Sar image denoising method based on non-divergence diffusion equation of adversarial attack prior
By generating adversarial attack samples adapted to the characteristics of SAR images and non-divergence diffusion equations, the problem of balancing speckle noise suppression and edge detail preservation in SAR images is solved, thereby improving robustness and stability under adversarial perturbation environments.
Patent Information
- Application Number
- CN202511870890.6
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- Filing Date
- 2025-12-12
- Publication Date
- 2026-02-27
- Estimated Expiration
- 2045-12-12
AI Technical Summary
Existing SAR image processing methods struggle to balance suppressing speckle noise with preserving edge details, and lack robustness against perturbation environments.
We employ a non-divergent diffusion equation based on adversarial attack priors. By generating adversarial attack samples adapted to the characteristics of SAR images, and combining the projection gradient descent algorithm and deep learning model, we construct a non-divergent diffusion equation and adaptively adjust the diffusion coefficient to remove speckle noise and improve robustness.
It effectively removes speckle noise while preserving image structural information, improving the model's robustness and stability against perturbation environments and adapting to different SAR image scenarios and denoising models.
Smart Images
Figure CN121304490B_ABST
Abstract
Description
TECHNICAL FIELD
[0001] The application belongs to the technical field of radar image processing, and relates to a SAR image denoising method based on a non-divergence diffusion equation of an adversarial attack prior. BACKGROUND
[0002] As an active microwave imaging system, synthetic aperture radar (SAR) has all-weather and all-day imaging capabilities and is widely used in military reconnaissance, environmental monitoring, resource exploration and other fields. However, speckle noise is inevitably generated in the SAR imaging process, which is multiplicatively distributed and seriously affects the image quality and subsequent target recognition.
[0003] Existing denoising methods mainly include two categories: one is the traditional filtering and diffusion equation method, which can reduce noise in uniform areas but often causes edge and detail blurring; the other is the deep learning-based model, which has good performance under ideal conditions but is sensitive to data distribution and noise type and lacks robustness in real complex scenarios or under adversarial attacks. Therefore, the existing technology is difficult to balance between noise suppression and detail preservation, and the stability and adaptability are not strong in the face of complex interference and adversarial disturbance, so a new denoising method is needed to improve the robustness and practicality of SAR image processing. SUMMARY
[0004] In view of the problem that the existing method is difficult to balance between suppressing speckle noise and preserving edges and details, and lacks robustness under adversarial disturbance, the purpose of the present application is to provide a SAR image denoising method based on a non-divergence diffusion equation of an adversarial attack prior, which can generate adversarial attack samples adapted to the characteristics of SAR images, use the adversarial disturbance ratio of deep learning as prior information to guide the spatial modulation of the diffusion coefficient, effectively remove speckle noise, and improve the robustness of the model under adversarial disturbance.
[0005] The technical solution for achieving the purpose of the present application is as follows:
[0006] An adversarial attack sample method adapted to the characteristics of SAR images, comprising the following steps:
[0007] S01: randomly generating an initial adversarial disturbance to construct an initial adversarial attack sample;
[0008] S02: obtaining a denoised SAR image through a neural network denoising model, performing adversarial attack through a projected gradient descent algorithm, and performing multiple iterations; the multiple iterations include calculating the loss value of the adversarial disturbance introduced by iteration, calculating the gradient direction; updating the disturbance noise and keeping the disturbance noise in the defined space through the projection operation; after multiple iterations, the final adversarial disturbance is obtained;
[0009] S03: Generate final adversarial attack samples based on the final adversarial perturbation.
[0010] In the preferred technical solution, step S01 includes:
[0011] Given a uniformly distributed random variable Introducing noise distribution In the process, the initial adversarial perturbation is generated. Generate an initial adversarial attack sample:
[0012] ;
[0013] in, For a clean image, This represents the upper bound of the disturbance amplitude.
[0014] In the preferred technical solution, the gradient direction is calculated in step S02 as follows:
[0015] ;
[0016] The noise disturbance is confined to a defined space using a truncation function, calculated as follows:
[0017] ;
[0018] The final counter-perturbation is obtained as follows:
[0019] ;
[0020] in, For the number of iterations, Let be an intermediate variable in the t-th iteration. Step size, The initial value is 0. Represent the sign function and extract the positive and negative directions of the gradient. Represents the loss function. Indicates the first Adversarial perturbations introduced in the next iteration. These are the weight parameters of the neural network denoising model. Indicates the distribution of noise gradient operator, To initialize the disturbance noise, This represents the truncation function.
[0021] This invention also discloses a SAR image denoising method based on the non-divergence diffusion equation with adversarial attack prior, comprising the following steps:
[0022] The final adversarial attack sample is generated using any of the above-described adversarial attack sample methods adapted to SAR image characteristics.
[0023] The obtained adversarial attack sample is input into the neural network denoising model to extract an image adversarial attack prior;
[0024] An image adversarial attack prior is used to construct a prior-based prior modulation term and a diffusion coefficient function;
[0025] A non-divergence diffusion equation based on the adversarial attack prior is constructed by combining the noise image, the degradation model, and the constructed prior modulation term and diffusion coefficient function, and a denoised SAR image is obtained by solving the non-divergence diffusion equation based on the adversarial attack prior.
[0026] In the preferred technical solution, the diffusion coefficient function adaptively adjusts the strength of diffusion according to the local features of the image for denoising, and is expressed as:
[0027] ;
[0028] wherein, represents convolution, represents gradient, is a Gaussian kernel with a standard deviation of is a contrast parameter, controls the sensitivity to the gradient, is an estimate of the clean image.
[0029] The prior modulation term is:
[0030] ;
[0031] wherein, is an adversarial prior modulation parameter, is a noise image, is a constant.
[0032] In the preferred technical solution, the non-divergence diffusion equation based on the adversarial attack prior is:
[0033] ;
[0034] wherein, is a noise image, is an image prior, is defined on a spatial region and a time interval .
[0035] represents a divergence operator, represents gradient, represents the pixel intensity of the image changing with time t, represents an initial value, represents a partial derivative, denotes a direction vector, is a prior modulation term, is a diffusion coefficient function.
[0036] In the preferred technical scheme, the non-divergence diffusion equation based on the adversarial attack prior is discretized by using a half-point difference format, and specifically includes:
[0037] The time step is set as , which is used to control the time span of each iteration, and the image of the first iteration is , and at the initial time , , is a noise image, and for a pixel with coordinates in the image, the pixel value of the iteration is , which is calculated by the following iteration formula:
[0038] ;
[0039] wherein, , , is a half-point coefficient, and is respectively:
[0040] ;
[0041] ;
[0042] ;
[0043] ;
[0044] wherein, denotes a Gaussian convolution of ;
[0045] The noisy image is gradually denoised by pixel by pixel and iteration by iteration, and finally a denoised image is obtained.
[0046] The application further discloses an adversarial attack sample system suitable for SAR image characteristics, which comprises:
[0047] An initial adversarial attack sample generation module randomly generates an initial adversarial disturbance to construct an initial adversarial attack sample;
[0048] The adversarial disturbance generation module obtains the denoised SAR image through a neural network denoising model, performs adversarial attack through a projected gradient descent algorithm, and performs multiple iterations; the multiple iterations include calculating a loss value of the adversarial disturbance introduced by iteration, calculating a gradient direction; updating the disturbance noise, and keeping the disturbance noise in a defined space through a projection operation; after multiple iterations, the final adversarial disturbance is obtained;
[0049] The adversarial attack sample generation module generates a final adversarial attack sample according to the final adversarial disturbance.
[0050] The application further discloses a SAR image denoising system based on a non-divergence diffusion equation of adversarial attack prior, which comprises:
[0051] The adversarial attack sample generation module generates a final adversarial attack sample by using the adversarial attack sample method suitable for SAR image characteristics according to any one of the above.
[0052] The image prior extraction module inputs the obtained adversarial attack sample into the neural network denoising model to extract an image adversarial attack prior.
[0053] The prior correlation function construction module constructs a prior modulation term and a diffusion coefficient function based on the image adversarial attack prior.
[0054] The model construction and solving module constructs a non-divergence diffusion equation based on the adversarial attack prior by combining the noise image, the degradation model and the constructed prior modulation term and diffusion coefficient function, and obtains the denoised SAR image by solving the non-divergence diffusion equation based on the adversarial attack prior.
[0055] The application further discloses a computer storage medium having a computer program stored thereon, and the computer program is executed to realize the SAR image denoising method based on the non-divergence diffusion equation of adversarial attack prior.
[0056] Compared with the prior art, the application has the following advantages:
[0057] The application specifically designs a technical scheme in which a projected gradient descent (PGD) algorithm is deeply combined with a SAR speckle denoising model, and the technical scheme can generate an adversarial attack sample suitable for SAR image characteristics. The SAR speckle denoising model can accurately fit the speckle noise distribution law of the SAR image, and provides a constraint basis conforming to a real data scene for the generation of the adversarial sample. The improved PGD algorithm can realize effective breakthrough of a model decision boundary in a small disturbance range by virtue of the iterative optimization capability of the PGD algorithm, and the combination of the two ensures the compatibility of the adversarial sample and the SAR image and the effectiveness of the attack. The application maintains strong image denoising capability and structure preservation capability in the adversarial attack scene.
[0058] The constructed non-divergence diffusion equation based on the adversarial attack prior has theoretical robustness guarantee on one hand, and the model is solved by a fast solving algorithm to finally output the despeckling result of the image. The stability and uniqueness of the solution of the diffusion equation are guaranteed, and good theoretical explainability is provided. The method is simple and efficient, can be combined with existing deep learning networks, and is easy to be applied to actual SAR imaging systems. BRIEF DESCRIPTION OF DRAWINGS
[0059] Figure 1 The flow chart of the adversarial attack sample method adapting to the characteristics of the SAR image of the embodiment;
[0060] Figure 2 The contrast chart of the texture loss caused by the adversarial attack;
[0061] Figure 3 The technical roadmap of the SAR image denoising method based on the non-divergence diffusion equation of the adversarial attack prior;
[0062] Figure 4 The despeckling results of different algorithms on the adversarial satellite Figure 1 ;
[0063] Figure 5 The despeckling results of different algorithms on the real SAR image of the TerraSAR-X satellite. DETAILED DESCRIPTION
[0064] The principle of the application is that the method uses the adversarial disturbance ratio of deep learning as prior information to guide the spatial modulation of the diffusion coefficient: a larger diffusion coefficient is used in the homogeneous region and the high-noise region to enhance the denoising; a smaller diffusion coefficient is used in the edge and detail region to maintain the structure information. By constructing a spatial adaptive diffusion operator, the application effectively removes the speckle noise while improving the robustness of the model in the adversarial disturbance environment.
[0065] Embodiment 1:
[0066] As shown in Figure 1 , an adversarial attack sample method adapting to the characteristics of the SAR image comprises the following steps:
[0067] S01: randomly generating an initial adversarial disturbance to construct an initial adversarial attack sample;
[0068] S02: obtaining a denoised SAR image through a neural network denoising model, performing adversarial attack through a projection gradient descent algorithm, and performing multiple iterations; the multiple iterations comprise calculating the loss value of the adversarial disturbance introduced by iteration, calculating the gradient direction; updating the disturbance noise, and maintaining the disturbance noise in the defined space through the projection operation; after multiple iterations, the final adversarial disturbance is obtained;
[0069] S03: Generate final adversarial attack samples based on the final adversarial perturbation.
[0070] Denoising algorithms need to have the ability to stably suppress high-frequency oscillations. However, such as Figure 2 As shown, neural networks exhibit a high degree of sensitivity to minute perturbations. In adversarial attack scenarios, they often misjudge effective textures in images as noise, leading to over-smoothing of the denoising results and ultimately causing the loss of key texture information.
[0071] To address the core issues of neural networks being sensitive to minute perturbations and prone to misjudging textures as noise, leading to over-smoothing and texture loss during denoising, this invention specifically designs a technical solution that deeply integrates the Projected Gradient Descent (PGD) algorithm with a SAR speckle denoising model. This solution is used to generate adversarial attack samples adapted to the characteristics of SAR images. The SAR speckle denoising model accurately matches the speckle noise distribution pattern of SAR images, providing a constraint basis that conforms to real data scenarios for the generation of adversarial samples. Meanwhile, the PGD algorithm, with its iterative optimization capability, can effectively break through the model's decision boundary within a range of minute perturbations. The combination of the two ensures both the compatibility of adversarial samples with SAR images and the effectiveness of the attack.
[0072] In this embodiment, to address the shortcomings of traditional PGD algorithms that are prone to getting trapped in local optima during iteration, resulting in insufficient robustness of adversarial examples, this invention further improves the PGD algorithm: by introducing a mechanism for randomly initializing the perturbation starting point, on the one hand, the algorithm can avoid getting trapped in local optima under a single initial state, allowing the perturbation to search for the optimal direction in a wider feasible domain; on the other hand, it can make the perturbation distribution of the generated adversarial examples more uniform, reducing the attack "bias" caused by fixed initial points, thereby significantly enhancing the attack generalization ability and robustness of adversarial examples under different SAR image scenarios and different denoising models—that is, adversarial examples can not only deceive the target denoising model, but also adapt to similar denoising algorithms to a certain extent, reducing the risk of attack failure due to model differences.
[0073] Given a regression model An input sample and its corresponding regression target (in (representing the model's weights), adversarial attacks can be described as the following optimization problem:
[0074] ;
[0075] in yes and loss function between is the threshold of the maximum allowed adversarial perturbation.
[0076] For the sake of clarity, the specific application logic of the improved PGD algorithm in the present application can be described as follows:
[0077] (1)
[0078] wherein, denotes the adversarial perturbation introduced in the th iteration, is the step size, : the updated adversarial perturbation after the th iteration. denotes the projection operation, which constrains the perturbation within the legal range centered at with a radius of . denotes the sign function, which extracts the positive and negative directions of the gradient. denotes the gradient operator of the perturbation . denotes the loss function, which measures the difference between the adversarial sample and the reference sample.
[0079] The projection mechanism ensures that the perturbation remains within the defined space . A clipping function is applied in each step to ensure that the perturbation is limited to the allowable interval :
[0080] ;
[0081] wherein denotes the clipping function, which limits the input value within the interval .
[0082] The deep learning-based despeckling model can be regarded as a regression problem. The present application is directed to the adversarial attack model PGD-SAR-RDCP for the SAR-RDCP image denoising algorithm. For the despeckling problem, the given input sample is a despeckling image , and the corresponding regression target is a potential clean image . In addition, let denote the adversarial sample. When these images are processed by the proposed deep convolutional neural network (DCNN)-based speckle noise removal model , high-quality speckle-free noise results and will be generated accordingly. We use the projected gradient descent (PGD) method to attack the SAR-RDCP despeckling model and generate noisy images after adversarial attack through several iterations. In this process, we iteratively update the speckle noise distribution a small perturbation In the random initialization step, we generate a random variable uniformly distributed introduce a noise distribution to form an adversarial noise . According to equation (1), this generates an initial adversarial attack sample:
[0083] ;
[0084] In the projected gradient descent process, the gradient ascent step is performed to maximize the residual, and the model is pushed in the direction of the loss gradient with a step size . Since the speckle noise component must be positive, the perturbation is constrained within a maximum threshold . The adversarial noise is then clipped, and the final adversarial sample is derived according to equation (1).
[0085] The calculation formula is:
[0086] ;
[0087] ;
[0088] The final adversarial perturbation is:
[0089] .
[0090] In another embodiment, a system for generating an adversarial attack sample that adapts to the characteristics of a SAR image includes:
[0091] An initial adversarial attack sample generation module that randomly generates an initial adversarial perturbation to construct an initial adversarial attack sample;
[0092] An adversarial perturbation generation module that obtains a denoised SAR image through a neural network denoising model, performs an adversarial attack through a projected gradient descent algorithm, and iterates multiple times; the multiple iterations include calculating the loss value of the adversarial perturbation introduced by iteration, calculating the gradient direction; update the perturbation noise, and keep the perturbation noise within the defined space through the projection operation; after multiple iterations, the final adversarial perturbation is obtained;
[0093] An adversarial attack sample generation module that generates a final adversarial attack sample based on the final adversarial perturbation.
[0094] The specific implementation is the same as the above method, which will not be repeated here.
[0095] In another embodiment, a SAR image denoising method based on a non-divergence diffusion equation of an adversarial attack prior includes the following steps:
[0096] The final adversarial attack sample is generated using any of the above-described adversarial attack sample methods adapted to SAR image characteristics.
[0097] The obtained adversarial attack samples are input into a neural network denoising model to extract the image adversarial attack prior.
[0098] By leveraging prior knowledge of image adversarial attacks, a priori modulation term and diffusion coefficient function are constructed.
[0099] By combining the noisy image, the degradation model, and the constructed prior modulation term and diffusion coefficient function, a non-divergent diffusion equation based on the adversarial attack prior is constructed. The denoised SAR image is obtained by solving the non-divergent diffusion equation based on the adversarial attack prior.
[0100] In a preferred embodiment, the diffusion coefficient function adaptively adjusts the diffusion intensity based on local features of the image for denoising, as expressed as:
[0101] ;
[0102] in, Represents convolution. Represents the gradient. The standard deviation is Gaussian kernel, For contrast parameters, Controlling sensitivity to gradients, An estimate for a clean image.
[0103] The prior modulation term is:
[0104] ;
[0105] in, To counteract prior modulation parameters, For noisy images, It is a constant.
[0106] In a preferred embodiment, the non-divergence diffusion equation based on the adversarial attack prior is:
[0107] ;
[0108] in, For noisy images, For image priors, Defined in spatial region and time interval superior;
[0109] Denotes the divergence operator, Represents the gradient. pixel intensity of an image representing a change over time t, representing an initial value, representing a partial derivative, representing a direction vector, is a priori modulation term, is a diffusion coefficient function.
[0110] In a preferred embodiment, the non-divergence diffusion equation based on the adversarial attack prior is discretized by using a half-point difference format, specifically including:
[0111] The time step is set to , which is used to control the time span of each iteration, and the first iteration image is , and at the initial time , , is a noisy image, for the pixel with coordinates in the image, the pixel value of the th iteration is calculated by the following iteration formula:
[0112] ;
[0113] wherein, , , is a half-point coefficient, respectively:
[0114] ;
[0115] ;
[0116] ;
[0117] ;
[0118] wherein, represents a Gaussian convolution of ;
[0119] The noisy image is gradually denoised by pixel by pixel and iteration by iteration, and finally a denoised image is obtained.
[0120] Another embodiment, a SAR image denoising system based on a non-divergence diffusion equation of an adversarial attack prior, comprising:
[0121] An adversarial attack sample generation module generates a final adversarial attack sample by using the adversarial attack sample method suitable for the characteristics of the SAR image according to any one of the above.
[0122] An image priori extraction module inputs the obtained adversarial attack sample into a neural network denoising model to extract an image adversarial attack priori;
[0123] A priori correlation function construction module uses the image adversarial attack priori to construct a priori modulation term and a diffusion coefficient function based on the priori;
[0124] A model construction and solving module combines the noise image, the degradation model and the constructed priori modulation term and diffusion coefficient function to construct a non-divergence diffusion equation based on the adversarial attack priori, and obtains the denoised SAR image by solving the non-divergence diffusion equation based on the adversarial attack priori.
[0125] From the input data to the final output despeckling result, the complete technical process is as shown in Figure 3 .
[0126] The following describes each implementation step in detail:
[0127] 1. Input basic data: take the noise image and the degradation model as input.
[0128] 2. Generate an adversarial attack sample: input the noise image into the neural network denoising model, and obtain the adversarial attack sample by means of the PGD-SAR-RDCP algorithm.
[0129] 3. Extract the image priori: input the adversarial attack sample into the neural network denoising model to extract the image adversarial attack priori.
[0130] 4. Construct the priori correlation function: use the image adversarial attack priori to construct the priori modulation term and the diffusion coefficient function based on the priori.
[0131] 5. Establish the despeckling model: combine the noise image, the degradation model and the constructed priori modulation term and diffusion coefficient function to establish the diffusion equation despeckling model based on the deep learning priori.
[0132] 6. Model solving and result output: on the one hand, the model has robustness theoretical guarantee; on the other hand, the model is solved by a fast solving algorithm, and finally the image despeckling result is output.
[0133] Obtain the deep learning adversarial attack priori
[0134] The present application obtains the adversarial attack image priori by means of the mature SAR speckle denoising network HTNet . The HTNet has mastered the internal structure, texture features and speckle noise distribution law of the SAR image after training, and the information learned by the HTNet can be used as the relevant priori knowledge of the SAR image. Using the HTNet as a feature extractor or analyzing its parameters can guide the generation of more targeted adversarial perturbations, and then obtain effective adversarial attack images.
[0135] Model construction
[0136] Let the noisy image be The image prior is The estimate of the unknown clean image is Defined in spatial region and time interval Above. This invention constructs a non-divergent diffusion equation based on the prior knowledge of adversarial attacks:
[0137] ;
[0138] in, Denotes the divergence operator, express gradient, Represents the pixel intensity of the image as a function of time t. This represents the initial value. This indicates the partial derivative. This represents the direction vector. To counteract the prior modulation factor, To counteract the prior modulation factor taking a larger value in homogeneous regions and a smaller value in edge regions, thus achieving edge-preserving denoising, diffusion is increased (for denoising) in homogeneous noise regions and decreased (for edge preservation) in edge / detail regions, achieving spatially adaptive speckle suppression and structure protection.
[0139] The diffusion coefficient function adaptively adjusts the diffusion intensity based on the local features of the image for noise reduction, specifically expressed as:
[0140] ;
[0141] in Represents convolution. The standard deviation is Gaussian kernel, For contrast parameters, Control the sensitivity to gradients.
[0142] Prior modulation terms:
[0143] ;
[0144] in, To counteract prior modulation parameters, To prevent division by zero of small constants. According to and The difference ratio adaptively adjusts the global / local diffusion intensity, where Provide a positive lower bound to ensure the stability of evolution.
[0145] The numerical format used by the model is as follows:
[0146] To convert the above diffusion equation into a calculation step that can be executed on a computer, the present application uses a half-point difference format to discretize the diffusion equation, as follows:
[0147] The time step is set to to control the time span of each iteration. Let be the image of the iteration, and at the beginning (0th iteration) ( be the initial image with noise). denote the coordinates of the image pixels. For the pixel with coordinates in the image, the pixel value of the iteration is calculated by the following iteration formula:
[0148] ;
[0149] where
[0150] ;
[0151] where denotes the Gaussian convolution of . The remaining half-point coefficients are calculated in the same way, and are respectively:
[0152] ;
[0153] ;
[0154] ;
[0155] This format meets the stable convergence and maintains the edges when appropriate and parameter values are met. This iterative calculation realizes step-by-step denoising of noisy images through pixel-by-pixel and iteration-by-iteration, and finally outputs the processed image. The final u is the denoised image.
[0156] In another embodiment, a computer storage medium stores a computer program that, when executed, implements the above SAR image denoising method based on the non-divergence diffusion equation of the adversarial attack prior.
[0157] The above denoising method is used here and will not be described again.
[0158] Experimental results:
[0159] In the SAR image speckle removal performance test, the APPNDE algorithm proposed in this invention was comprehensively compared with eight existing mainstream speckle removal algorithms (AA algorithm, Shan algorithm, Frac algorithm, SAR-CNN algorithm, SAR-DRN algorithm, SAR-RDCP algorithm, SAR-CAM algorithm, and HTNet algorithm), and its performance advantage was verified from both objective indicators and subjective effects. Table 1 shows the comparison of SAR image speckle removal results for different algorithms:
[0160]
[0161] In terms of the three core evaluation metrics—PSNR (Peak Signal-to-Noise Ratio), SSIM (Structural Similarity), and DG (Speckle Suppression Specific Index)—the APPNDE algorithm's PSNR value is significantly higher than the other eight comparison algorithms, its SSIM value is closer to 1, and its DG value also reaches the optimal level, fully demonstrating its objective performance advantages in reducing image distortion, preserving image structural information, and suppressing speckle noise.
[0162] From a subjective perspective, the effect of removing freckles ( Figure 4 and Figure 5 From this perspective, such as Figure 4 , 5 As shown, different image despec effects are applied, among which... Figure 4 , 5 In the image, (a) is a noisy image, (b) is the AAP-NDDE result, (c) is the HTNet result, (d) is the Frac result, (e) is the SAR-CNN result, (f) is the SAR-RDCP result, (g) is the SAR-DRN result, (h) is the SAR-CAM result, (i) is the AA result, and (j) is the Shan result. The SAR image processed by the APPNDE algorithm effectively removes speckle noise and improves image clarity while preserving detailed textures (such as target edges and microstructures). It avoids the problems of "over-smoothing leading to detail loss" or "noise residue" found in some contrast algorithms, and its overall speckle removal effect is superior to all contrast algorithms.
[0163] The above embodiments are preferred embodiments of the present invention, but the embodiments of the present invention are not limited to the above embodiments. Any changes, modifications, substitutions, combinations, or simplifications made without departing from the spirit and principle of the present invention shall be considered equivalent substitutions and shall be included within the protection scope of the present invention.
Claims
1. A SAR image denoising method based on a non-divergence diffusion equation with adversarial attack prior, characterized in that, Includes the following steps: The final adversarial attack sample is generated using an adversarial attack sample method adapted to the characteristics of SAR images; The obtained adversarial attack samples are input into a neural network denoising model to extract the image adversarial attack prior. Utilizing prior knowledge of image adversarial attacks, a priori modulation term and diffusion coefficient function are constructed. The diffusion coefficient function adaptively adjusts the diffusion intensity based on local image features for denoising, and is expressed as: in, Represents convolution. Represents the gradient. The standard deviation is Gaussian kernel, For contrast parameters, Controlling sensitivity to gradients, An estimate for a clean image; The prior modulation term is: in, To counteract prior modulation parameters, For image priors, For noisy images, It is a constant; By combining the noisy image, the degradation model, and the constructed prior modulation term and diffusion coefficient function, a non-divergent diffusion equation based on the adversarial attack prior is constructed. The denoised SAR image is obtained by solving the non-divergent diffusion equation based on the adversarial attack prior.
2. The SAR image denoising method based on the non-divergence diffusion equation with adversarial attack prior as described in claim 1, characterized in that, The non-divergence diffusion equation based on the prior of adversarial attacks is as follows: in, For noisy images, Defined in spatial region and time interval superior; Denotes the divergence operator, Represents the gradient. Represents the pixel intensity of the image as a function of time t. Indicates the initial value. This indicates the partial derivative. Represents the direction vector. For the prior modulation term, This is a function of the diffusion coefficient.
3. The SAR image denoising method based on the non-divergence diffusion equation with adversarial attack prior as described in claim 1, characterized in that, The non-divergence diffusion equation based on the adversarial attack prior is discretized using a half-point difference scheme, specifically including: Set the time step to Used to control the time span of each iteration, the first The next iteration image is And initially For coordinates in the image The pixels, its first pixel value of the next iteration Calculated using the following iterative formula: in, , , The coefficients are half-point coefficients, respectively: in, express Gaussian convolution; The noisy image is gradually denoised by pixel-by-pixel and iteratively, and finally the denoised image is obtained.
4. A SAR image denoising system based on a non-divergence diffusion equation with adversarial attack prior, used to implement the SAR image denoising method based on a non-divergence diffusion equation with adversarial attack prior as described in any one of claims 1-3, characterized in that, include: The adversarial attack sample generation module uses an adversarial attack sample method adapted to the characteristics of SAR images to generate the final adversarial attack sample. The image prior extraction module inputs the obtained adversarial attack samples into the neural network denoising model to extract the image adversarial attack prior; The prior correlation function construction module utilizes prior knowledge of image adversarial attacks to construct prior modulation terms and diffusion coefficient functions based on prior knowledge. The model building and solution module combines the noisy image, the degradation model, and the constructed prior modulation term and diffusion coefficient function to construct a non-divergent diffusion equation based on the adversarial attack prior. The denoised SAR image is obtained by solving the non-divergent diffusion equation based on the adversarial attack prior.
5. A computer storage medium having a computer program stored thereon, characterized in that, When the computer program is executed, it implements the SAR image denoising method based on the non-divergence diffusion equation with adversarial attack prior as described in any one of claims 1-3.