coupling. When embedding watermarks, the encoder may introduce redundant or decoding-irrelevant features, which the decoder cannot effectively utilize, resulting in information flow mismatch and limiting the accuracy of watermark extraction, especially under strong noise interference.

[0004] To address the coupling problem between codecs, existing technologies have introduced invertible neural networks (INNs) to construct watermarking systems. INNs utilize their theoretically bijective (reversible) property to model watermark embedding and extraction as a pair of reversible processes, thus naturally ensuring tight coupling between the processes, as seen in methods such as HiNet and CIN. Despite the theoretical advantages of INNs, in remote sensing image applications, existing INN methods still face two prominent drawbacks: I. Insufficient Structural Adaptability: Existing methods lack embedding strategies tailored to the structural characteristics of remote sensing images. Remote sensing images are characterized by high resolution and rich semantic information, with key information (such as feature edges and textures) concentrated in high-frequency regions. Existing INN methods typically embed watermarks indiscriminately throughout the image, easily introducing significant visual distortion in high-frequency regions, damaging the semantic content of the image, and affecting its usability in downstream tasks such as target detection and feature classification.

[0005] II. Lack of Robustness in Noisy Environments: The bidirectional mapping of INNs is highly sensitive to input perturbations. In steganography tasks, the carrier is usually lossless, but in watermarking tasks, watermarked images are subjected to various noise attacks during transmission. This noise can disrupt the accurate reversible mapping relationship of INNs, leading to a mismatch between the forward embedding path and the reverse extraction path, causing a sharp decline in watermark recovery accuracy. This makes it difficult to meet the high requirements for robust copyright protection of remote sensing images in cross-platform, long-distance transmission.

[0006] In summary, existing technologies lack a watermarking solution that can simultaneously adapt to the semantic structural features of remote sensing images and maintain high robustness under complex noise interference. Summary of the Invention

[0007] The purpose of this invention is to address the lack of a watermarking method in the existing technology that can simultaneously adapt to the semantic structural features of remote sensing images and maintain high robustness under complex noise interference, and to propose a robust watermarking method for remote sensing images based on an improved reversible neural network.

[0008] This invention is achieved through the following technical solution: A robust watermarking method for remote sensing images based on an improved reversible neural network includes the following steps: S1. Collect the original remote sensing images and binary watermark sequences, preprocess the original remote sensing images, and form training samples. S2. Input the training samples into the watermarking model, which includes an improved reversible neural network, a watermarking processing module, an image enhancement module, a dual-domain fusion module, an adversarial discriminator, and a noise layer, and execute the forward embedding path to generate a watermarked image. S3. Pass the watermark image through the noise layer and apply randomly selected noise attack to generate a disturbed watermark image; S4. Input the disturbed watermark image into the watermark model and execute the reverse extraction path to obtain the extracted watermark information. S5. Calculate the multi-objective loss function, which is based on the original remote sensing image, the binary watermark sequence, the watermark image, and the extracted watermark information. S6. Optimize the parameters of the watermarking model according to the multi-objective loss function, and repeat steps S2 to S5 until the model converges.

[0009] A storage device that stores instructions and data for implementing a robust watermarking method for remote sensing images based on an improved reversible neural network.

[0010] A robust watermarking device for remote sensing images based on an improved reversible neural network includes: a processor and a storage device; the processor loads and executes instructions and data in the storage device to implement a robust watermarking method for remote sensing images based on an improved reversible neural network.

[0011] The present invention has the following beneficial effects: 1. Imperceptibility: Thanks to the constraints of the low-frequency embedding strategy and the high-frequency wavelet loss, the watermark is effectively confined to non-critical regions of the image, while adversarial training further optimizes the visual quality. Experiments show that the generated watermarked images have an average PSNR higher than 39 dB and an SSIM higher than 0.96 on the PatternNet and AID datasets, indicating that they are almost visually indistinguishable from the original images, effectively ensuring the visual quality and downstream application value of remote sensing images.

[0012] 2. Robustness against attacks: Through a robust enhancement mechanism and an improved reversible neural network structure, the model exhibits extremely strong stability against various complex noise attacks. Under combined attacks involving eight common perturbations, including Gaussian noise, JPEG compression, and cropping, the average accuracy of watermark extraction reaches 98.93%, significantly outperforming mainstream deep watermarking methods such as HiDDeN, MBRS, and HiNet-M, with particularly pronounced advantages in high-noise and compressed environments.

[0013] 3. Generalization and Stability: The key modules proposed in this invention effectively improve the model's performance under different datasets and unknown noise intensities. Cross-dataset (PatternNet and AID) test results are stable, and the watermark extraction accuracy curve decreases gradually under different noise intensities, demonstrating good generalization ability and environmental adaptability.

[0014] 4. Synergistic effectiveness of module design: The key modules proposed in this invention, such as the low-frequency embedding strategy, the improved reversible neural network, the watermarking module, and the image enhancement module, can all independently bring performance improvements. At the same time, they work together to improve the imperceptibility of watermark embedding and the robustness of extraction, resulting in a good synergistic gain effect. Attached Figure Description

[0015] To more clearly illustrate the technical solutions of the embodiments of the present invention, the accompanying drawings used in the description of the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0016] Figure 1 This is a schematic diagram of the process of a robust watermarking method for remote sensing images based on an improved reversible neural network according to the present invention. Figure 2 This is a diagram of the overall architecture of the watermark model; Figure 3 This is a network structure diagram of the watermark processing module; Figure 4 This is a structural diagram of the reversible block in an improved reversible neural network; Figure 5 This is the network structure diagram of the dual-domain fusion module; Figure 6 This is a schematic diagram of the hardware device of the present invention. Detailed Implementation

[0017] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0018] Example 1 Please see Figure 1 As shown, this invention is a robust watermarking method for remote sensing images based on an improved reversible neural network, comprising the following steps: S1. Collect the original remote sensing images and binary watermark sequences, preprocess the original remote sensing images, and form training samples. Specifically, this invention prepares a set of original remote sensing images (such as those from PatternNet or AID datasets) and corresponding binary watermark information sequences. The images are preprocessed and paired with randomly generated watermark sequences to form training samples.

[0019] S2. Input the training samples into the watermarking model, which includes an improved reversible neural network, a watermarking processing module, an image enhancement module, a dual-domain fusion module, an adversarial discriminator, and a noise layer, and execute the forward embedding path to generate a watermarked image. It should be noted that the forward embedding path described in step S2 is as follows: S21. Input the binary watermark sequence into the watermark processing module, and generate robust watermark features through channel attention mechanism and sub-pixel convolution upsampling. It should be noted that in step S21, the watermark processing module processes the binary watermark sequence including the following steps: S211. Reshape the binary watermark sequence into a two-dimensional tensor; S212. Increase the number of channels through convolutional layers; S213. Upsample to the target resolution using subpixel convolution; S214. Channel weights are generated through a channel attention mechanism to enhance the watermark features and output robust watermark features.

[0020] S22. Perform discrete wavelet transform on the original remote sensing image to decompose it into low-frequency sub-band and high-frequency sub-band, and obtain the frequency domain representation. S23. Input the robust watermark feature and the frequency domain representation into the improved reversible neural network, and after processing through multiple reversible blocks, obtain the iterative watermark feature and frequency domain representation; It should be noted that, in step S23, the reversible block processing in the improved reversible neural network includes the following steps: For the i-th reversible block, input robust watermark features Frequency domain representation Output the watermark features after iteration. Frequency domain representation ,in: in, Represents the Hadamard product. It is an exponential function. , , It is a dense block.

[0021] S24. The iterated watermark features are fused with the original frequency domain representation to obtain the frequency domain representation of the watermark image. S25. Perform inverse discrete wavelet transform on the frequency domain representation of the watermark image to generate a spatial domain watermark image.

[0022] As one embodiment, specifically, during the training phase, the original remote sensing image and the corresponding binary watermark sequence are input into the constructed watermark model, and a forward embedding path is executed to generate a watermark image. Then, the watermark image is passed through a noise layer containing multiple noise types to simulate real perturbation, generating a perturbed watermark image. Next, the perturbed watermark image is input into the watermark model, and a reverse extraction path is executed to obtain the extracted watermark information. During the training phase, the parameters of the watermark model are optimized using a multi-objective loss function until the model converges, resulting in a trained watermark model. Specifically, the model training process can be divided into three stages: watermark embedding, noise attack, and watermark extraction, as follows: Figure 2 As shown.

[0023] The first stage is the watermark embedding stage, which involves embedding the watermark into the original remote sensing image. and binary watermark Input watermark model. Binary watermark. First, input the watermark processing module, such as... Figure 3 As shown.

[0024] This module will The data is reshaped into a two-dimensional tensor, and the number of channels is increased through convolutional layers. Then, subpixel convolution is used to upsample to the target resolution. This operation effectively avoids the checkerboard artifact effect caused by using transposed convolution as the upsampling method.

[0025] Next, a channel attention module is used to generate channel weights to enhance the watermark features, ultimately outputting robust watermark features. .

[0026] Meanwhile, the original image It is decomposed into low-frequency subbands and high-frequency subbands through discrete wavelet transform, and its frequency domain representation is obtained. Next, and A common-input improved reversible neural network, the network contains A set of reversible blocks with the same structure, the specific structure of which is as follows: Figure 4 As shown.

[0027] With the first Taking a reversible block as an example and As input, we get output. and This can be expressed as a formula:

[0028]

[0029] in This indicates the Hadamard product operation. This represents an exponential function with a base of constant e, used to enhance the nonlinear expressive power in feature transformation, thereby capturing deeper watermark features. , , It is a dense block. The iteration variable is obtained after n invertible blocks. and Unlike previous methods that directly... Unlike the frequency domain representation of the final watermark image, this method introduces a carrier-feature fusion operation, retaining only the iterative variables of the watermark information. and frequency domain representation of the carrier image Element-wise addition and fusion are performed to construct the final frequency domain representation of the watermarked image. As shown in the following equation. The starting point for this improvement is that forward embedding networks often suffer from information attenuation after deep mapping. Without guidance from the original image, the embedding result will deviate from the input distribution, leading to visual degradation of the watermark image. The fusion operation not only enhances the structural consistency between the watermark image and the original image in the frequency domain but also provides stable initial features for subsequent decoding. Finally, for... Perform inverse discrete wavelet transform to generate a watermarked image in the spatial domain. : .

[0030] S3. Pass the watermark image through the noise layer and apply randomly selected noise attack to generate a disturbed watermark image; As one embodiment, the next step is the noise attack stage, which generates the watermarked image. An input noise layer is used to simulate attacks that may be encountered in real-world transmission. This embodiment supports various noise types, including Gaussian noise, salt-and-pepper noise, Gaussian blur, scaling, contrast adjustment, JPEG compression, cropping, Cropout, and Dropout. For non-differentiable JPEG compression, a differentiable function based on Fourier series is used for approximation, as shown in the following equation. In each training batch, a noise type is randomly selected and applied to the input noise layer. Obtain the disturbed watermark image .

[0031] .

[0032] S4. Input the disturbed watermark image into the watermark model and execute the reverse extraction path to obtain the extracted watermark information. It should be noted that the reverse extraction path described in step S4 includes the following steps: S41. Input the disturbed watermark image into the image enhancement module, perform discrete wavelet decomposition, and only perform denoising processing based on adaptive threshold on the high-frequency sub-band to reconstruct the enhanced image. It should be noted that in step S41, the image enhancement module processes the disturbed watermark image in the following steps: S411. Perform discrete wavelet decomposition on the disturbed watermark image to obtain high-frequency sub-band and low-frequency sub-band; S412. Only the high-frequency subband is denoised using an adaptive thresholding method based on BayesShrink. S413. Perform inverse discrete wavelet transform on the denoised high-frequency subband and the original low-frequency subband to reconstruct the enhanced image.

[0033] S42. Input the enhanced image into the dual-domain fusion module, extract spatial domain features and frequency domain features, generate an attention weight map, perform weighted fusion, and output structured auxiliary variables; It should be noted that in step S42, the dual-domain fusion module generates structured auxiliary variables, which includes the following steps: S421. Extract spatial domain features from the enhanced image; S422. Extract the low-frequency subband features of the discrete wavelet transform of the enhanced image; S423. Generate an attention weight map through convolution and concatenation operations; S424. Use attention weight maps to perform weighted fusion of spatial domain features and frequency domain features, and output structured auxiliary variables.

[0034] S43. Input the frequency domain representation of the enhanced image and the structured auxiliary variables into the reverse path of the improved reversible neural network, process them through multiple reversible blocks, and extract the watermark features. S44. Input the watermark features into a reverse watermark processing module that is structurally symmetrical with the watermark processing module to recover the binary watermark information.

[0035] As one embodiment, the final stage is the watermark extraction stage, which involves extracting the disturbed watermark image. Input the watermark model to extract the watermark.

[0036] first, It is sent to the image enhancement module. This module... Discrete wavelet decomposition is performed, processing only the high-frequency subbands. An adaptive thresholding method based on BayesShrink is used to obtain the optimal threshold for each high-frequency subband. Thresholding is applied to the high-frequency coefficients to suppress noise, and finally, the enhanced image is reconstructed. .

[0037] Next, the image will be enhanced. Input the dual-domain fusion module, such as Figure 5 As shown. This module also extracts The spatial domain features and their DWT low-frequency subband features are used to generate an attention weight map through convolution and concatenation operations. The two types of features are then weighted and fused to output a structured auxiliary variable that is strongly correlated with the image content. This replaces the randomly sampled Gaussian variables in traditional INNs. This design explicitly models the complementarity between the image spatial and frequency domains, effectively improving the extraction network's ability to perceive watermarks.

[0038] Next Frequency domain representation with auxiliary variables The reverse path of the common input improved invertible neural network. The transformation process is the reverse of the forward path, for the ... There are invertible blocks, and their formulas are as follows, where That lineage eventually obtained the watermark feature. Finally, Input a reverse structure watermarking module (and) Figure 3 (Structurally symmetrical) to ultimately recover the binary watermark information .

[0039]

[0040]

[0041] S5. Calculate the multi-objective loss function, which is based on the original remote sensing image, the binary watermark sequence, the watermark image, and the extracted watermark information. It should be noted that in step S5, the multi-objective loss function is a weighted sum of the encoding loss, decoding loss, adversarial loss, and high-frequency wavelet loss, wherein: The encoding loss is the mean square error between the watermarked image and the original image; The decoding loss is the mean square error between the extracted watermark information and the binary watermark sequence; The adversarial discriminator is used to calculate the adversarial loss, which is specifically the loss that encourages the watermarked image to deceive the discriminator. The high-frequency wavelet loss is the mean square error between the watermarked image and the original image in the high-frequency wavelet subband.

[0042] As one example, the above three stages guide model parameter optimization through a multi-objective loss function. Total Loss It is a weighted sum of multiple losses: .in: (1) The encoding loss is constrained by the pixel-level difference between the watermarked image and the original image.

[0043] (2) To account for decoding loss, we constrain the consistency between the extracted watermark and the original watermark.

[0044] (3) To combat losses, the generated watermarked images are encouraged to deceive the discriminator.

[0045] (4) The high-frequency wavelet loss constrains the difference between the watermarked image and the original image in the high-frequency subband, guiding the watermark to be embedded in the low frequency.

[0046] S6. Optimize the parameters of the watermarking model according to the multi-objective loss function, and repeat steps S2 to S5 until the model converges.

[0047] As one example, in this embodiment, the network is implemented in the PyTorch framework, trained on an NVIDIA RTX 3080Ti platform, using Adam as the optimizer, with an initial learning rate of 0.0001, a batch size of 8, and 50 epochs trained for each noise configuration. The weights of the loss function... , , , The values ​​were set to 1, 0.01, 0.0001, and 1 respectively, and cross-validation determined them to be the optimal combination that strikes a balance between imperceptibility and robustness. For JPEG and Crop noise, two types of strong noise, the weights were set to 0.5, and for Combined noise, the weights were set to 2 to enhance training focus.

[0048] Finally, in the application phase, this invention utilizes a pre-trained watermarking model. The target remote sensing image to be protected and the specified copyright watermark information are input into the model, and only the aforementioned forward embedding path is executed to generate a visually high-quality, watermarked remote sensing image for public distribution.

[0049] During the verification phase, potentially disturbed watermarked images are acquired for verification. These images are then input into a trained watermark model, and a reverse extraction path is executed (without requiring the original carrier image) to recover the watermark information. Copyright authentication can be completed by comparing the extracted watermark with the preset watermark.

[0050] Example 2 Please see Figure 6 , Figure 6 This is a schematic diagram of the hardware device operation according to an embodiment of the present invention. The hardware device specifically includes: a remote sensing image robust watermarking device 401 based on an improved reversible neural network, a processor 402, and a storage device 403.

[0051] A robust watermarking device 401 for remote sensing images based on an improved reversible neural network: The robust watermarking device 401 for remote sensing images based on an improved reversible neural network implements the robust watermarking method for remote sensing images based on an improved reversible neural network.

[0052] Processor 402: The processor 402 loads and executes the instructions and data in the storage device 403 to implement the robust watermarking method for remote sensing images based on an improved reversible neural network.

[0053] Storage device 403: The storage device 403 stores instructions and data; the storage device 403 is used to implement the robust watermarking method for remote sensing images based on an improved reversible neural network.

[0054] The key technical point of this invention lies in a series of innovative designs that work together, as follows: 1. Frequency-Domain Guided Low-Frequency Embedding Strategy: This invention abandons the traditional method of indiscriminately embedding watermarks in the spatial or full-frequency domains, and innovatively proposes a frequency-domain guided strategy. The core of this strategy lies in decomposing the carrier image into different frequency bands through discrete wavelet transform, and selectively embedding the watermark information primarily into the low-frequency sub-bands with strong anti-interference capabilities. This effectively avoids high-frequency regions that carry key semantic information of remote sensing images (such as edges and textures), thus ensuring the imperceptibility of the watermark at the source and reducing damage to the subsequent analysis and application value of the image.

[0055] 2. Bidirectional Information Preservation Mechanism in Improved INN: Addressing the information decay and mapping mismatch issues in deep transformations of invertible neural networks under noise, this invention makes two key improvements to the standard INN: A "carrier-feature fusion" operation is introduced at the end of the forward embedding path: the watermark features obtained in the final iteration are added element-wise to the frequency domain representation of the original carrier image. This operation uses the structural information of the original image as a strong guide, effectively mitigating the visual degradation of the watermark image and ensuring the quality of the generated image.

[0056] A "structured prior" is introduced at the beginning of the reverse extraction path: a content-related auxiliary variable is generated using a dual-domain fusion module, leveraging the spatial and frequency domain features of the disturbed image itself, replacing the random Gaussian variable used in traditional INNs. This provides valuable initial information for the reverse extraction path, significantly improving the stability of reverse mapping under noise interference and the accuracy of watermark recovery.

[0057] 3. Robust Enhancement Mechanism Integrating Feature Enhancement and Image Denoising: To comprehensively improve the model's performance under complex perturbations, this invention designs a robust enhancement mechanism consisting of two modules: Watermarking Module: This module preprocesses the watermark before embedding. Its key features are the introduction of a channel attention mechanism and sub-pixel convolutional upsampling. The former can adaptively enhance the watermark feature channels that contribute more to robustness, while the latter avoids the checkerboard artifacts caused by common upsampling methods, together generating more expressive and stable robust watermark features.

[0058] Image enhancement module: This module preprocesses the disturbed image before extraction. Its key feature is that it performs denoising only on the high-frequency subbands of the image based on an adaptive threshold. This approach effectively suppresses noise while preserving the low-frequency information embedded in the watermark to the greatest extent possible, creating favorable conditions for subsequent accurate extraction.

[0059] A dynamic adversarial training framework for real-world scenarios: This invention integrates a noise layer containing various types of noise during the training phase, and dynamically and randomly selects the noise type to apply in each training batch. This design simulates the uncertainty in real-world environments, jointly driving the model to learn a highly robust watermark embedding distribution that can generalize to various unknown attacks.

[0060] In the description of this specification, references to terms such as "an embodiment," "example," "specific example," etc., indicate that a specific feature, structure, material, or characteristic described in connection with that embodiment or example is included in at least one embodiment or example of the invention. In this specification, illustrative expressions of the above terms do not necessarily refer to the same embodiment or example. Furthermore, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in one or more embodiments or examples.

[0061] The preferred embodiments of the present invention disclosed above are merely illustrative of the invention. These preferred embodiments do not exhaustively describe all details, nor do they limit the invention to the specific implementations described. Clearly, many modifications and variations can be made based on the content of this specification. This specification selects and specifically describes these embodiments to better explain the principles and practical applications of the invention, thereby enabling those skilled in the art to better understand and utilize the invention. The invention is limited only by the claims and their full scope and equivalents.

Claims

1. A robust watermarking method for remote sensing images based on an improved reversible neural network, characterized in that: Includes the following steps: S1. Collect the original remote sensing images and binary watermark sequences, preprocess the original remote sensing images, and form training samples. S2. Input the training samples into the watermarking model, which includes an improved reversible neural network, a watermarking processing module, an image enhancement module, a dual-domain fusion module, an adversarial discriminator, and a noise layer, and execute the forward embedding path to generate a watermarked image. S3. Pass the watermark image through the noise layer and apply randomly selected noise attack to generate a disturbed watermark image; S4. Input the disturbed watermark image into the watermark model and execute the reverse extraction path to obtain the extracted watermark information. S5. Calculate the multi-objective loss function, which is based on the original remote sensing image, the binary watermark sequence, the watermark image, and the extracted watermark information. S6. Optimize the parameters of the watermarking model according to the multi-objective loss function, and repeat steps S2 to S5 until the model converges.

2. The robust watermarking method for remote sensing images based on an improved reversible neural network according to claim 1, characterized in that, The forward embedding path described in step S2 is as follows: S21. Input the binary watermark sequence into the watermark processing module, and generate robust watermark features through channel attention mechanism and sub-pixel convolution upsampling. S22. Perform discrete wavelet transform on the original remote sensing image to decompose it into low-frequency sub-band and high-frequency sub-band, and obtain the frequency domain representation. S23. Input the robust watermark feature and the frequency domain representation into the improved reversible neural network, and after processing through multiple reversible blocks, obtain the iterative watermark feature and frequency domain representation; S24. The iterated watermark features are fused with the original frequency domain representation to obtain the frequency domain representation of the watermark image. S25. Perform inverse discrete wavelet transform on the frequency domain representation of the watermark image to generate a spatial domain watermark image.

3. The robust watermarking method for remote sensing images based on an improved reversible neural network according to claim 1, characterized in that, The reverse extraction path described in step S4 includes the following steps: S41. Input the disturbed watermark image into the image enhancement module, perform discrete wavelet decomposition, and only perform denoising processing based on adaptive threshold on the high-frequency sub-band to reconstruct the enhanced image. S42. Input the enhanced image into the dual-domain fusion module, extract spatial domain features and frequency domain features, generate an attention weight map, perform weighted fusion, and output structured auxiliary variables; S43. Input the frequency domain representation of the enhanced image and the structured auxiliary variables into the reverse path of the improved reversible neural network, process them through multiple reversible blocks, and extract the watermark features. S44. Input the watermark features into a reverse watermark processing module that is structurally symmetrical with the watermark processing module to recover the binary watermark information.

4. The robust watermarking method for remote sensing images based on an improved reversible neural network according to claim 2, characterized in that, In step S21, the watermark processing module processes the binary watermark sequence including the following steps: S211. Reshape the binary watermark sequence into a two-dimensional tensor; S212. Increase the number of channels through convolutional layers; S213. Upsample to the target resolution using subpixel convolution; S214. Channel weights are generated through a channel attention mechanism to enhance the watermark features and output robust watermark features.

5. A robust watermarking method for remote sensing images based on an improved reversible neural network according to claim 2, characterized in that, In step S23, the reversible block processing in the improved reversible neural network includes the following steps: For the i-th reversible block, input robust watermark features Frequency domain representation Output the watermark features after iteration. Frequency domain representation ,in: in, Represents the Hadamard product. It is an exponential function. , , It is a dense block.

6. The robust watermarking method for remote sensing images based on an improved reversible neural network as described in claim 3, characterized in that: In step S41, the image enhancement module processes the disturbed watermark image using the following steps: S411. Perform discrete wavelet decomposition on the disturbed watermark image to obtain high-frequency sub-band and low-frequency sub-band; S412. Only the high-frequency subband is denoised using an adaptive thresholding method based on BayesShrink. S413. Perform inverse discrete wavelet transform on the denoised high-frequency subband and the original low-frequency subband to reconstruct the enhanced image.

7. A robust watermarking method for remote sensing images based on an improved reversible neural network according to claim 3, characterized in that, In step S42, the dual-domain fusion module generates structured auxiliary variables by including the following steps: S421. Extract spatial domain features from the enhanced image; S422. Extract the low-frequency subband features of the discrete wavelet transform of the enhanced image; S423. Generate an attention weight map through convolution and concatenation operations; S424. Use attention weight maps to perform weighted fusion of spatial domain features and frequency domain features, and output structured auxiliary variables.

8. The robust watermarking method for remote sensing images based on an improved reversible neural network as described in claim 1, characterized in that, In step S5, the multi-objective loss function is a weighted sum of encoding loss, decoding loss, adversarial loss, and high-frequency wavelet loss, wherein: The encoding loss is the mean square error between the watermarked image and the original image; The decoding loss is the mean square error between the extracted watermark information and the binary watermark sequence; The adversarial discriminator is used to calculate the adversarial loss, which is specifically the loss that encourages the watermarked image to deceive the discriminator. The high-frequency wavelet loss is the mean square error between the watermarked image and the original image in the high-frequency wavelet subband.

9. A storage device, characterized in that: The storage device stores instructions and data to implement the robust watermarking method for remote sensing images based on an improved reversible neural network as described in any one of claims 1 to 8.

10. A robust watermarking device for remote sensing images based on an improved reversible neural network, characterized in that: include: A processor and a storage device; the processor loads and executes instructions and data in the storage device to implement the robust watermarking method for remote sensing images based on an improved reversible neural network as described in any one of claims 1 to 8.

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