CN108932688B - Double-layer frame optical watermarking method based on ghost imaging calculation - Google Patents

Abstract

The invention discloses a double-layer frame optical watermarking method based on ghost imaging calculation, which comprises the following steps: 1) encoding the original watermark image into a series of intensity values by using a computed ghost imaging method, rearranging the intensity data into a two-dimensional temporary image as a new watermark of a first layer; 2) dividing the main image into a plurality of smaller blocks, dividing the watermark image into smaller blocks, and selecting some important blocks to form a reference image; identifying a reference image composed of important blocks by calculating spatial frequency coefficients thereof; 3) embedding the watermark into a new watermark by using a singular value decomposition method; 4) performing an extraction process on which a singular value decomposition transformation is performed to obtain modulated singular values; the synthesized blocks form a one-to-one mapping with their original positions, the newly generated watermark is reconstructed by performing an inverse singular value decomposition with a matrix, and the original watermark is restored to an image that can be verified. The method of the invention enlarges the space of the secret key and improves the security.

Description

Double-layer frame optical watermarking method based on ghost imaging calculation

Technical Field

The invention belongs to the technical field of digital watermarking, and relates to a double-layer frame optical watermarking method based on ghost imaging calculation.

Background

Due to the rapid development of optical information processing technology and the internet, more and more researchers are focusing on the security of information storage and transmission by using an optical method. Digital watermarking has been studied in recent years as an effective means of image encryption, information hiding, and optical authentication. Various transformations are applied to image security technologies, such as fractional fourier transformation, fresnel transformation, fractional mellin transformation, rotation transformation and the like, most of schemes are vulnerable to the threats of several common attacks due to the inherent linearity of optical transformation, and have poor robustness, so that the research progress of the digital watermarking technology is slow.

Disclosure of Invention

The invention aims to provide a double-layer frame optical watermarking method based on ghost imaging calculation, and solves the problems of poor robustness and weak attack resistance in the prior art.

The invention adopts the technical scheme that a double-layer frame optical watermarking method based on ghost imaging calculation is implemented according to the following steps:

step 1, encoding an original watermark image into a series of intensity values by using a computational ghost imaging method, and rearranging the intensity data into a two-dimensional temporary image as a new watermark of a first layer;

step 2, dividing the main image into a plurality of smaller blocks, dividing the watermark image into smaller blocks, wherein each block has p × q pixels, and selecting some important blocks to form a reference image f ' (mu, v) so that the reference image f ' (mu, v) has the same size as the new watermark w ' (mu, v); as an effective parameter for measuring the overall activity level in the reference image, the spatial frequency can reflect the definition of the reference image, and the reference image consisting of important blocks is identified by calculating the spatial frequency coefficient of the spatial frequency;

step 3, modifying the singular value of the reference image by using a singular value decomposition method, and embedding the singular value into a new watermark;

step 4, in order to retrieve the hidden watermark in the main image, an extraction process should be performed, which is similar to the embedding process described above, but implemented in the reverse order; reconstructing the modulated reference image again, with the position of the selected block known, on which the singular value decomposition transformation is performed to obtain modulated singular values; the synthesized blocks and their original positions form a one-to-one mapping, and the watermark image is finally generated in the second layer; the newly generated watermark is reconstructed by performing an inverse singular value decomposition with a matrix, and the original watermark is restored to an image that can be verified.

The beneficial effects of the invention are as follows:

1) the singular values have good stability, which shows that when the image is disturbed, such as cut, filtered and rotated, the coefficients do not change greatly; and there is no strict requirement on the size of the image in the singular value decomposition process.

2) Unlike conventional methods, the original watermark is verified visually, and by using a non-linear correlation algorithm, it can be authenticated without explicit observation, with two layers that enhance the security of the watermark. Besides optical parameters such as wavelength and propagation distance, a series of phase-only masks are used as security keys, so that the key space can be enlarged, and the security can be improved. The results demonstrate the feasibility and effectiveness of the watermarking mechanism of the present invention.

3) Due to optical parameters such as optical wavelength, propagation distance and a large number of phase masks, which are considered as security keys, it is difficult for an eavesdropper to retrieve the original watermark even if he knows the mechanism of the first layer. Meanwhile, an eavesdropper cannot easily destroy the existence of the provided watermark by analyzing common attacks.

Drawings

FIG. 1 is a flow chart of an embodiment;

fig. 2a is the original main image "pepper", fig. 2b is the original watermark "flower";

FIG. 3 is a schematic diagram of a computational ghost imaging encoding system;

fig. 4a is a watermark main image "pepper", fig. 4b is a watermark "flower" restored using a second order correlation algorithm, and fig. 4c is a watermark "flower" restored using an SL algorithm;

fig. 5a is a watermark reconstructed using 192 measured intensities, fig. 5b is a corresponding non-linear correlation graph, the reconstructed watermark having less measured intensities;

6a, 6b, 6c, 6d are block watermarked host images from top, bottom, left and right, respectively;

FIGS. 7a, 7b, 7c, 7d are non-linear correlation plots corresponding to FIGS. 6a, 6b, 6c, 6d, respectively;

fig. 8 is a non-linear correlation diagram corresponding to different noise intensities, where k is 0.4 in fig. 8a, 0.6 in fig. 8b, 0.8 in fig. 8c, and 1.0 in fig. 8 d;

FIGS. 9a and 9b are non-linear correlation graphs corresponding to wavelength errors of + -40 nm, respectively; FIGS. 9c and 9d are graphs showing the non-linear correlation corresponding to the propagation distance error, which is + -5 nm;

10a, 10b are non-linear dependence plots corresponding to leaked 50% and 60% phase masks, respectively, during watermark reconstruction;

fig. 11a is a 64 × 64 pixel grayscale image of the central portion of the image "Lena", fig. 11b is the reconstructed watermark, and fig. 11c is a non-linear correlation diagram.

Detailed Description

The watermarking method of the present invention is described in detail below with reference to the accompanying drawings and the detailed description.

The invention discloses a double-layer frame optical watermarking method based on ghost imaging calculation, which utilizes the optical technology of ghost imaging. In the first layer, the original watermark is encoded into a very small number of measured intensity values in the process of computing the ghost image to form the new watermark. In the second layer, important blocks selected from the main image based on spatial frequency are combined into a reference image, which is embedded with a new watermark by using singular value decomposition. Unlike other watermarking methods, by computing the nonlinear correlation between the original watermark and the reconstructed watermark, the original watermark information can be verified without being clearly visualized. Besides optical parameters such as wavelength and propagation distance, a series of phase-only masks are used as security keys, so that the key space can be enlarged, and the security can be improved. The result proves the feasibility and effectiveness of the proposed watermarking mechanism, and provides an effective choice for related work.

Referring to fig. 1, the implementation flow of the double-layer frame optical watermarking method based on the computed ghost imaging is based on the above working principle, wherein gamma is a weighting factor,

is the singular value of the original watermark and,

is the singular value of the reference image,

for the corrected reference image singular values, the following steps are carried out:

step 1, encoding an original watermark image into a series of intensity values by using a computational ghost imaging method, and rearranging the intensity data into a two-dimensional temporary image as a new watermark of a first layer;

using the computed ghost imaging technique, the resulting optical intensity value expression is:

B _i ＝∫∫dμdνI _i (μ,ν)T(μ,ν) (1)

where T (μ, v) is the transfer function and (μ, v) denotes the transverse coordinates in the object plane, the measured optical intensity being determined by the speckle pattern I _i (μ, v) determined directly; assume that the number of measured intensities is K, and<·>representing the ensemble averaging calculation, the decoded restored image mathematical expression is:

where G (μ, v) represents the decoded recovered image, B represents the measured optical intensity, I (μ, v) represents the speckle pattern, B _i Denotes the optical intensity of the I-th measurement, I _i (μ, v) represents the speckle pattern corresponding to the ith measurement;

step 2, dividing the main image into a plurality of smaller blocks, dividing the watermark image into smaller blocks, wherein each block has p × q pixels, and selecting some important blocks to form a reference image f ' (mu, v) so that the reference image f ' (mu, v) has the same size as the new watermark w ' (mu, v); as an effective parameter for measuring the overall activity level in the reference image, the spatial frequency can reflect the definition of the reference image, and the reference image consisting of important blocks is identified by calculating the spatial frequency coefficient of the spatial frequency.

Assume that the main image size is M × N pixels, which satisfies the condition: m x N > K, the main image can be divided into non-overlapping blocks, assuming Blk represents the smaller blocks divided from the main image, and the spatial frequency expression is:

step 3, modifying the singular value of the reference image by using a singular value decomposition method, and embedding the singular value into a new watermark;

assuming that the reference image is f '(mu, v) and the new watermark is w' (mu, v), two singular value decomposition transformations are performed on the reference image and the new watermark, and the expression is:

wherein i ═ f ', w', U _i (mu, v) and S _i (μ, V) is an orthogonal matrix, V _i (μ, v) is a diagonal matrix, the superscript T denotes transposition, and the symbol x denotes convolution operation.

Step 4, in order to retrieve the hidden watermark in the main image, an extraction process should be performed, which is similar to the embedding process described above, but implemented in the reverse order; reconstructing the modulated reference image again, with the position of the selected block known, on which the singular value decomposition transformation is performed to obtain modulated singular values; the synthesized blocks and their original positions form a one-to-one mapping, and the watermark image is finally generated in the second layer; the newly generated watermark is reconstructed by performing an inverse singular value decomposition with a matrix, the original watermark is restored to an image that can be verified,

the recovered watermark G (μ, v) can be effectively authenticated, with the expression:

NC(μ,v)＝|IFT{|c(μ,v)| ^ρ-1 c(μ,v)}| ² (6)

c(μ,v)＝FT{G(μ,v)}conj{FT{w(μ,ν)}} (7)

wherein FT {. is a two-dimensional Fourier transform, IFT {. is an inverse Fourier transform, conj {. is a complex conjugate of a calculation parameter, ρ is the strength of applied nonlinearity, w (μ, ν) is an original watermark image, and NC (μ, ν) and c (μ, ν) each represent an intermediate variable in the Fourier transform process.

Examples

As shown in fig. 2a and 2b, in the USC-SIPI image database, a gray scale image "pepper" with a pixel size of 128 × 128 is selected as a main image; a binary image "flower" with a pixel size of 64 x 64 is selected for use as the watermark. The size of a non-overlapped block divided from the main image is set to 4 × 4 pixels, i.e., p ═ 4 and q ═ 4. Setting the actual weighting factor of the new watermark embedded in the reference image to 1 x 10 using singular value based decomposition ^-5 The applied non-linear intensity is set to ρ 0.4. The method comprises the following specific steps:

step 1, encoding an original watermark image 'flower' into a series of measured intensity values by using a computational ghost imaging method, rearranging the intensity data into a two-dimensional temporary image as a new watermark of a first layer, wherein the expression of the obtained optical measured intensity value is as follows:

B _i ＝∫∫dμdνI _i (μ,ν)T(μ,ν) (1)

where T (μ, v) is the transfer function and (μ, v) denotes the transverse coordinates in the object plane, the measured optical intensity being determined by the speckle pattern I _i (μ, ν) was determined directly. Assume that the number of measured intensities is K, and<·>representing the ensemble averaging calculation, the mathematical expression for the decoded restored image is:

step 2, dividing the main image 'pepper' into a plurality of blocks with the pixel size of 4 multiplied by 4, and selecting some important blocks to form a reference image so that the important blocks have the same size with the new watermark; the main image size is 128 × 128 pixels, which satisfies the condition: 128 x 128 > K, the main image can be divided into a plurality of non-overlapping small blocks. As an effective measure of the overall activity level in an image, the spatial frequency may reflect the sharpness of the image, and important blocks may be identified by calculating their spatial frequency coefficients. Let Blk denote the smaller blocks partitioned from the main image, the spatial frequency expression is:

step 3, modifying the singular value of the reference image by using a singular value decomposition method, and embedding the singular value into a new watermark; assuming that the reference image is f '(μ, v) and the new watermark is w' (μ, v), two singular value decomposition transformations are performed on the reference image and the watermark, with the expression:

wherein, U _i (mu, v) and S _i (μ, ν) (i ═ f ', w') is an orthogonal matrix, V _i And (mu, v) (i ═ f ', w') is a diagonal matrix, the superscript T denotes transposition, and the symbol x denotes convolution operation.

In order to retrieve the hidden watermark in the watermarked image, an extraction process should be performed, similar to the embedding process described above, but in the reverse order, step 4. In case the position of the selected block is known, the modulated reference image is reconstructed again, on which the singular value decomposition transformation is performed to obtain the modulated singular values. The synthesized blocks form a one-to-one mapping with their original positions, and the watermark image is finally generated in the second layer. The newly generated watermark is reconstructed by performing an inverse singular value decomposition with a matrix, and the original watermark is restored to an image that can be verified. If the reconstructed object does not need to be visually observed, a nonlinear correlation algorithm can be used for verifying the existence of the object, in the scheme provided by the invention, the recovered watermark G (mu, v) can be effectively authenticated, and the expression is as follows:

NC(μ,ν)＝|IFT{|c(μ,v)| ^ρ-1 c(μ,ν)}| ² (6)

c(μ,ν)＝FT{G(μ,ν)}conj{FT{w(μ,ν)}}(7)

where FT {. and IFT {. denotes two-dimensional Fourier transform and inverse Fourier transform, respectively, conj {. calculates the complex conjugate of the parameter, ρ is the strength of the applied nonlinearity, and w (μ, v) is the original watermark image.

To evaluate the quality of the watermark image, its peak signal-to-noise ratio (PSNR) with the original main image is mathematically expressed as:

where, f is the main image map,

is a watermark image, the coordinates (μ, v) are omitted for simplicity. The Mean Square Error (MSE) between them is expressed as:

furthermore, the quality of the recovered watermark may be evaluated in a similar manner.

Experimental verification

1) Feasibility numerical experiment

The experimental setup was set up as shown in fig. 3, with SLM representing the spatial light modulator; BD represents a bucket detector, and the SLM is located in front of the expander and faces the He-Ne laser; the BD is positioned behind the expander, and the SLM and the BD are both connected with a computer (processor); a plane wave emitted at 632.8nm with a He-Ne type laser was chosen for illumination. During ghost imaging of the original watermark, a series of random phase masks are generated

Are input sequentially into the spatial light modulator with a resolution of 64 x 64 pixels with a pixel pitch of 20 μm. The propagation distance between the spatial light modulator and the detector plane is 7.4cm and the laser beam waist is 740 μm.

The watermark image with PSNR 56.2114dB when K1760 measured intensities are used in the ghost imaging process is shown in fig. 4a, indicating that the watermark image has good imperceptibility. Fig. 4b shows a watermark recovered using a second order correlation algorithm, which can achieve a high PSNR watermark when a construction algorithm based on compressed sensing is employed. Using Smooth l ₀ (SL ₀ ) The recovered watermark with PSNR of 42.4962dB is shown in fig. 4c, with no perceptual degradation from the point of view of the human visual system. Fig. 5a shows a watermark reconstructed with 192 measured intensities (i.e. only 4.69% of the Nyquist limit), which is similar to noise and in which the information is not clearly represented. However, in the corresponding non-linear correlation diagram shown in fig. 5b, there is a significant peak on the noise background, which means that the watermark can be validated effectively without clear visualization.

2) Robust analysis

It is known that when the watermark image is contaminated by noise or largely damaged (e.g., pixel loss) is large, i.e., the watermark image is disturbed by a noise attack or a shading attack, the watermark may not be recovered. Since the original watermark is embedded in significant blocks having intermediate-valued spatial frequency coefficients, a large portion of the blocks may be distributed in one area of the watermark image. If the area is occluded, the watermark will not be retrieved. To verify the capacity of the present invention, 50% of the pixels are cropped from the top, bottom, left and right sides in the watermark image as shown in fig. 6a, 6b, 6c, 6 d. Using only K192 measured intensities, corresponding non-linear correlation plots are shown in fig. 7a, 7b, 7c, 7d, respectively, from which it can be seen that the retrieved results still contain useful information to generate a good correlation signal to verify the presence of the watermark.

To evaluate the effect of noise attack, the watermark image is contaminated by gaussian random noise (with zero mean and uniform standard deviation), which is mathematically expressed as:

wherein the content of the first and second substances,

is the contaminated watermark image and k is the noise intensity.When k is set to 0.4, 0.6, 0.8 and 1.0, the corresponding non-linear correlation plots are shown in fig. 8a, 8b, 8c, 8d, respectively, where sharp spikes are clearly observed. Therefore, the present invention is more tolerant to these attacks.

3) Security analysis

Similar to other schemes based on computational ghost imaging, a series of phase masks used to compute the speckle pattern can be considered a security key in addition to the wavelength of light and the propagation distance. If one of the security keys is wrong, the retrieved watermark will not contain sufficient information about the original key. When the wrong wavelength with an error of ± 40nm is used for the reconstruction, the calculated non-linear dependence is shown in fig. 9a and 9 b. Similarly, when error propagation distances with errors of 5mm are used in the retrieval process, the resulting non-linear dependence plots are as in fig. 9c and 9 d. When 50% and 60% masks are revealed, the resulting non-linear dependence is shown in fig. 10a and 10 b. In fact, when 50% of the mask is known, an eavesdropper may sometimes obtain a map with peaks. Knowing 60% of the mask ensures that he can observe a significant peak at each turn, which means that information can only be acquired if an eavesdropper should intercept at least 60% of the phase mask. Obviously, when a series of phase masks are used only as security keys, it can enlarge the key space, and the present invention has higher security.

Notably, the grayscale image as a watermark can be effectively embedded in the main image, and a small amount of measured intensity can be captured for verification in the computational ghost imaging process. However, a grayscale watermark has a larger spectral range and more information than a binary image, and the number of measured intensity values should be increased to some extent. As shown in fig. 11a, a 64 × 64-pixel grayscale image, which is the central portion of the image "Lena", is considered as a watermark embedded in the main image "pepper" shown in fig. 2 a. The reconstructed watermark using the second order correlation algorithm is shown in fig. 11b as noise when using K-320 measured intensities (i.e. 7.81% of the Nyquist limit). A corresponding non-linear correlation plot is shown in fig. 11c, where a spike may be obtained to verify the presence of the original watermark.

Claims (1)

1. A double-layer frame optical watermarking method based on computational ghost imaging is characterized by comprising the following steps:

step 1, encoding the original watermark image into a series of intensity values by using a computational ghost imaging method, rearranging the intensity data into a two-dimensional temporary image as a new watermark of a first layer,

the specific process is that,

using the computed ghost imaging technique, the resulting optical intensity value expression is:

B _i ＝∫∫dμdνI _i (μ,ν)T(μ,ν) (1)

where T (μ, v) is the transfer function and (μ, v) denotes the transverse coordinates in the object plane, the measured optical intensity being determined by the speckle pattern I _i (μ, ν) directly; assume that the number of measured intensities is K, and<·>representing the ensemble averaging calculation, the decoded restored image mathematical expression is:

wherein G (μ, v) represents the decoded restored image, B represents the measured optical intensity, I (μ, v) represents the speckle pattern, B represents the speckle pattern, and _i denotes the optical intensity of the I-th measurement, I _i (μ, ν) denotes the speckle pattern corresponding to the ith measurement;

step 2, dividing the main image into a plurality of smaller blocks, dividing the watermark image into smaller blocks, wherein each block has p × q pixels, and selecting some important blocks to form a reference image f ' (mu, v) so that the reference image f ' (mu, v) has the same size as the new watermark w ' (mu, v); the reference image composed of the important blocks is identified by calculating the spatial frequency coefficient thereof, and the specific process is,

assume that the main image size is M × N pixels, which satisfies the condition: m x N > K, the main image can be divided into non-overlapping blocks, assuming Blk represents the smaller blocks divided from the main image, and the spatial frequency expression is:

step 3, modifying the singular value of the reference image by using a singular value decomposition method, and embedding the singular value into a new watermark,

assuming that the reference image is f '(mu, v) and the new watermark is w' (mu, v), two singular value decomposition transformations are performed on the reference image and the new watermark, and the expression is:

wherein i ═ f ', w', U _i (. mu.,. nu.) and S _i (mu, V) is an orthogonal matrix, V _i (mu, ν) is a diagonal matrix, the superscript T represents transposition, and the symbol x represents convolution operation;

step 4, an extraction process is performed, which is similar to the embedding process described above, but is carried out in the reverse order; reconstructing the modulated reference image again, with the position of the selected block known, on which the singular value decomposition transformation is performed to obtain modulated singular values; the synthesized blocks and their original positions form a one-to-one mapping, and the watermark image is finally generated in the second layer; the newly generated watermark is reconstructed by performing an inverse singular value decomposition with a matrix, and the original watermark is restored to an image that can be verified, in a specific process,

the recovered watermark G (μ, ν) can be effectively authenticated, with the expression:

NC(μ,ν)＝|IFT{|c(μ,ν)| ^ρ-1 c(μ,ν)}| ² (6)

c(μ,ν)＝FT{G(μ,ν)}conj{FT{w(μ,ν)}} (7)

wherein FT {. is a two-dimensional Fourier transform, IFT {. is an inverse Fourier transform, conj {. is a complex conjugate of a calculation parameter, ρ is the strength of applied nonlinearity, w (μ, ν) is an original watermark image, and NC (μ, ν) and c (μ, ν) each represent an intermediate variable in the Fourier transform process.

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