High-concealment image watermarking method based on Hadamard calculation ghost imaging
By using Hadamma matrix and Hal wavelet transformation in the computational ghost imaging technology, combining chaotic modulation and visual entropy selection technology, the problem of poor imaging quality in computational ghost imaging technology is solved, and high concealment and high-quality image watermarking effect is achieved.
Patent Information
- Application Number
- CN202411799203.1
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2024-12-09
- Publication Date
- 2025-03-07
AI Technical Summary
Existing computational ghost imaging technology faces the problem of poor imaging quality in the field of image watermarking, especially when the number of measurements is small, the quality of the reconstruction image is low.
Using Hadamar-based computational ghost imaging method, the Hadamar matrix of the cake-cutting sequence generated by the cake cutting strategy is used as a phase mask, combined with Hahal wavelet transformation and chaotic modulation technology, it is embedded in the watermark into the host image, and the reference image is selected through the calculation of visual entropy and edge entropy.
It significantly improves the security of the watermark system and the quality of the reconstructed image, reduces the calculation cost, enhances the invisibility and robustness of the watermark, and improves the ability to resist attacks.
Smart Images
Figure CN119579387A_ABST
Abstract
Description
Technical Field
[0001] The invention belongs to the technical field of information security, and in particular relates to a high-concealment image watermarking method based on Hadamard calculation ghost imaging. Background Art With the rapid development of information technology, the security of image data has become increasingly prominent, becoming a key factor affecting personal privacy protection, business secret security and digital copyright maintenance. In many optical encryption schemes, the original image is usually converted into a noisy ciphertext image, which often has obvious visual features and easily attracts the attention of crackers. Once they realize the existence of the encrypted image, they may exploit the inherent weaknesses of the encryption method to decrypt it. In this context, image watermarking technology has developed rapidly due to its ability to effectively reduce the attention of crackers. By embedding some secret information into the host image, it can not only protect copyright but also enhance the security of information. Computational ghost imaging technology has stood out in the field of image watermarking with its significant advantages in multi-wavelength adaptability, breaking through the bottleneck of traditional technology, and efficient data reconstruction and compression, bringing revolutionary changes to the field of image watermarking. In actual image watermarking applications, computational ghost imaging technology still faces some problems that need to be solved. For example, the problem of imaging quality. When using a random matrix or a Gaussian matrix as a modulated phase mask, if you want to restore an object image of considerable quality, the number of measurements required is usually much greater than the number of pixels in the reconstructed image. When the number of measurements is small, the quality of the reconstructed image is quite low. Therefore, it is urgent and necessary to comprehensively improve and innovate a more complete and more secure digital image watermarking method based on computational ghost imaging. Summary of the invention
[0002] The purpose of the present invention is to provide a highly concealed image watermarking method based on Hadamard calculation ghost imaging, which solves the problem of poor imaging quality of existing ghost imaging methods.
[0003] The technical solution adopted by the present invention is a highly concealed image watermarking method based on Hadamard calculation ghost imaging, which is implemented according to the following steps: Step 1: Get the original watermark image The intensity sequence , the light intensity sequence Rearrange to new watermark image ; Step 2: New watermark image Perform chaotic scrambling to obtain a real watermark image ; Step 3: Host image Based on Haar wavelet transform, it is decomposed into four sub-bands, namely low-frequency sub-bands , horizontal high-pass vertical low-pass sub-band , horizontal low-pass vertical high-pass sub-band , diagonal high-pass subband ; Step 4: Diagonal high-pass subbands Divide the image into blocks, sort all the blocks and select the middle blocks to combine them into a reference image ; Step 5: Put the real watermark image Embedded into reference image In the example above, we get the reference image with embedded watermark. ; Step 6: Repeat steps 4 to 5 to embed the three randomly selected interference images into the sub-bands , , middle; Step 7: Obtain the host image embedded with the watermark through the inverse transform of the Haar wavelet . The present invention is also characterized in that: The specific process of step 1 is: Step 1.1, use the 2nd order basic block to construct the Hadamard matrix of the natural sequence of any order, then the 2nd order basic block is expressed as: (1) have The Hadamard matrix of a natural sequence of order is expressed as: (2) Assume that the original watermark image The size is pixels, and satisfy ,in is an integer, then the size of the Hadamard matrix of the natural sequence is also ; Step 1.2, using the cake cutting strategy, first convert the The Hadamard matrix is rearranged row by row and integrated into indivual The matrix of pixels is sorted in ascending order according to the number of connected domains. Rearrange the matrices and then flatten each matrix into row vectors to form the Hadamard matrix of the cake-cutting sequence, and the Hadamard matrix of the cake-cutting sequence is used as a phase mask embedded in the spatial light modulator (SLM) in computational ghost imaging; Step 1.3, project the Hadamard matrix of the cake-cutting sequence obtained in step 1.2 onto the original watermark image in sequence The original watermark image is obtained by detecting with a bucket detector. The intensity sequence , light intensity sequence The length is The one-dimensional vector of is expressed as: (3) In formula (3), Represents the horizontal and vertical coordinates of the original watermark image, The Hadamard matrix representing the cake-cutting sequence, The horizontal and vertical coordinates of the Hadamard matrix elements representing the cake-cutting sequence; Step 1.4, set the light intensity sequence By converting the row and column arrangement into a new watermark image .
[0004] In step 2, obtain the real watermark image The expression is: (4) In formula (4), represents the chaotic random phase mask, Represents the horizontal and vertical coordinates of the elements in the chaotic random phase mask.
[0005] In step 3, the expression for decomposing the four subbands is: (6) In formula (6), represents the Haar wavelet transform, Represents the host image The pixel horizontal and vertical coordinates.
[0006] The specific process of step 4 is: diagonal high-pass subband Split into Pixels of non-overlapping blocks are selected, and the visual entropy and edge entropy of each block are calculated. The visual entropy and edge entropy of each block are summed up, and each block is arranged in descending order according to the summation result. The blocks in the middle after arrangement are combined into the real watermark image. Reference image of the same size ; Among them, the expression of visual entropy is: (7) In formula (7), is the intensity value The possibility of occurrence, , ; is an image block containing 256 gray levels; The expression of edge entropy is: (8) In formula (8), is the intensity value uncertainty.
[0007] In step 5, obtain the reference image embedded with the watermark The expression is: (9) In formula (9), Weight factor.
[0008] In step 7, the host image with embedded watermark is obtained The expression is: (10) In formula (10), represents the inverse transform of Haar wavelet transform; represents the subband of the image with the real watermark, , , Indicates a subband with an interfering image added.
[0009] It also includes the watermark extraction process, specifically: Step A: embedding the watermarked host image Decomposed into four subbands using Haar wavelet transform , , , ,in Contains the reference image that constitutes the embedded watermark ; Step B, from Extract the middle block selected according to the sum of visual entropy and edge entropy, and combine the extracted blocks into a reference image embedded with watermark according to the combination method in the watermark embedding process. ; Step C, using weight factors The real watermark image From the reference image embedded with watermark Take it out, the expression is: (12) Step D: put the real watermark Perform inverse chaotic mapping to obtain a new watermark image , the expression is: (13) Step E: for the new watermark image Perform row-column conversion to obtain the light intensity sequence ; Step F, reconstruct the original watermark image using formula (14) , the expression is: (14).
[0010] The beneficial effects of the present invention are: (1) The highly concealed image watermarking method based on Hadamard computational ghost imaging adopts the Hadamard matrix of the cake-cutting sequence generated by the cake-cutting strategy as a phase mask and is applied to computational ghost imaging technology, making the entire watermarking system more secure, with lower computational cost, and higher quality and imaging efficiency of the reconstructed image compared to the image reconstructed using a random matrix, significantly optimizing the reconstruction effect and showing extremely high application potential and practical value; (2) The present invention is a highly concealed image watermarking method based on Hadamard computational ghost imaging. The host image is transformed by Haar wavelet transform and one of the sub-bands is selected as the actual host image for embedding the watermark, making the watermark more difficult to distinguish visually and increasing its camouflage properties. In addition, three interference images for disturbing illegal users are respectively embedded in the other three sub-bands, further increasing the camouflage properties. The multi-level decomposition of Haar wavelet transform optimizes the watermark embedding process and improves the anti-attack capability. (3) The highly concealed image watermarking method based on Hadamard computational ghost imaging of the present invention utilizes human visual characteristics and selects a partial area combination of one of the sub-bands as a reference image for watermark embedding according to the calculation of visual entropy and edge entropy. This selection method not only improves the invisibility of the watermark, but also enhances the robustness of the watermark, while performing secondary camouflage; (4) The highly concealed image watermarking method of the present invention is based on Hadamard computational ghost imaging. Since parameters such as light wavelength, propagation distance and phase mask generated by cake-cutting strategy are used as secret keys, the security of the scheme is greatly improved. In addition, due to the highly nonlinear characteristics of Logistic mapping, the generated key sequence has extremely high sensitivity. Even a slight change will lead to completely different results, thereby greatly improving the robustness of the watermarking system. BRIEF DESCRIPTION OF THE DRAWINGS Figure 1 is a flow chart of the watermark embedding process in the method of the present invention; Figure 2 is a flow chart of the watermark extraction process in the method of the present invention; Figure 3 is the host image in the method of the present invention; Figure 4 is the original watermark image in the method of the present invention; Figure 5are three interference images in the method of the present invention; Figure 6 A host image embedded with a watermark in the method of the present invention; Figure 7 The original watermark image reconstructed in the watermark extraction process of the method of the present invention; Figure 8 The image after Gaussian filtering optimization is applied to the reconstructed original watermark image; Fig. 9 The CC value comparison diagram between the original watermark image reconstructed at different sampling rates and the original watermark image; Fig.10 The original watermark image and nonlinear correlation graph reconstructed when the sampling rate is only 4.688%; Fig.11 The original watermark image and nonlinear correlation graph reconstructed when the sampling rate is only 3.125%; Fig.12 The original watermark image and nonlinear correlation graph reconstructed when the noise intensity is 0.2; Fig.13 The original watermark image and nonlinear correlation graph reconstructed when the noise intensity is 0.4; Fig.14 The original watermark image and nonlinear correlation graph reconstructed when the noise intensity is 0.6; Fig.15 The original watermark image and nonlinear correlation graph reconstructed when the noise intensity is 0.8; Fig.16 The host image, the extracted watermark image and the nonlinear correlation graph when the occluded area reaches 25% of the upper left corner of the host image embedded with the watermark; Fig.17 The host image, the extracted watermark image and the nonlinear correlation graph when the occluded area reaches 25% above the host image embedded with the watermark. DETAILED DESCRIPTION
[0011] The present invention is described in detail below with reference to the accompanying drawings and specific embodiments.
[0012] Example 1 The highly concealed image watermarking method based on Hadamard computational ghost imaging of the present invention is specifically implemented according to the following steps: Including watermark embedding process: Step 1: Generate the Hadamard matrix of the cake-cutting sequence, use the Hadamard matrix of the cake-cutting sequence as a phase mask, and use a bucket detector to detect the original watermark image. The intensity sequence , the light intensity sequence Rearrange to new watermark image ; Step 2: the new watermark image obtained in step 1 and chaotic random phase mask generated by logistic mapping Modulate to get the real watermark image ; Step 3: To enhance the security of the watermark system, the host image Based on Haar wavelet transform, it is decomposed into four sub-bands, namely low-frequency sub-bands , horizontal high-pass vertical low-pass sub-band , horizontal low-pass vertical high-pass sub-band , diagonal high-pass subband ; The expression is: (6) In formula (6), represents the Haar wavelet transform, Represents the host image The pixel horizontal and vertical coordinates; Step 4: Diagonal high-pass subbands Divide the image into blocks, sort all the blocks and select the middle blocks to combine them into a reference image , whose size is similar to the real watermark image Consistent size; Step 5: Use weighting factors The real watermark image Embedded into reference image In the example above, we get the reference image with embedded watermark. ; The expression is: (9) Step 6: Randomly select three interference images with the same size as the real watermark image to disturb the illegal user, repeat steps 4 and 5, and embed the three interference images into , , in subband; Step 7: Obtain the host image embedded with the watermark through the inverse transform of the Haar wavelet ; The expression is: (10) In formula (10), represents the inverse transform of Haar wavelet transform; represents the subband of the image with the real watermark, , , Indicates a subband with an interfering image added.
[0013] Example 2 Based on Example 1, the specific process of step 1 is as follows: Step 1.1, use the 2nd order basic block to construct the Hadamard matrix of the natural sequence of any order, then the 2nd order basic block is expressed as: (1) have The Hadamard matrix of a natural sequence of order is expressed as: (2) Assume that the original watermark image The size is pixels, and satisfy ,in is an integer, then the size of the Hadamard matrix of the natural sequence is also ; Step 1.2, using the cake cutting (CC) strategy, first convert the The Hadamard matrix is rearranged row by row and integrated into indivual The matrix of pixels is sorted in ascending order according to the number of connected domains. Rearrange the matrices and then flatten each matrix into row vectors to form the Hadamard matrix of the cake-cutting sequence, and the Hadamard matrix of the cake-cutting sequence is used as a phase mask embedded in the spatial light modulator (SLM) in computational ghost imaging; The element values in the Hadamard matrix of a natural sequence have only two results, +1 and -1, and the distribution in space is square and symmetrical. In addition, the Hadamard matrix of a natural sequence is also an orthogonal matrix, which means that any two columns or rows selected from it are orthogonal. The key to the Hadamard matrix of a natural sequence being able to be used as a measurement matrix and produce excellent reconstruction effects is that it has two important properties: the irrelevance of columns and the orthogonality of rows. If the Hadamard matrix is arranged in increasing order according to the number of connected domains, the coherent region of each speckle will naturally show a transition from wide to narrow. If each Hadamard matrix to be sorted is imagined as a cake, then we can count how many pieces the cake needs to be cut into, and each piece can be regarded as a connected region. This method is called a cake cutting strategy. Step 1.3, after embedding the Hadamard matrix of the cake-cutting sequence obtained in step 1.2 into the spatial light modulator (SLM) of the actual computational ghost imaging system, the original watermark image is obtained by detecting with a bucket detector. The intensity sequence , light intensity sequence The length is The one-dimensional vector of is expressed as: (3) In formula (3), Represents the horizontal and vertical coordinates of the original watermark image, The Hadamard matrix representing the cake-cutting sequence, The horizontal and vertical coordinates of the Hadamard matrix elements representing the cake-cutting sequence; the light intensity sequence is the light intensity sequence corresponding to the Hadamard matrix of the i-th cake-cutting sequence; Step 1.4, set the light intensity sequence By converting the row and column arrangement into a new watermark image , new watermark image The size is .
[0014] Example 3 Based on Example 2, in step 2, a real watermark image is obtained. The expression is: (4) In formula (4), represents the chaotic random phase mask, represents the horizontal and vertical coordinates of the elements in the chaotic random phase mask; Among them, the chaotic random phase mask is obtained The process is: Assuming the initial value is and the bifurcation parameter , we can get a length of A one-dimensional random sequence is converted into a two-dimensional matrix by row-column conversion. X , , the two-dimensional matrix X Chaotic random phase mask obtained by phase modulation , chaotic random phase mask The phase function is distributed in between; (5) In formula (5), is the bifurcation parameter; is the iteration parameter, ; is the initial value; from At the beginning, the chaotic system begins to bifurcate periodically; when When , the sequence of iterative values generated is in a chaotic state. When the initial value of the parameter changes slightly, completely different non-periodic and non-convergent random iterative values will be generated. The closer the value is to 4, the better the randomness of the chaotic system.
[0015] In the method of the present invention, chaotic mapping technology is used to generate random phase masks. In this process, the initial value of the chaotic function and the bifurcation parameter are set as private key elements; this design ensures that the phase mask The generation of watermarks is highly random and secure, because chaotic systems are extremely sensitive to small changes in initial values and parameters and can produce completely different output sequences. Therefore, these private keys play a vital role in ensuring the unpredictability and anti-attack capabilities of watermarks.
[0016] Example 4 Based on Example 3, the specific process of step 4 is as follows: Diagonal high-pass subband Split into Pixels of non-overlapping blocks are selected, and the visual entropy and edge entropy of each block are calculated. The visual entropy and edge entropy of each block are summed up, and each block is arranged in descending order according to the summation result. The blocks in the middle after arrangement are combined into the real watermark image. Reference image of the same size ; As a common method for evaluating image structure and content, visual entropy achieves global quantitative evaluation by comprehensively considering the intensity value distribution of all pixels in the image.
[0017] Among them, the expression of visual entropy is: (7) In formula (7), is the intensity value The possibility of occurrence, , ; is an image block containing 256 gray levels; When the intensity values of adjacent pixels are independent of each other when processing image blocks, it is necessary to further consider the spatial correlation between pixel gray levels. This can be achieved by introducing the concept of edge entropy, which can quantify the complexity of edge information in image blocks.
[0018] The expression of edge entropy is: (8) In formula (8), is the intensity value uncertainty.
[0019] Obviously, it is crucial to select the right block combination as the reference image. If the blocks located in the front of the image are selected, the watermark image may be deformed or distorted unnecessarily because these blocks usually contain more details and edge information. On the contrary, if the blocks located in the back of the image are selected, although these blocks may be smoother, they may also lack sufficient details and cause the watermark information to become blurred or difficult to recognize after embedding, thereby causing the loss of watermark information. Therefore, the present invention selects blocks located in the middle of the image to form a reference image. These middle blocks usually contain enough details to support the embedding of the watermark, but will not cause the deformation of the watermark due to excessive complexity.
[0020] Example 5 On the basis of Example 4, the method of the present invention further includes a watermark extraction process, specifically: Step A: embedding the watermarked host image Decomposed into four subbands using Haar wavelet transform , , , ,in Contains the reference image that constitutes the embedded watermark ; The expression is: (11) Step B, from Extract the middle block selected according to the sum of visual entropy and edge entropy, and combine the extracted blocks into a reference image embedded with watermark according to the combination method in the watermark embedding process. ; Step C, using weight factors The real watermark image From the reference image embedded with watermark take it out; The expression is: (12) Step D: put the real watermark Perform inverse chaotic mapping to obtain a new watermark image ; The expression is: (13) Step E: for the new watermark image Perform row-column conversion to obtain the light intensity sequence ; Step F, reconstruct the original watermark image using formula (14) ; The expression is: (14).
[0021] Example 6 In this embodiment, the selected host image is an image in the USC-SIPI image test database, such as Figure 3 As shown, specifically The grayscale image "Barb" of pixels; Figure 4 As shown in the figure, the original watermark image is randomly generated to simulate the actual target scene. The binary image “Zheng” (the target image in the computational ghost imaging technique).
[0022] It is worth noting that in the actual image transmission process, the sender of the image needs to transmit the Hadamard matrix of the cake-cutting sequence to the receiver in addition to embedding the watermarked host image. , bifurcation parameters , initial value , weight factor The correct watermark image can be extracted through the watermark extraction process only if the correct secret key is mastered by the receiver.
[0023] In this embodiment, the calculation of ghost imaging, chaotic modulation, watermark embedding, and watermark extraction are all implemented by digital simulation, and the solution is implemented by MATLAB simulation.
[0024] The specific process of watermark embedding is as follows: Figure 1 As shown, in step 1, we can obtain The Hadamard matrix of the natural sequence is obtained by using the cake-cut (CC) strategy. The Hadamard matrix of the natural sequence is rearranged row by row and integrated into 64 A matrix of pixels (that is, The values of are all 8), and the 64 matrices are reordered in ascending order according to the number of connected domains, and each matrix is flattened into 64 row vectors to form the Hadamard matrix of the cake-cutting sequence, whose size is also , in order to fully sample the original watermark image "Zheng", it is necessary to Sampling, that is, 4096 samplings are required. Therefore, at least 4096 Hadamard matrices of the cake-cutting sequence need to be generated to complete the full sampling. After the Hadamard matrices of the cake-cutting sequence are embedded into the spatial light modulator (SLM) of the actual computational ghost imaging system, the light intensity sequence of the original watermark image "Zheng" is detected by the bucket detector. , we can get , whose length is 4096.
[0025] Step 2: Add the new watermark image and chaotic random phase mask generated by logistic mapping (Size is ) is modulated by formula (4), and the actual watermark image size is ; Bifurcation Parameter of Logistic Map Set to 3.99995, initial value Set to 0.35, and use formula (5) to get a length of A one-dimensional random sequence is converted into a two-dimensional matrix by row-column conversion. X , , the two-dimensional matrix X Chaotic random phase mask obtained by phase modulation , and its size is .
[0026] Step 3: Decompose the host image "Barb" into four sub-bands based on Haar wavelet transform, which are low-frequency sub-bands , horizontal high-pass vertical low-pass sub-band , horizontal low-pass vertical high-pass sub-band , diagonal high-pass subband ; Step 4: The diagonal high-pass subband Decompose into Pixel non-overlapping blocks are selected, the visual entropy and edge entropy of each block are calculated, the visual entropy and edge entropy of each block are summed, each block is sorted in descending order according to the summed result, and the 4 blocks in the middle after sorting (blocks ranked 14-17) are combined as the reference image , the size is .
[0027] Step 5: Use the weight factor The real watermark image Embedded into reference image In the example above, we get the reference image with embedded watermark. , and its size is ; The actual weight factor used for fusion between the reference image and the true watermarked image Set to ; Step 6, select the size The binary images "Dan", "Yin", and "Yu" are used as three interference images, such as Figure 5 Repeat steps 4 and 5 to embed the three interference images into , , in subband; Step 7: Obtain the host image embedded with the watermark by inverse transform of Haar wavelet according to formula (10): ,like Figure 6 As shown, no effective information of the watermarked image can be obtained visually.
[0028] When the receiver receives the host image embedded with the watermark and the phase mask , bifurcation parameters , initial value , weighting factor After waiting for the secret key, you can Figure 2 The watermark extraction process shown extracts the correct watermark image.
[0029] Step A: embedding the watermarked host image Formula (11) is used to perform Haar wavelet transform and decompose it into four subbands , , , ,in Contains the reference image that constitutes the embedded watermark ; Step B, from Extract the middle block selected according to the sum of visual entropy and edge entropy, and combine the extracted 4 blocks (blocks ranked 14-17) into a reference image embedded with watermark ; What needs to be noted here is that we need to remember the important positions in advance; Step C, using the weight factor The real watermark image From the reference image embedded with watermark take it out; Step D: put the real watermark The new watermark image is obtained by inverse chaotic mapping using formula (13): ; Step E: for the new watermark image Perform row-column conversion to obtain the light intensity sequence ; Step F, reconstruct the original watermark image using formula (14) ,like Figure 7 As shown; and the reconstructed original watermark image is optimized by Gaussian filtering, and the obtained image is as follows Figure 8 shown.
[0030] After reconstructing the original watermark image, the feasibility analysis of the method of the present invention needs to be carried out. In order to prove that the method of the present invention has good security and robustness, the following two evaluation indicators are needed to verify the feasibility of the system: (1) In order to evaluate the security performance of the watermark, the original watermark image used in the method of the present invention and the reconstructed original watermark image are subjected to correlation coefficient (CC) analysis. If the value of the correlation coefficient is close to 1, it indicates that there is a high correlation between adjacent pixels. On the contrary, if the value is close to 0, it means that the correlation between adjacent pixels is low. The mathematical calculation formula of the correlation coefficient can be expressed as:
[0031] In the formula, represents the expected value calculation, is the original watermark image, Represents the reconstructed original watermark image.
[0032] (2) In order to verify the practical feasibility of the method of the present invention in a deeper level, we need to add another evaluation index to the method of the present invention, that is, to perform nonlinear correlation coefficient (NC) analysis between the original watermark image and the reconstructed original watermark image. The mathematical calculation expression is:
[0033] In the formula, represents Fourier transform, represents the inverse Fourier transform, Used to compute the complex conjugate of a parameter. represents the intensity coefficient of nonlinearity, which is set to 0.4 in this embodiment; is the original watermark image, Represents the reconstructed original watermark image.
[0034] The specific analysis is: Sampling rate analysis: In order to verify the imaging quality of the Hadamard calculation ghost imaging of the cake-cutting sequence in the proposed scheme, the image is reconstructed at different sampling rates. Fig. 9It can be seen that even when the sampling rate is 6.25%, the outline of the binary image can still be seen, and the correlation coefficient analysis of the reconstructed image is performed. The numerical values in the figure show the feasibility of the proposed scheme. In order to further verify the analysis of the sampling rate, the watermark image was reconstructed when the sampling rate was only 4.688% and 3.125%, respectively. It can be found that no effective information can be seen from the image. Therefore, a nonlinear correlation analysis was performed on the reconstructed original watermark image, as shown in Figure 2. Fig.10 and Fig.11 As shown in the figure, it can be seen that the peak in the middle of the nonlinear coefficient correlation diagram can indicate that the reconstructed original watermark image is related to the original watermark image, and it contains the content of the original watermark image. This shows that although the reconstructed original watermark image has a decrease in visual quality, it contains the effective information of the original watermark image, which shows the high efficiency of the method of the present invention.
[0035] Gaussian noise attack: In order to verify the robustness of the method of the present invention, the noise (such as random Gaussian noise) attack analysis of the host image embedded with the watermark is very important. Therefore, in the method of the present invention, Gaussian random noise with different intensity coefficients is used to attack the host image embedded with the watermark. The interference mode of Gaussian random noise on the host image embedded with the watermark can be expressed as:
[0036] in, and They represent the original watermarked host image and the watermarked host image after noise interference, is the noise intensity coefficient, is the Gaussian noise function.
[0037] Gaussian random noise with different scale factors is used to attack the host image embedded with the watermark and different reconstruction algorithms are used to reconstruct the original watermark image. Fig.12 , Fig.13 , Fig.14 and Fig.15 The noise intensity coefficient is The original watermark image reconstructed when the coefficients are set to 0.4, 0.6, 0.8 and 1.0 respectively and the corresponding nonlinear correlation graph. It can be seen from the figure that despite the interference of Gaussian noise, the structural information of the reconstructed original watermark image can still be obtained. In addition, the quality of the reconstructed original watermark image decreases with the increase of the Gaussian random noise intensity coefficient, but the effective watermark information can still be identified. Similarly, after further nonlinear correlation coefficient analysis, it can be seen from the figure that the peak in the middle can indicate that the reconstructed original watermark image is related to the original watermark image, and it contains the content of the original watermark image. This shows that although the reconstructed original watermark image has a decrease in visual quality, it contains the effective information of the original watermark image, which further shows that the method of the present invention has strong robustness to Gaussian noise attacks.
[0038] Occlusion Noise Attack: To examine the impact of occlusion attack on the original watermarked image, in which the data in specific regions of the original watermarked image are replaced with zeros, which means the intensity information of some pixels is lost. Fig.16 and Fig.17 The occluded host images embedded with watermarks are shown, where 25% and 25% of the intensity values are lost from the upper left corner and the upper side, respectively, and the corresponding reconstructed original watermark images are shown. From the corresponding nonlinear correlation graph, it can be seen that the original watermark image reconstructed under the occlusion noise attack cannot obtain effective information through visual detection, but the peak in the middle of the nonlinear coefficient correlation graph shows that the reconstructed original watermark image is related to the original watermark image, and it contains the content of the original watermark image. This shows that although the reconstructed original watermark image has a decrease in visual quality, it contains effective information of the original watermark image, proving that the method of the present invention is feasible.
Claims
1. A highly concealed image watermarking method based on Hadamard computational ghost imaging, characterized in that: Follow these steps to implement: Step 1: Get the original watermark image The intensity sequence , the light intensity sequence Rearrange to new watermark image ; Step 2: New watermark image Perform chaotic scrambling to obtain a real watermark image ; Step 3: Host image Based on Haar wavelet transform, it is decomposed into four sub-bands, namely low-frequency sub-band , horizontal high-pass vertical low-pass sub-band , horizontal low-pass vertical high-pass sub-band , diagonal high-pass subband ; Step 4: Diagonal high-pass subbands Divide the image into blocks, sort all the blocks and select the middle blocks to combine them into a reference image ; Step 5: Put the real watermark image Embedded into reference image In the example above, we get the reference image with embedded watermark. ; Step 6: Repeat steps 4 to 5 to embed the three randomly selected interference images into the sub-bands , , middle; Step 7: Obtain the host image embedded with the watermark through the inverse transform of the Haar wavelet .
2. The highly concealed image watermarking method based on Hadamard computational ghost imaging according to claim 1 is characterized in that: The specific process of step 1 is: Step 1.1, use the 2nd order basic block to construct the Hadamard matrix of the natural sequence of any order, then the 2nd order basic block is expressed as: （1） have The Hadamard matrix of a natural sequence of order is expressed as: （2） Assume that the original watermark image The size is pixels, and satisfy ,in is an integer, then the size of the Hadamard matrix of the natural sequence is also ; Step 1.2, using the cake cutting strategy, first convert the The Hadamard matrix is rearranged row by row and integrated into indivual The matrix of pixels is sorted in ascending order according to the number of connected domains. Rearrange the matrices and then flatten each matrix into row vectors to form the Hadamard matrix of the cake-cutting sequence, and the Hadamard matrix of the cake-cutting sequence is used as a phase mask embedded in the spatial light modulator (SLM) in computational ghost imaging; Step 1.3, project the Hadamard matrix of the cake-cutting sequence obtained in step 1.2 onto the original watermark image in sequence The original watermark image is obtained by detecting with a bucket detector. The intensity sequence , light intensity sequence The length is The one-dimensional vector of is expressed as: （3） In formula (3), Represents the horizontal and vertical coordinates of the original watermark image, The Hadamard matrix representing the cake-cutting sequence, The horizontal and vertical coordinates of the Hadamard matrix elements representing the cake-cutting sequence; Step 1.4, set the light intensity sequence By converting the row and column arrangement into a new watermark image .
3. The highly concealed image watermarking method based on Hadamard computational ghost imaging according to claim 2 is characterized in that: In step 2, the real watermark image is obtained The expression is: （4） In formula (4), represents the chaotic random phase mask, Represents the horizontal and vertical coordinates of the elements in the chaotic random phase mask.
4. The highly concealed image watermarking method based on Hadamard computational ghost imaging according to claim 3 is characterized in that: In step 3, the expression for decomposing the four subbands is: （6） In formula (6), represents the Haar wavelet transform, Represents the host image The pixel horizontal and vertical coordinates.
5. The highly concealed image watermarking method based on Hadamard computational ghost imaging according to claim 4 is characterized in that: The specific process of step 4 is: diagonal high-pass subband Split into The non-overlapping blocks of pixels are selected, the visual entropy and edge entropy of each block are calculated, the visual entropy and edge entropy of each block are summed, and each block is arranged in descending order according to the summation result, and the blocks in the middle after arrangement are combined into the real watermark image. Reference image of the same size ; Among them, the expression of visual entropy is: （7） In formula (7), is the intensity value The possibility of occurrence, , ; is an image block containing 256 gray levels; The expression of edge entropy is: （8） In formula (8), is the intensity value uncertainty.
6. The highly concealed image watermarking method based on Hadamard computational ghost imaging according to claim 5 is characterized in that: In step 5, the reference image with embedded watermark is obtained The expression is: （9） In formula (9), Weight factor.
7. The highly concealed image watermarking method based on Hadamard computational ghost imaging according to claim 6 is characterized in that: In step 7, the host image with embedded watermark is obtained The expression is: （10） In formula (10), represents the inverse transform of Haar wavelet transform; represents the subband of the image with the real watermark, , , Indicates a subband with an interfering image added.
8. The highly concealed image watermarking method based on Hadamard computational ghost imaging according to claim 7 is characterized in that: It also includes the watermark extraction process, specifically: Step A: embedding the watermarked host image Decomposed into four subbands using Haar wavelet transform , , , ,in Contains the reference image that constitutes the embedded watermark ; Step B, from Extract the middle block selected according to the sum of visual entropy and edge entropy, and combine the extracted blocks into a reference image embedded with watermark according to the combination method in the watermark embedding process. ; Step C, using weight factors The real watermark image From the watermarked reference image Take it out, the expression is: （12） Step D: put the real watermark Perform inverse chaotic mapping to obtain a new watermark image , the expression is: （13） Step E: for the new watermark image Perform row-column conversion to obtain the light intensity sequence ; Step F, reconstruct the original watermark image through formula (14) , the expression is: （14）。