Image watermark embedding and extraction method based on GSVD embedding algorithm

Abstract

The application belongs to the technical field of digital watermarking, and discloses an image watermark embedding and extracting method based on a GSVD embedding algorithm, and the embedding comprises the following steps: decomposing a host image into subblocks of different frequencies through one-dimensional Haar discrete wavelet transform to obtain a plurality of first components of the host image; performing singular value decomposition on a first red component in low frequencies in a horizontal direction and in high frequencies in a vertical direction in the plurality of first components by using an SVD algorithm to obtain a first decomposition result; embedding an original watermark image into a singular value matrix of the host image through a GSVD embedding algorithm, and obtaining a matrix after embedding the watermark through vector synthesis; performing singular value decomposition on the matrix by using the SVD algorithm to obtain a second decomposition result; obtaining a second red component containing watermark information through inverse singular value decomposition based on the first decomposition result and the second decomposition result; and performing inverse wavelet transform based on the plurality of components and the second red component to obtain a final host image after embedding the watermark.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of digital watermarking, and particularly relates to an image watermark embedding and extracting method based on a GSVD embedding algorithm. BACKGROUND

[0002] As a core technical means to protect image information security, image watermarking technology has become a key research direction in the field of information security in recent years. According to the visibility of watermark, image watermarking methods can be divided into two categories: visible watermark and invisible watermark. Among them, the visible watermark technology realizes the copyright declaration by superimposing a semi-transparent mark (such as text, LOGO) on the surface of the document, image and video carrier. Its core characteristics are identifiability and anti-removal. That is, under the premise of not significantly affecting the readability of the carrier content, it is necessary to ensure that the mark is difficult to be simply erased. However, with the rapid iteration of digital image processing technologies such as image inpainting, edge filling and AI watermark removal algorithm, attackers can use professional tools to remove the visible watermark without trace, which poses a serious challenge to the security protection capability of the visible watermark technology.

[0003] Corresponding to the visible watermark, the invisible watermark technology has higher security and wider application scenarios, and can cover copyright protection of multiple types of carriers such as text, image, audio and video. Its core advantage lies in the visual imperceptibility of the watermark. The copyright owner can embed his unique identity as a watermark into the host carrier. When a copyright dispute occurs, the watermark information can be extracted and verified through a special algorithm, thereby completing the right protection of the carrier copyright. Therefore, the invisible digital watermark technology has irreplaceable practical value in the fields of product anti-counterfeiting, copyright tracing and information secret transmission.

[0004] In the current mainstream digital watermark embedding scheme, the additive watermark method is still a common means in the industry, that is, the watermark is embedded into the host image by directly superimposing the watermark information. However, in the watermark extraction process, most watermark methods based on SVD have significant technical limitations: the extraction process needs to rely on the original watermark template or the original host image, which not only leads to false positive detection problems in the system, but also greatly increases the vulnerability of the system to pseudo attack. Attackers can bypass the detection mechanism by forging the original information, thereby damaging the security of the watermark system.

[0005] Therefore, the design and optimization of the watermark system have become the core research focus in the field of information security. It is of positive and important significance to promote the progress of the field of image copyright protection research to propose a watermark embedding algorithm with high security and high reliability, solve the false positive false report problem in the existing watermark system and the problem of being vulnerable to pseudo attack. SUMMARY

[0006] The present application aims at solving the problems in the prior art, and provides the following scheme:

[0007] An image watermark embedding method based on GSVD embedding algorithm, comprising the following steps:

[0008] decomposing a color host image into sub-blocks of different frequencies by one-dimensional Haar discrete wavelet transform to obtain a plurality of first components of the host image in horizontal and vertical directions;

[0009] performing singular value decomposition on a first red component LH r in the low frequency in the horizontal direction and the high frequency in the vertical direction among the plurality of first components using an SVD algorithm to obtain a first decomposition result (U, S, V), wherein U and V represent orthogonal matrices of LH r , and S represents a singular value matrix of LH r ;

[0010] embedding an original watermark image w into the singular value matrix S of LH r of the color host image by a GSVD embedding algorithm to obtain a unitary matrix U1, a unitary matrix V1, a square matrix X1, a non-negative diagonal matrix C1 and a non-negative diagonal matrix S1;

[0011] obtaining a matrix W after embedding the watermark by vector synthesis of the unitary matrix V1, the square matrix X1 and the non-negative diagonal matrix S1;

[0012] performing singular value decomposition on the matrix W by the SVD algorithm to obtain a second decomposition result (Uh, Sh, Vh), wherein Uh and Vh represent orthogonal matrices of W, and Sh represents a singular value matrix of W, and (Uh, Sh) is saved as side information;

[0013] obtaining a second red component LH r ' containing watermark information by inverse singular value decomposition based on the first decomposition result and the second decomposition result;

[0014] performing inverse wavelet transform based on the plurality of components and the second red component LH r ' to obtain a final host image IW after embedding the watermark.

[0015] Preferably, the plurality of first components include low frequency components LL in horizontal and vertical directions, low frequency in horizontal direction and high frequency in vertical direction LH, high frequency in horizontal direction and low frequency in vertical direction HL, and high frequency components HH in horizontal and vertical directions.

[0016] Preferably, the method for obtaining the matrix W after embedding the watermark comprises:

[0017] ,

[0018] wherein VS represents vector synthesis, and i represents an imaginary unit.

[0019] The application further provides an image watermark extraction method based on the GSVD embedding algorithm, which is used for extracting the watermark in the image obtained by the embedding method, and comprises the following steps:

[0020] The embedded watermark host image is decomposed into sub-blocks of different frequencies through one-dimensional haar discrete wavelet transform, to obtain several second components of the embedded watermark host image in horizontal and vertical directions;

[0021] The third red component LHT r in the low frequency in the horizontal direction and the high frequency in the vertical direction of the second components is singular value decomposed by using the SVD algorithm, to obtain a third decomposition result (UT, ST, VT), wherein UT and VT represent orthogonal matrices of LHT r , and ST represents a singular value matrix of LHT r ;

[0022] The singular value matrix W' containing the watermark is obtained by combining the side information (Uh, Sh) and the third decomposition result;

[0023] The singular value matrix W' is vector decomposed to obtain a unitary matrix V1', a square matrix X1' and a non-negative diagonal matrix S1' corresponding to the watermark image;

[0024] The watermark F is recovered based on the unitary matrix V1', the square matrix X1' and the non-negative diagonal matrix S1'.

[0025] Preferably, the second components comprise low frequency components LLT in horizontal and vertical directions, low frequency in the horizontal direction and high frequency in the vertical direction LHT, high frequency in the horizontal direction and low frequency in the vertical direction HLT and high frequency components HHT in horizontal and vertical directions.

[0026] Preferably, the method for obtaining the watermark F comprises:

[0027] ,

[0028] Wherein, alpha represents the watermark embedding strength, and T represents the transpose of the matrix.

[0029] Compared with the prior art, the application has the following beneficial effects:

[0030] (1) Compared with the watermark-host embedding paradigm commonly used in existing watermarking schemes, this invention achieves watermark embedding by constructing a watermark-host joint embedding mechanism based on GSVD, breaking through the limitations of traditional additive methods; (2) This watermarking method can achieve efficient semi-blind extraction, and the extraction process does not require the participation of the original host image and the original watermark template, which simplifies the process while ensuring the practicality of the system; (3) The method proposed in this invention can effectively avoid the risk of false positives in the watermark detection process and ensure the accuracy of watermark ownership confirmation; (4) Compared with the widely used SVD-based watermarking system, the method proposed in this invention can resist spoofing attacks; (5) The GSVD-based embedding algorithm proposed in this invention can be extended to any additive watermark embedding method. Attached Figure Description

[0031] To more clearly illustrate the technical solution of the present invention, the drawings used in the embodiments are briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0032] Figure 1 This is a schematic diagram of the image watermark embedding method according to an embodiment of the present invention;

[0033] Figure 2 This is a schematic diagram of the image watermark extraction method according to an embodiment of the present invention;

[0034] Figure 3 The embodiments of the present invention include the original watermarked image, the original host image, the host image after embedding the watermark, and the watermarked image extracted without any attacks, wherein... Figure 3 Image (a) is the original watermark image. Figure 3 (b) is the original host image. Figure 3 (c) The host image after embedding the watermark. Figure 3 (d) The watermarked image extracted without any attack;

[0035] Figure 4 for Figure 3 (c) shows the watermarked image extracted after being subjected to different image processing attacks, where... Figure 4 In the middle (a), the extraction result is when subjected to 0.01 Gaussian noise. Figure 4 (b) shows the extraction result when subjected to 0.05 Gaussian noise. Figure 4 (c) shows the extraction results when subjected to 0.1 Gaussian noise. Figure 4 (d) represents the extraction result under a 6.25% shear attack. Figure 4 (e) represents the extraction result under a 12.5% ​​shear attack.Figure 4 Middle (f) is the extraction result when subjected to 25% shear attack, Figure 4 Middle (g) is the extraction result when subjected to median filter attack, Figure 4 Middle (h) is the extraction result when subjected to low-pass filter attack, Figure 4 Middle (i) is the extraction result when subjected to 0.5 Gaussian blur attack, Figure 4 Middle (j) is the extraction result when subjected to screenshot attack, Figure 5 Middle (k) is the extraction result when subjected to Moire attack;

[0036] Figure 5 is the visual result of the present embodiment against the first camouflage attack, wherein, Figure 5 Middle (a) is the original test watermark image f1, Figure 5 Middle (b) is the original test watermark image f2, Figure 5 Middle (c) is the host image after embedding watermark Figure 5 Middle (a), Figure 5 Middle (d) is the host image after embedding watermark Figure 5 Middle (b), Figure 5 Middle (e) is the watermark image extracted from Figure 5 Middle (c), Figure 5 Middle (f) is the watermark image extracted from Figure 6 Middle (d);

[0037] Figure 6 is the visual result of the present embodiment against the second camouflage attack, wherein, Figure 5 Middle (a) is the host image after embedding watermark Figure 6 Middle (a), Figure 5 Middle (b) is the host image after embedding watermark Figure 6 Middle (b), Figure 6 Middle (c) is the watermark image extracted from Figure 7 Middle (a);

[0038] Figure 7 is the visual result against the third camouflage attack, wherein, Figure 5 Middle (a) is the host image after embedding watermark Figure 7 Middle (a), Figure 5 Middle (b) is the host image after embedding watermark Figure 7 Middle (b), Figure 7 Middle (c) is a randomly generated noise image, Figure 7 Middle (d) is the watermark image extracted from Figure 7 Middle (c) using watermark f1 side information, Figure 7 Middle (e) is the watermark image extracted from Figure 1 Middle (c) using watermark f2 side information. DETAILED DESCRIPTION

[0039] The technical solutions in the embodiments of the present application will be described clearly and completely below with reference to the drawings in the embodiments of the present application. Obviously, the described embodiments are only part of the embodiments of the present application, rather than all the embodiments. Based on the embodiments in the present application, all other embodiments obtained by a person of ordinary skill in the art without creative work fall within the protection scope of the present application.

[0040] In order to make the above objectives, characteristics and advantages of the present application more apparent, the present application will be further described in detail below with reference to the drawings and specific embodiments.

[0041] Embodiment one:

[0042] In this embodiment, as shown in the figure, an image watermark embedding method based on a GSVD embedding algorithm includes the following steps: Figure 2

[0043] S1. Decompose a color host image into sub-blocks of different frequencies by one-dimensional Haar discrete wavelet transform to obtain several first components of the host image in horizontal and vertical directions:

[0044] ,

[0045] wherein DWT represents discrete wavelet transform, haar represents wavelet transform base, IH represents the color host image, LL represents low-frequency components in horizontal and vertical directions of the color host image, LH represents low-frequency in horizontal direction and high-frequency in vertical direction (including a first red component LH r , a first green component LH g and a first blue component LH b ) of the color host image, HL represents high-frequency in horizontal direction and low-frequency in vertical direction of the color host image, and HH represents high-frequency components in horizontal and vertical directions of the color host image.

[0046] S2. Perform singular value decomposition on the first red component LH r in the low-frequency in horizontal direction and the high-frequency in vertical direction LH of the several first components by using an SVD algorithm to obtain a first decomposition result (U, S, V):

[0047] ,

[0048] wherein U and V represent orthogonal matrices of LH r , and S represents a singular value matrix of LH r .

[0049] ​S3. Embedding the original watermark image w into the LH component of the color host image by the GSVD embedding algorithm to obtain a singular value matrix S of the LH component of the color host image: r ,

[0050] ,

[0051] wherein, a represents the watermark embedding strength.

[0052] S4. Obtaining the matrix W after embedding the watermark by vector synthesis of the unitary matrix V1, the square matrix X1 and the non-negative diagonal matrix S1.

[0053] The method for obtaining the matrix W after embedding the watermark comprises:

[0054] ,

[0055] wherein, VS represents vector synthesis, and i represents the imaginary unit.

[0056] S5. Performing singular value decomposition on the matrix W by the SVD algorithm to obtain a second decomposition result (Uh, Sh, Vh):

[0057] ,

[0058] wherein, Uh and Vh represent the orthogonal matrix of W, and Sh represents the singular value matrix of W, and the matrix (Uh, Sh) is saved as side information for watermark extraction.

[0059] S6. Based on the first decomposition result and the second decomposition result, obtaining the second red component LH r ’ containing the watermark information by inverse singular value decomposition:

[0060] ,

[0061] wherein, T represents the transpose of the matrix.

[0062] S7. Performing inverse wavelet transform on the plurality of components and the second red component LH r ’ to obtain a final host image IW after embedding the watermark:

[0063] .

[0064] Embodiment two:

[0065] In this embodiment, as shown in Figure 3 , an image watermark extraction method based on the GSVD embedding algorithm comprises the following steps:

[0066] S1. decompose the host image after embedding the watermark into sub-blocks of different frequencies by one-dimensional Haar discrete wavelet transform, to obtain several second components of the host image after embedding the watermark in horizontal and vertical directions;

[0067] ,

[0068] wherein, DWT represents discrete wavelet transform, haar represents wavelet transform base, IW represents the host image after embedding the watermark, LLT represents low-frequency components of the host image after embedding the watermark in horizontal and vertical directions, LHT represents low-frequency components of the host image after embedding the watermark in horizontal direction and high-frequency components (including the second red component LHT r , the second green component LHT g and the second blue component LHT b ) in vertical direction, HLT represents high-frequency components in horizontal direction and low-frequency components in vertical direction, and HHT represents high-frequency components in horizontal and vertical directions.

[0069] S2. perform singular value decomposition on the third red component LHT r in the low-frequency components in horizontal direction and the high-frequency components in vertical direction LHT in the several second components by using SVD algorithm, to obtain the third decomposition result (UT, ST, VT):

[0070] ,

[0071] wherein, UT and VT represent orthogonal matrices of LHT r , and ST represents the singular value matrix of LHT r .

[0072] S3. combine the side information matrix (Uh, Sh) and the third decomposition result to obtain the singular value matrix W' containing the watermark:

[0073] ,

[0074] wherein, T represents the transpose of the matrix.

[0075] S4. perform vector decomposition on the singular value matrix W' to obtain the unitary matrix V1', the square matrix X1' and the non-negative diagonal matrix S1' corresponding to the watermark image:

[0076] ,

[0077] wherein, VD represents vector decomposition.

[0078] S5. restore the watermark F based on the unitary matrix V1', the square matrix X1' and the non-negative diagonal matrix S1'.

[0079] Methods for obtaining watermark F include:

[0080] ,

[0081] Where α represents the watermark embedding strength, and T represents the transpose of the matrix.

[0082] Figure 3 Image (a) is the original watermark image. Figure 3 (b) is the original host image. Figure 3 Image (c) is the host image after the watermark has been embedded. Figure 3 As can be seen in (c), the host image after embedding the watermark is indistinguishable from the original host image to the naked eye. The watermarked image extracted without any attack is shown below. Figure 4 As shown in (d), it can be seen that when the host image is not attacked, the extracted watermark image is indistinguishable from the input watermark image to the naked eye. Furthermore, to quantitatively evaluate the extraction results, this invention calculated the correlation coefficient between the original watermark image and the extracted watermark image. The calculated correlation coefficient between the watermark image extracted from the host and the original watermark is 1. These results indicate that there is no difference between the extracted watermark image and the original watermark image, and the GSVD-embedded watermarking method proposed in this invention can be effectively used for the extraction of watermarks from color natural host images.

[0083] The attacks employed by this invention on the host image after embedding the watermark include: Gaussian noise attacks with intensities of 0.01, 0.05, and 0.1; cropping attacks with intensities of 6.25%, 12.5%, and 25%; median filtering attacks with a filtering window size of 2×2; Gaussian low-pass filtering attacks with a filtering window size of 3×3; Gaussian blur attacks with an intensity of 0.5; screenshot attacks; and simulated moiré pattern attacks. Figure 3 for Figure 5 In Figure (c), the watermarked images extracted after being subjected to different image processing attacks are shown. It can be seen that the extracted watermark still contains the main information of the original watermark. Notably, even when the host image with the embedded watermark is subjected to a screenshot attack, the main information of the extracted watermark can still be identified. To quantitatively evaluate the extraction results, this invention calculated the correlation coefficient between the original watermark image and the extracted watermark image. The calculated correlation coefficients between the watermark image extracted from the host and the original watermark are 0.9994, 0.8562, 0.5067, 0.9041, 0.8778, 0.8235, 0.9852, 0.9404, 0.9935, 0.5326, and 0.3392, respectively. These results demonstrate that the GSVD-based watermarking method proposed in this invention has a certain degree of robustness against various image processing attacks, especially screenshot attacks.

[0084] Example Three

[0085] In this example, three kinds of forgery attack tests for the present application will be introduced.

[0086] (1) The first forgery attack (FA1) test procedure mainly contains three stages, and the implementation principle is as follows:

[0087] The first stage is the embedding stage, and the watermark embedding method of the first embodiment of the present application is used to embed two watermark images f1 and f2 into the color host image IH respectively, to obtain two corresponding embedded watermark host images IW1 and IW2, and the corresponding side information and :

[0088] ,

[0089] Among them, Embedding represents the embedding watermark operation.

[0090] The second stage is the extraction stage, and the watermark extraction process of the second embodiment of the present application is used to attempt to extract the watermark from the host image IW1 containing the watermark image f1 using the side information of the watermark image f2, and the extracted watermark is F1. Similarly, the watermark is attempted to be extracted from the host image IW2 containing the watermark image f2 using the side information of the watermark image f1, and the extracted watermark is F2.

[0091] ,

[0092] Among them, Extracting represents the watermark extraction operation.

[0093] The third stage is the verification stage. If the extracted watermark F1 is similar to the watermark image f2, or the extracted watermark F2 is similar to the watermark image f1, it means that the watermark system is insecure, that is, it cannot resist the first forgery attack:

[0094] .

[0095] Figure 5 To resist the visual results of the first forgery attack, Figure 5 (c) and Figure 5 (d) in (d) are respectively embedded into the host image to obtain the embedded watermark result, Figure 5 (a) and Figure 5 (b) in (b) are respectively embedded into the host image to obtain the embedded watermark result, Figure 5 (e) and Figure 5 (f) are respectively extracted fromFigure 5 In (c) and Figure 6 The extracted watermark results. It can be seen that the extracted watermark results do not contain the main information of the original watermark. In addition, the CC values of the two extracted watermark images are 0.0423 and 0.0330, respectively. The above results show that without the correct side information, the watermark information cannot be successfully recovered, and the watermarking scheme based on the GSVD algorithm proposed in the present application can resist the first forgery attack.

[0096] (2) The second forgery attack (Forgery Attack 2, FA2) test process also includes three stages, and the implementation principle is as follows:

[0097] The first stage is the embedding stage, and the watermark embedding process of the first embodiment of the present application is used to embed the watermark image f1 into the color host image IH to obtain the corresponding embedded watermark host image IW1 and side information . Then the watermark image f2 is embedded into the host image IW1 containing the watermark to obtain the embedded watermark host image IW2 and side information :

[0098] .

[0099] The second stage is the extraction stage, and the watermark extraction process of the second embodiment of the present application is used to attempt to extract the watermark from the host image IW1 containing the watermark image f1 using the side information of the watermark image f2, and the extracted watermark is F1:

[0100] .

[0101] The third stage is the verification stage. If the extracted watermark F1 is similar to the watermark image f2, it means that the watermark system is insecure, i.e., it cannot resist the second forgery attack:

[0102] .

[0103] Figure 6 The visual results for resisting the second forgery attack, Figure 6 In (a) and Figure 5 In (b) are the results of embedding the watermark Figure 5 In (a) into the host image and embedding the watermark Figure 6 In (b) into the image IW1, Figure 6 In (c) is the result of extracting the watermark from Figure 7The extracted watermark image in (a). It can be seen that the extracted watermark does not contain the main information of the original watermark. In addition, the CC value of the extracted watermark image is 0.0351. The above results show that the blind watermarking scheme based on GSVD proposed in the present application can resist the second forgery attack.

[0104] (3) The third forgery attack (FA3) test process also includes three stages, and the implementation principle is as follows:

[0105] The first stage is the embedding stage. The watermark embedding process of the first embodiment of the present application is used to embed the watermark image f1 into the color host image IH, to obtain the corresponding embedded watermark host image IW1 and the side information . Similarly, the watermark image f2 is embedded into the color host image IH, to obtain the corresponding embedded watermark host image IW2 and the side information :

[0106] .

[0107] The second stage is the extraction stage. The watermark extraction process of the second embodiment of the present application is used to attempt to extract the watermark from a randomly generated noise image X using the side information of the watermark image f1, and the extracted watermark is F1. Similarly, the side information of the watermark image f2 is used to attempt to extract the watermark from the randomly generated noise image X, and the extracted watermark is F2:

[0108] .

[0109] The third stage is the verification stage. If the extracted watermark F1 is similar to the watermark image f1, or the extracted watermark F2 is similar to the watermark image f2, it means that the watermark system is insecure, that is, it cannot resist the third forgery attack:

[0110] .

[0111] Figure 7 The visual results of resisting the third forgery attack, Figure 7 (a) and Figure 5 (b) are the results of embedding the watermark Figure 5 (a) and Figure 7 (b) into the host image respectively, Figure 7 (c) is a randomly generated noise image X, Figure 7 (d) and Figure 7 (e) are the results of extracting the watermark from ​The extracted watermark results of the middle (c) can be seen that the extracted watermark results do not contain the main information of the original watermark. In addition, the CC values of the two extracted watermark images are 0.0124 and 0.0201 respectively. The above results show that the watermark scheme based on the GSVD algorithm proposed in the present application can resist the third kind of camouflage attack.

[0112] The above-described embodiments are only descriptions of the preferred modes of the present application, and do not limit the scope of the present application. Without departing from the design spirit of the present application, various modifications and improvements to the technical solutions of the present application made by those skilled in the art shall fall within the protection scope determined by the claims of the present application.

Claims

1. An image watermark embedding method based on a GSVD embedding algorithm, characterized in that, The method comprises the following steps: decomposing a color host image into sub-blocks of different frequencies by one-dimensional Haar discrete wavelet transform to obtain a plurality of first components of the host image in horizontal and vertical directions; performing singular value decomposition on the first red component LH in the low frequency in the horizontal direction and the high frequency LH in the vertical direction among the several first components to obtain a first decomposition result (U, S, V), wherein U and V represent orthogonal matrices of LH r , and S represents a singular value matrix of LH r . r performing singular value decomposition on the first red component LH in the low frequency in the horizontal direction and the high frequency LH in the vertical direction among the several first components to obtain a first decomposition result (U, S, V), wherein U and V represent orthogonal matrices of LH r , and S represents a singular value matrix of LH r . r performing singular value decomposition on the first red component LH in the low frequency in the horizontal direction and the high frequency LH in the vertical direction among the embedding the original watermark image w into the LH of the color host image by GSVD embedding algorithm r singular value matrix S of the LH of the color host image, to obtain unitary matrix U1, unitary matrix V1, square matrix X1, non-negative diagonal matrix C1 and non-negative diagonal matrix S1; obtaining a matrix W after embedding the watermark by vector synthesis of the unitary matrix V1, the square matrix X1 and the non-negative diagonal matrix S1; performing singular value decomposition on the matrix W by using the SVD algorithm to obtain a second decomposition result (Uh, Sh, Vh), wherein Uh and Vh represent orthogonal matrices of W, and Sh represents a singular value matrix of W, and (Uh, Sh) is saved as side information; based on the first decomposition result and the second decomposition result, a second red component LH containing watermark information is obtained by inverse singular value decomposition r ’; based on a number of said components and said second red component LH r inverse wavelet transform is performed to obtain the final watermarked host image IW.

2. The image watermark embedding method based on the GSVD embedding algorithm according to claim 1, characterized in that, The plurality of first components include: low-frequency components LL in horizontal and vertical directions, low-frequency in horizontal direction and high-frequency in vertical direction LH, high-frequency in horizontal direction and low-frequency in vertical direction HL, and high-frequency components HH in horizontal and vertical directions.

3. The image watermark embedding method based on GSVD embedding algorithm according to claim 1, characterized in that, The method for obtaining the matrix W after embedding the watermark comprises: ， wherein VS represents vector synthesis, and i represents an imaginary unit.

4. A method for extracting a watermark from an image embedded by the method of any one of claims 1-3, wherein the method comprises: The method comprises the following steps: ​ decomposing the host image after embedding the watermark into sub-blocks of different frequencies by one-dimensional Haar discrete wavelet transform to obtain a plurality of second components of the host image after embedding the watermark in horizontal and vertical directions; The SVD algorithm was used to analyze the third red component (LHT) in the low-frequency horizontal direction and high-frequency vertical direction of several second components. r Perform singular value decomposition to obtain the third decomposition result (UT, ST, VT), where UT and VT represent LHT. r The orthogonal matrix, ST represents LHT r The singular value matrix; obtaining a singular value matrix W' containing the watermark by combining the side information (Uh, Sh) and the third decomposition result; performing vector decomposition on the singular value matrix W' to obtain a unitary matrix V1', a square matrix X1' and a non-negative diagonal matrix S1' corresponding to the watermark image; restoring the watermark F based on the unitary matrix V1', the square matrix X1' and the non-negative diagonal matrix S1'.

5. The method of claim 4, wherein the GSVD-based embedding algorithm is defined as The plurality of second components include: low-frequency components LLT in horizontal and vertical directions, low-frequency in horizontal direction and high-frequency in vertical direction LHT, high-frequency in horizontal direction and low-frequency in vertical direction HLT, and high-frequency components HHT in horizontal and vertical directions.

6. The method of claim 4, wherein the GSVD-based embedding algorithm is defined as The method for obtaining the watermark F comprises: ， wherein α represents watermark embedding strength, and T represents transposition of a matrix.

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