An improved anchor point-based PRNU blind image clustering forensics method

Abstract

The application relates to a PRNU blind image clustering forensics method based on improved anchor points, which comprises the following steps: extracting photoresponse non-uniformity noise residuals through wavelet decomposition to construct a PRNU characteristic data set; compressing the high-dimensional PRNU characteristic dimension by using an orthogonal projection matrix, screening representative samples in a low-dimensional subspace to construct an anchor point matrix, and realizing light-weight linear expression of low-dimensional characteristics by means of the anchor points. A characteristic reconstruction model is built by fusing the orthogonal projection matrix and the anchor point matrix, a unified optimization function is constructed by introducing a reconstruction error constraint, a global kernel norm regular term and a local row sparse regular term, an optimal matrix is solved by using ALM combined with ADM iteration, and unmarked images are automatically clustered according to shooting equipment by relying on the converged representation coefficients. The application sets double orthogonal constraints for the projection and anchor point matrices, realizes bidirectional mapping of characteristics, makes the error matrix row sparse by relying on the norm, separates effective sensor fingerprints from noise, resists interference caused by image shooting and compression, and effectively improves the clustering robustness.

Description

Technical Field

[0001] This invention belongs to the field of digital image forensics and machine learning subspace clustering technology, specifically involving a PRNU blind image clustering forensics method based on improved anchor points. Background Technology

[0002] PRNU (Photometric Response Nonuniformity) is an inherent pixel noise generated during the manufacturing process of image sensors. This noise possesses two core characteristics: device uniqueness and long-term stability, making it a crucial evidentiary feature in the field of source tracing and evidence collection for digital image cameras. In scenarios such as forensic image authentication, device tracing of malicious online images, and multi-source image classification, it is often necessary to perform blind clustering on batches of images from unknown sources to automatically classify image sets produced by the same capturing device. Therefore, unsupervised clustering algorithms based on PRNU fingerprints have extremely high engineering application value. Conventional PRNU fingerprints are two-dimensional matrices with the same resolution as the original image. High-resolution images correspond to extremely high-dimensional PRNU features, which can lead to massive memory storage overhead and explosive computational complexity in matrix operations. Directly using the original PRNU features for clustering is difficult to implement on large-scale image datasets.

[0003] Existing technologies generally map high-dimensional PRNU features to a low-dimensional subspace by learning a projection matrix, compressing dimensionality while preserving device-specific fingerprint information and filtering out irrelevant noise from image content. However, this approach has significant drawbacks: simple linear projection only achieves dimensionality compression and cannot uncover the complex global relationships and local nearest neighbor structures hidden within the PRNU data, resulting in weak feature discrimination and low clustering accuracy; introducing global-local structured constraints to strengthen data relationship modeling significantly increases the computational cost of multi-variable joint solutions, making it difficult to handle large-scale image datasets with tens of thousands of images, thus limiting its practicality. Summary of the Invention

[0004] The technical problem of this invention is that the existing PRNU camera source-blind clustering scheme has high computational overhead for high-dimensional fingerprint features; anchor point selection is difficult to balance efficiency and clustering stability; it cannot simultaneously mine the global and local structure of the data; image noise easily interferes with the clustering results; hard clustering assignment is an NP-hard problem, requiring multi-module step-by-step optimization of projection, anchor points, and structural constraints, resulting in loss of feature information, insufficient clustering accuracy and robustness, and difficulty in meeting the needs of large-scale image source tracing and evidence collection.

[0005] The purpose of this invention is to solve the above-mentioned problems and propose a PRNU blind image clustering forensics method based on improved anchor points, comprising the following steps: S1: After preprocessing the acquired images, the non-uniformity noise residual of the light response of the images is extracted by wavelet decomposition algorithm, and then the PRNU feature dataset is constructed. S2: Construct an orthogonal projection matrix to map high-dimensional PRNU features to a lower-dimensional subspace; S3: Select multiple representative samples as anchor points in the low-dimensional subspace after dimensionality reduction, construct an anchor point matrix, and then use the anchor point matrix to linearly represent the low-dimensional features to complete the lightweight reconstruction of low-dimensional data. S4: Combine the orthogonal projection matrix and anchor point matrix to construct the original feature reconstruction model, and introduce reconstruction error constraints, global nuclear norm regularization term and local row sparsity regularization term to build a unified optimization objective function. Then, use the augmented Lagrange algorithm and alternating direction minimization algorithm to iteratively solve the optimal solution of all matrices. Based on the converged representation coefficients, complete the automatic clustering of unlabeled images according to the shooting device.

[0006] Furthermore, in step S1, wavelet decomposition is used to extract the PRNU noise residual due to non-uniformity of optical response, including the following sub-steps: 1) The original image is denoised using a wavelet denoising filtering algorithm to obtain a denoised image; 2) Calculate the pixel residual between the original image and the denoised image, and then separate and extract the PRNU noise residual due to non-uniform light response.

[0007] Furthermore, step S2 includes the following sub-steps: 1) Given an original dataset X, introduce a projection matrix P to project the high-dimensional original dataset onto a low-dimensional subspace, and solve for the corresponding low-dimensional representation matrix H. The mapping relationship expression for data decomposition is: ; In the formula, Represents the projection matrix. Represents a low-dimensional representation matrix; 2) To ensure the orthogonality-preserving property of the projection transformation and eliminate redundant correlations between projection components, orthogonality constraints are applied to the projection matrix. The expression for the orthogonality constraints is as follows: ; In the formula, Represents the projection matrix The transpose of the matrix, Represents the identity matrix.

[0008] Preferably, step S3 includes the following sub-steps: 1) Select m representative anchor points, where the number of anchor points m is less than the total number of samples n, and define the anchor point matrix. coefficient matrix ; 2) Coefficient matrix Record the linear representation weights of each sample relative to the anchor point, used to represent the samples. Mapping relationships within the anchor point space; 3) Multiplying the anchor matrix and the coefficient matrix yields the low-dimensional sample set, expressed as: ； In the formula, the anchor point matrix Used to capture key features of low-dimensional subspaces; coefficient matrix Characterizes the linear combination relationship of each sample based on the anchor point.

[0009] Furthermore, step S4 includes the following sub-steps: 1) Using the projection matrix P, data recovery from the low-dimensional latent representation to the original feature space is achieved. The expression for sample reconstruction is: ; In the formula, Represents the anchor point matrix. This represents a low-dimensional representation in the anchor space. Represents the projection matrix. This represents the original space reconstruction sample obtained after decoding; 2) Using the error matrix Norm constraints on the sparsity of the error matrix constrain reconstruction error and suppress data noise.

[0010] Preferably, step S4 includes introducing a global-local structured regularization term to construct a joint optimization objective function that integrates global and local structure constraints. The constraints include representation matrix reconstruction and orthogonality constraints, coefficient matrix equivalence constraints, and clustering assignment constraints. The objective function expressions are as follows: ; In the formula, Represents the global structure regularization coefficient. Represents the local structure regularity coefficient. This represents the nuclear norm regularization term, used to mine the global correlation structure between samples. The term represents a row sparse regularization term used to induce row sparseness in the coefficient matrix Z.

[0011] Preferably, in step S4, the constraints include orthogonal constraints, coefficient matrix equivalence constraints, and clustering assignment constraints, with the following expressions: Reconstruction and Orthogonal Constraints: ; Equivalence constraints of coefficient matrix: ; Clustering assignment constraints: ; In the formula, A represents the anchor point matrix, Z represents the low-dimensional representation in the anchor point space, P represents the projection matrix, E represents the reconstruction error, and the coefficient X represents the original space reconstruction sample obtained after decoding. This represents the transpose of the projection matrix.

[0012] Preferably, the introduction of global-local structured regularization terms also includes block-based iterative optimization of the joint optimization objective function using the augmented Lagrange multiplier method (ALM) combined with the alternating direction minimization method (ADM).

[0013] Furthermore, the block-based iterative optimization includes constructing the augmented Lagrange function corresponding to the objective function based on the augmented Lagrange multiplier method, and using the alternating direction minimization method to decompose the multivariate joint optimization problem into multiple single-variable sub-optimization problems, solving them individually and iteratively updating the variables.

[0014] Compared with the prior art, the beneficial effects of the present invention include: 1) The present invention proposes a PRNU blind image clustering forensics method based on improved anchor points. It selects a small number of anchor points in a low-dimensional subspace to replace all samples to construct a representation dictionary, transforms the inter-sample calculation into sample-anchor point operation, and integrates it with orthogonal projection in the same framework, which significantly reduces the amount of computation and is suitable for large-scale PRNU image datasets.

[0015] 2) The present invention proposes a PRNU blind image clustering forensics method based on improved anchor points. It sets up dual orthogonal constraints of projection matrix and anchor point matrix, achieves high-dimensional PRNU dimensionality reduction through forward mapping, reconstructs the original features through reverse decoding, and combines norm-induced error matrix row sparsity to distinguish effective sensor fingerprints from image noise, effectively suppressing interference caused by shooting and compression, and improving clustering robustness.

[0016] 3) The present invention proposes a PRNU blind image clustering forensics method based on improved anchor points. It integrates anchor point learning, orthogonal projection, noise reduction regularization, and structured constraints into the same objective function, and uses ALM and ADM to simultaneously iteratively optimize all variables, avoiding fingerprint feature loss caused by step-by-step modeling. The performance is stable under multi-size PRNU features. Attached Figure Description

[0017] The present invention will be further described below with reference to the accompanying drawings and embodiments.

[0018] Figure 1 This is a flowchart illustrating the PRNU blind image clustering forensics method based on improved anchor points, according to an embodiment of the present invention.

[0019] Figure 2 This is a schematic diagram comparing the performance of different algorithms in the embodiments of the present invention with that of the present invention.

[0020] Figure 3 This is a schematic diagram comparing the algorithm performance of different numbers of anchor points in an embodiment of the present invention. Detailed Implementation

[0021] like Figure 1 As shown, a PRNU blind image clustering forensics method based on improved anchor points includes the following steps: S1: After preprocessing the acquired images, the non-uniformity noise residual of the light response of the images is extracted by wavelet decomposition algorithm, and then the PRNU feature dataset is constructed.

[0022] In step S1, wavelet decomposition is used to extract the PRNU noise residual due to non-uniformity of optical response, which includes the following sub-steps: 1) The original image is denoised using a wavelet denoising filtering algorithm to obtain a denoised image; 2) Calculate the pixel residual between the original image and the denoised image, and then separate and extract the PRNU noise residual due to non-uniform light response.

[0023] Specifically, as shown in Table 1, a high dynamic range image library containing mobile phones from multiple brands such as Huawei, Xiaomi, Apple, Samsung, and ASUS was selected. Five different mobile phone models were randomly selected, and 20 images were collected from each device, for a total of 100 images to form the test dataset. All original images were preprocessed uniformly, and the extracted PRNU noise residuals were uniformly cropped to a size of 512×512.

[0024] Table 1

[0025] A wavelet denoising filtering algorithm is used to denoise a single original image I to obtain a clean image. Calculate the pixel residuals to separate the PRNU features of a single image. The formula for calculating the pixel residuals is: ; In the formula, I represents the original image, F(I) represents the image after denoising, and X represents the PRNU feature of the image.

[0026] All original images were preprocessed uniformly, and the extracted PRNU noise residuals were uniformly cropped to a size of 512×512.

[0027] A wavelet denoising filtering algorithm is used to denoise a single original image I to obtain a clean image. The pixel residual is calculated and the single-image PRNU features are separated. All 100 images are traversed to assemble a high-dimensional PRNU feature dataset X, D=512×512=262144, and the total number of samples N=100.

[0028] S2: Construct an orthogonal projection matrix to map high-dimensional PRNU features to a lower-dimensional subspace.

[0029] 1) Given an original dataset X, introduce a projection matrix P to project the high-dimensional original dataset onto a low-dimensional subspace, and solve for the corresponding low-dimensional representation matrix H. The mapping relationship expression for data decomposition is: ; In the formula, Represents the projection matrix. Represents a low-dimensional representation matrix; 2) To ensure the orthogonality-preserving property of the projection transformation and eliminate redundant correlations between projection components, orthogonality constraints are applied to the projection matrix. The expression for the orthogonality constraints is as follows: ; In the formula, Represents the projection matrix The transpose of the matrix, Represents the identity matrix.

[0030] Specifically, we set the dimension K of the low-dimensional subspace, construct the orthogonal projection matrix P to satisfy the orthogonal constraint condition, and map the high-dimensional dataset X to the low-dimensional subspace through the mapping relationship to obtain the low-dimensional feature H, thereby completing the high-dimensional feature compression and reducing the matrix operation.

[0031] S3: Select multiple representative samples as anchor points in the low-dimensional subspace after dimensionality reduction, construct an anchor point matrix, and then use the anchor point matrix to linearly represent the low-dimensional features, thus completing the lightweight reconstruction of low-dimensional data.

[0032] 1) Select m representative anchor points, where the number of anchor points m is less than the total number of samples n, and define the anchor point matrix. coefficient matrix ; 2) Coefficient matrix Record the linear representation weights of each sample relative to the anchor point, used to represent the samples. Mapping relationships within the anchor point space; 3) Multiplying the anchor matrix and the coefficient matrix yields the low-dimensional sample set, expressed as: ； In the formula, the anchor point matrix Used to capture key features of low-dimensional subspaces; coefficient matrix Characterizes the linear combination relationship of each sample based on the anchor point.

[0033] The dataset has 5 true clusters. The optimal number of anchor points is selected as m=2c=10. Ten representative anchor points are learned in the low-dimensional space H to form the anchor point matrix A, which satisfies the orthogonality constraint. The low-dimensional representation relationship is established as the sample-anchor point coefficient matrix.

[0034] S4: Combine the orthogonal projection matrix and anchor point matrix to construct the original feature reconstruction model, and introduce reconstruction error constraints, global nuclear norm regularization term and local row sparsity regularization term to build a unified optimization objective function. Then, use the alternating direction minimization algorithm to iteratively solve the optimal solution of all matrices, and complete the automatic clustering of unlabeled images according to the shooting device based on the converged representation coefficients.

[0035] Step S4 includes the following sub-steps: 1) Using the projection matrix P, data recovery from the low-dimensional latent representation to the original feature space is achieved. The expression for sample reconstruction is: ; In the formula, Represents the data transformation matrix. This represents the low-dimensional latent representation of the sample. Represents the back projection matrix. This represents the original space reconstruction sample obtained after decoding; 2) Construct an error matrix The norm constraint error matrix is ​​used to constrain reconstruction bias and suppress data noise.

[0036] A global-local structured regularization term is introduced to construct a joint optimization objective function that integrates global and local structure constraints. The constraints include reconstruction and orthogonality constraints, coefficient matrix equivalence constraints, and clustering assignment constraints, expressed as follows: ; In the formula, Represents the global structure regularization coefficient. Represents the local structure regularity coefficient. This represents the nuclear norm regularization term, used to mine the global pairwise association structure of samples. The term represents a row sparse regularization term used to induce row sparseness in the coefficient matrix Z.

[0037] The constraints include orthogonality constraints, coefficient matrix equivalence constraints, and clustering assignment constraints, with the following expressions: Reconstruction and Orthogonal Constraints: ; Equivalence constraints of coefficient matrix: ; Clustering assignment constraints: ; In the formula, A represents the anchor point matrix, Z represents the low-dimensional representation in the anchor point space, P represents the projection matrix, E represents the reconstruction error, and the coefficient X represents the original space reconstruction sample obtained after decoding. This represents the transpose of the projection matrix.

[0038] The introduction of global-local structured regularization terms also includes block-based iterative optimization of the joint objective function using the augmented Lagrange multiplier method (ALM) combined with the alternating direction minimization method (ADM).

[0039] Block-based iterative optimization involves constructing the augmented Lagrange function corresponding to the objective function based on the augmented Lagrange multiplier method, and using the alternating direction minimization method to decompose the multivariate joint optimization problem into multiple single-variable sub-optimization problems, solving them individually and iteratively updating the variables.

[0040] Specifically, set the hyperparameters as follows: global regularization coefficient λ = 0.1, local regularization coefficient γ = 0.05; Constrained reconstruction error row sparsity to filter image noise; nuclear norm Capture global correlations among samples; Induce Z-row sparsity by retaining only the non-zero rows corresponding to the cluster centers.

[0041] An augmented function is constructed based on the augmented Lagrange multiplier method. An alternating direction minimization method is used to update all variables P, A, Z, E, J, and W in blocks, with a convergence threshold set. The iteration stops when the change in the objective function is less than the threshold, and the optimal coefficient matrix Z is output.

[0042] Based on the weight distribution of the optimal coefficient matrix Z, 100 images are automatically grouped to achieve camera source blind clustering in the case of no labeling.

[0043] To evaluate the technical effectiveness of this invention, the accuracy of clustering algorithms in estimating the number of clusters was compared and evaluated. It should be noted that image resolutions vary between different mobile phone manufacturers; therefore, in the specific experiments, the extracted PRNU features were uniformly processed and adjusted to a size of 512×512. Subsequently, to evaluate the algorithm's performance under different PRNU feature sizes and ensure the comprehensiveness and reliability of the experimental results, the clustering performance was comprehensively compared with that of the aforementioned algorithms. Furthermore, to comprehensively compare the clustering performance of this invention with that of the aforementioned algorithms, seven commonly used metrics were used to evaluate the clustering performance: Accuracy (ACC), Normalized Mutual Information (NMI), Purity (PUR), Precision (PRE), Recall (REC), F-score (F1), and Adjusted Random Number Index (ARI). Higher values ​​for all metrics indicate better clustering performance. In addition, a comparative analysis was conducted on the predicted number of clusters and the actual number of clusters, Np / Ng. To demonstrate the technical effects of this invention, the clustering method of this invention is compared with the mainstream source camera clustering algorithms of today, namely SSC-NC (non-negativity-constrained sparse subspace clustering), BCSC (blind image camera source clustering), CCC (correlation-association clustering), and JPGL (projection matrix low-dimensional subspace clustering).

[0044] like Figure 2 As shown in Table 2, different algorithms are demonstrated in... Experimental results on the dataset show that the improved algorithm (Anchor) significantly improves upon the JPGL algorithm in several key metrics. Particularly in ACC and NMI, the Anchor algorithm achieves 0.8900 and 0.8278 respectively, compared to JPGL's 0.8700 and 0.7990, demonstrating higher accuracy and stability. Compared to other baseline algorithms, the Anchor algorithm also exhibits significant advantages. In ACC, the Anchor algorithm improves by approximately 5.95% compared to BCSC's 0.8400, and in NMI, it improves by approximately 6.07% (from 0.7805 to 0.8278). Furthermore, the Anchor algorithm also significantly outperforms BCSC in PRE and REC, with PRE improving from 0.7635 to 0.7829 (an improvement of approximately 2.5%) and REC from 0.7884 to 0.8578 (an improvement of approximately 8.8%). These improvements demonstrate the effectiveness of the Anchor algorithm in enhancing accuracy, precision, and recall, making it superior to baseline algorithms in clustering performance and model robustness.

[0045] Table 2

[0046] We also conducted a sensitivity analysis on the number of anchor points in the proposed algorithm. The range of variation is [c, 6c], where c represents the number of clusters. Figure 3 The comparison is visually illustrated with different anchor point numbers. As the number of anchor points changes, the ACC and NMI indices do not show a linear increase, but rather fluctuate. Specifically, when the number of anchor points is 2c, the ACC and NMI reach their optimal values ​​of 0.8900 and 0.8278, respectively, indicating that the proposed algorithm exhibits the best clustering effect at this point. Further increases or decreases in the number of anchor points, while maintaining good performance, do not lead to further improvement. This demonstrates that the choice of anchor point number has a significant impact on algorithm performance, and selecting an appropriate number of anchor points plays a crucial role in improving clustering results. Other detailed clustering evaluation metrics are shown in Table 3. Therefore, there is a trade-off between "improved representational ability" and "increased instability" when choosing the number of anchor points; a moderate m (such as 2c) often yields the best results.

[0047] Table 3

[0048] The sensitivity of the improved algorithm to the PRNU size was evaluated by cropping features to 128×128, 256×256, and 512×512, with all features using center cropping. Furthermore, to isolate the influence of size, while keeping the backbone network and training protocol fixed, [further details needed]. The dataset was evaluated, and the hyperparameters λ, γ, and K for each size were re-estimated. As shown in Table 4, increasing the PRNU feature size affects the dataset. The recognition performance is significantly affected.

[0049] Table 4

[0050] Figure 3 The performance comparison under different PRNU feature sizes is visually demonstrated. Looking at the ACC metric, when the feature size increased from 128×128 to 256×256, the accuracy achieved a significant leap from 0.6100 to 0.7600, a 24.6% improvement. Simultaneously, the NMI and ARI metrics, which measure cluster consistency, also showed a multiplied increase, indicating that medium-sized features can effectively capture and characterize key information in sensor fingerprints. When the feature size was further expanded to 512×512, the performance gain continued to increase, with the ACC finally reaching a peak of 0.8900, and the NMI metric again significantly increasing by 48.0% compared to the previous stage, reaching 0.8278. This indicates that larger feature windows can capture more detailed pixel-level noise residuals, thus significantly enhancing the robustness of sensor fingerprints. It is noteworthy that the trends of ACC, PRNU, and F1, among other multidimensional metrics, remained highly consistent across different sizes. This synchronous growth strongly supports the conclusion that "increasing the amount of feature information can effectively suppress random interference and reduce outliers." In conclusion, it is clear that the 512×512 PRNU feature size has an absolute advantage in pursuing ultimate accuracy.

[0051] The above embodiments are merely preferred technical solutions of the present invention and should not be considered as limitations on the present invention. The scope of protection of the present invention should be the technical solution described in the claims, including equivalent substitutions of the technical features described in the claims. That is, equivalent substitutions and improvements within this scope are also within the scope of protection of the present invention.

Claims

1. A PRNU blind image clustering forensics method based on improved anchor points, characterized in that, Includes the following steps: S1: After preprocessing the acquired images, the non-uniformity noise residual of the light response of the images is extracted by wavelet decomposition algorithm, and then the PRNU feature dataset is constructed. S2: Construct an orthogonal projection matrix to map high-dimensional PRNU features to a lower-dimensional subspace; S3: Select multiple representative samples as anchor points in the low-dimensional subspace after dimensionality reduction, construct an anchor point matrix, and then use the anchor point matrix to linearly represent the low-dimensional features to complete the lightweight reconstruction of low-dimensional data. S4: Combine the orthogonal projection matrix and anchor point matrix to construct the original feature reconstruction model, and introduce reconstruction error constraints, global nuclear norm regularization term and local row sparsity regularization term to build a unified optimization objective function. Then, use the augmented Lagrange multiplier method (ALM) and the alternating direction minimization algorithm (ADM) to iteratively solve the optimal solution of all matrices. Based on the converged representation coefficients, complete the automatic clustering of unlabeled images according to the shooting device.

2. The PRNU blind image clustering forensics method based on improved anchor points according to claim 1, characterized in that, In step S1, the extraction of the PRNU noise residual due to non-uniform optical response using wavelet decomposition includes the following sub-steps: 1) The original image is denoised using a wavelet denoising filtering algorithm to obtain a denoised image; 2) Calculate the pixel residual between the original image and the denoised image, and then separate and extract the PRNU noise residual due to non-uniform light response.

3. The PRNU blind image clustering forensics method based on improved anchor points according to claim 1, characterized in that, Step S2 includes the following sub-steps: 1) Given an original dataset X, introduce a projection matrix P to project the high-dimensional original dataset onto a low-dimensional subspace, and solve for the corresponding low-dimensional representation matrix H. The mapping relationship expression for data decomposition is: ； In the formula, Represents the projection matrix. Represents a low-dimensional representation matrix; 2) To ensure the orthogonality-preserving property of the projection transformation and eliminate redundant correlations between projection components, orthogonality constraints are applied to the projection matrix. The expression for the orthogonality constraints is as follows: ； In the formula, Represents the projection matrix The transpose of the matrix, Represents the identity matrix.

4. The PRNU blind image clustering forensics method based on improved anchor points according to claim 1, characterized in that, Step S3 includes the following sub-steps: 1) Select m representative anchor points, where the number of anchor points m is less than the total number of samples n, and define the anchor point matrix. coefficient matrix ; 2) Coefficient matrix Record the linear representation weights of each sample relative to the anchor point, used to represent the samples. Mapping relationships within the anchor point space; 3) Multiplying the anchor matrix and the coefficient matrix yields the low-dimensional sample set, expressed as: ； In the formula, the anchor point matrix Used to capture key features of low-dimensional subspaces; coefficient matrix Characterizes the linear combination relationship of each sample based on the anchor point.

5. The PRNU blind image clustering forensics method based on improved anchor points according to claim 1, characterized in that, Step S4 includes the following sub-steps: 1) Using the projection matrix P, data recovery from the low-dimensional latent representation to the original feature space is achieved. The expression for sample reconstruction is: ； In the formula, A represents the anchor matrix, Z represents the low-dimensional representation in the anchor space, P represents the projection matrix, and the coefficients are... This represents the original space reconstruction sample obtained after decoding; 2) Using the error matrix The norm constraint of the error matrix is ​​used to constrain the sparsity of the reconstruction error and suppress data noise.

6. The PRNU blind image clustering forensics method based on improved anchor points according to claim 1, characterized in that, Step S4 includes introducing a global-local structured regularization term and constructing a joint optimization objective function that integrates global and local structure constraints. The constraints include orthogonal constraints on the representation matrix, equivalence constraints on the coefficient matrix, and clustering assignment constraints. The objective function expressions are as follows: ； In the formula, Represents the global structure regularization coefficient. Represents the local structure regularity coefficient. This represents the nuclear norm regularization term, used to mine the global correlation structure between samples. The term represents a row sparse regularization term used to induce row sparseness in the coefficient matrix Z.

7. The PRNU blind image clustering forensics method based on improved anchor points according to claim 6, characterized in that, In step S4, the constraints include constraints characterizing matrix orthogonality constraints, coefficient matrix equivalence constraints, and clustering assignment constraints, with the following expressions: Reconstruction and Orthogonal Constraints: ; Equivalence constraints of coefficient matrix: ; Clustering assignment constraints: ; In the formula, A represents the anchor point matrix, Z represents the low-dimensional representation in the anchor point space, P represents the projection matrix, E represents the reconstruction error, and the coefficient X represents the original space reconstruction sample obtained after decoding. This represents the transpose of the projection matrix.

8. The PRNU blind image clustering forensics method based on improved anchor points according to claim 6, characterized in that, The introduction of global-local structured regularization terms also includes using the augmented Lagrange multiplier method (ALM) combined with the alternating direction minimization method (ADM) to perform block-based iterative optimization of the joint optimization objective function.

9. The PRNU blind image clustering forensics method based on improved anchor points according to claim 8, characterized in that, The block-based iterative optimization includes constructing the augmented Lagrange function corresponding to the objective function based on the augmented Lagrange multiplier method, and using the alternating direction minimization method to decompose the multivariate joint optimization problem into multiple single-variable sub-optimization problems, solving them individually and iteratively updating the variables.

Images