CN109493270B - Watermark image restoration method based on SLT-DM - Google Patents

Abstract

The invention discloses a watermark image restoration method based on SLT-DM, which firstly eliminates overflow problem caused by watermark embedding through anti-overflow processing, synthesizes and restores the change quantity caused by watermark embedding and image overflow processing and the change quantity caused by dither modulation by an anti-overflow dither modulation method into restored information to embed images without overflow, and ensures that the restored information does not jump out of a dither interval when being added on a first low-frequency coefficient by controlling the restored information to be less than half of the quantization step length of the dither modulation, thereby ensuring that the images can be restored completely and reversibly, and the restoration does not need any additional information, and other problems of reducing embeddable capacity, influencing image quality, increasing additional information and the like can not be caused.

Description

A watermark image restoration method based on SLT-DM

Technical Field

The invention belongs to the technical field of image digital watermarking, and in particular refers to a watermark image restoration method based on SLT-DM for application fields with high losslessness requirements such as medical imaging systems and military imaging systems.

Background Art

With the development of Internet technology and the innovation of new media technology, digital media technology has made breakthrough progress, changing the dominant position of traditional media in the process of information dissemination. As digital media becomes more abundant, a series of problems about them have also emerged. Among them, how to effectively protect the copyright of digital media and prevent digital media from being illegally copied or used has become an important aspect. Digital Right Management (DRM) is currently the main means of copyright protection for digital media disseminated on the Internet. Digital watermarking, as an important technology of DRM, has also received more and more attention. Watermarks are increasingly closely combined with copyright protection in various digital media application scenarios, such as audio and video photos, medical images, 3D images, videos, etc.

Unlike traditional digital watermarking methods, in some fields such as medical imaging systems, military imaging systems, and remote sensing applications, any changes in the original digital content may affect the final decision-making process, so the watermark operation on the original digital content is required to be lossless. The watermarking scheme that meets this lossless requirement is called a lossless watermarking scheme. Lossless watermarks include reversible watermarks and zero watermarks.

Reversible watermarking schemes expect that after the embedded data is removed, the digital content can be restored completely losslessly. Most lossless watermarking schemes require a lossless environment to transmit the watermarked media, because minor changes such as channel noise or JPEG compression can destroy the hidden watermark. In practical applications, non-malicious attacks such as channel noise and lossy compression and malicious illegal attacks often occur. Even if the watermarked media undergoes these attacks, the lossless watermarking scheme must have the ability to protect copyrights, so robustness is of practical significance for lossless watermarking. Lossless watermarking schemes that can effectively resist attacks on digital media are called robust lossless watermarking schemes.

The design of a robust reversible watermark algorithm often faces a series of problems: the robustness, invisibility, embedding capacity, and reversibility of the watermark need to be considered during the design. However, these four requirements not only face a series of challenges themselves, but also constrain each other. This requires that the design of the watermark cannot only consider one requirement alone, but needs to consider each requirement comprehensively. The robustness, invisibility, and embedding capacity of the watermark are the classic triangle of the watermark algorithm. How to improve and balance them is what the watermark algorithm has always pursued. Robust reversible watermarking adds reversibility to the classic triangle, but it itself has a severe challenge: the overflow problem. Overflow often destroys reversibility, resulting in the watermark operation being not completely reversible.

In order to solve the overflow problem, robust reversible watermarking algorithms often use a local-map-based solution to record sub-blocks that can embed watermarks without causing overflow or sub-blocks that require special processing to avoid overflow. However, this will greatly reduce the embedding capacity and increase the computational complexity. Some methods will also weaken invisibility; some algorithms use the method of directly recording overflow information, but this will result in huge additional information; some algorithms directly ignore the overflow problem, but in this way the watermark operation cannot be completely reversibly restored. Although these processing methods suppress overflow, they often lead to new problems: 1) too much additional information; 2) reduced embedding capacity; 3) reduced invisibility; 4) increased computational complexity, and do not completely solve the problem.

Summary of the invention

Considering that the existing image reversible methods cannot solve the image overflow problem well, the present invention provides a watermark image restoration method based on SLT (Slantlet transform)-DM (Dither Modulation), in which the change caused by watermark embedding and anti-overflow processing is embedded in the frequency domain of the image, so that the image can be completely reversibly restored after watermark embedding and anti-overflow processing, and no additional information is required.

In order to achieve the above technical objectives, the present invention adopts the following technical solutions:

A watermark image restoration method based on SLT-DM comprises the following steps:

Watermark embedding process:

Step A10, preprocessing the original image;

If the original image is a color image, then the G channel layer of the original image is taken as the preprocessed image; if the original image is a grayscale image, then the original image is taken as the preprocessed image; the preprocessed image is divided into non-overlapping preprocessed image sub-blocks B _0i of size N×N, where i represents the sequence number corresponding to the image sub-block;

Step A20, embedding a watermark;

Traverse all pre-processed image sub-blocks B _0i , transform the pre-processed image sub-block B _0i from the spatial domain to the frequency domain, calculate the embedding factor E _0i according to the intermediate frequency coefficient matrix of the pre-processed image sub-block B _0i , embed the watermark bit into the intermediate frequency coefficient matrix of the pre-processed image sub-block B _0i , and then transform the image sub-block after watermark embedding from the frequency domain to the spatial domain to obtain the watermark embedded image sub-block B _1i ;

Step A30, anti-overflow processing;

Traverse all watermark embedded image sub-blocks B _1i , perform anti-overflow processing on the watermark embedded image sub-blocks B _1i , and obtain anti-overflow watermark image sub-blocks B _2i ;

Step A40, embedding restoration information;

Dc1，Dc2，Dc3是控制因子，且Dvalue₂×Dc₂为大于1的整数，|Dvalue₁/Dc₁|＜0.5，Dvalue＜0.5H，H表示第一次抖动调制和第二次抖动调制的量化步长；将总差值Dvalue嵌入到第一次抖动调制处理后的第一低频系数LL_2i(1,1)'，得到嵌入还原信息的第一低频系数LL_2i(1,1)'_EM：LL_2i(1,1)'_EM＝LL_2i(1,1)'+Dvalue，再将嵌入还原信息后的图像从频率域变换到空间域，得到最终水印嵌入图像子块B₃；Traverse all anti-overflow watermark image sub-blocks B _2i , transform the anti-overflow watermark image sub-block B _2i from the spatial domain to the frequency domain, and calculate the embedding factor E _2i embedded with the watermark according to the intermediate frequency coefficient matrix of the anti-overflow watermark image sub-block B _2i ; perform the first dithering modulation processing on the first low-frequency coefficient LL _2i (1,1) of the anti-overflow watermark image sub-block B _2i to obtain the first low-frequency coefficient LL _2i (1,1)' subjected to the first dithering modulation processing; calculate the embedding factor difference Dvalue ₁ according to the embedding factor E _0i of the pre-processed image sub-block B _0i and the embedding factor E _2i embedded with the watermark of the anti-overflow watermark image _sub -block B _2i as follows: Dvalue ₁ = E _2i -E _0i ; according to the first low-frequency coefficient LL _2i (1,1) of the anti-overflow watermark image sub-block B 2i and the first low-frequency coefficient LL _2i after the first dithering modulation processing (1,1)', calculate the first low-frequency coefficient difference Dvalue ₂ as: Dvalue ₂ =LL _2i (1,1)'-LL _2i (1,1); the total difference Dvalue synthesized by the embedded factor difference Dvalue ₁ and the first low-frequency coefficient difference Dvalue2 is:

Dc1, Dc2, Dc3 are control factors, and Dvalue ₂ ×Dc ₂ is an integer greater than 1, |Dvalue ₁ /Dc ₁ |＜0.5, Dvalue＜0.5H, H represents the quantization step of the first dither modulation and the second dither modulation; the total difference Dvalue is embedded into the first low-frequency coefficient LL _2i (1,1)' after the first dither modulation process to obtain the first low-frequency coefficient LL _2i (1,1)' _EM embedded with restored information: LL _2i (1,1)' _EM ＝LL _2i (1,1)'+Dvalue, and then the image after the embedded restored information is transformed from the frequency domain to the spatial domain to obtain the final watermark embedded image sub-block B ₃ ;

Image restoration process:

Step C10, traverse all final watermark embedded image sub-blocks B _3i , transform the final watermark embedded image sub-block B _3i from the spatial domain to the frequency domain, and calculate the embedding factor E _3i according to the intermediate frequency coefficient matrix of the final watermark embedded image sub-block B _3i ;

Step C20, perform a second dithering modulation on the first low-frequency coefficient LL _3i (1,1) of the final watermark embedded image sub-block B _3i to obtain the first low-frequency coefficient LL _3i (1,1)' after the second dithering modulation, calculate the total difference Dvalue embedded in the first low-frequency coefficient LL _3i (1,1) according to formula (24), and then calculate the embedding factor difference Dvalue ₁ and the first low-frequency coefficient difference Dvalue ₂ according to formula (25) from the total difference Dvalue:

Dvalue=LL _3i (1,1)-LL _3i (1,1)'(24);

Step C30, according to the embedding factor E _3i of the final watermark embedded image sub-block B _3i and the embedding factor difference Dvalue ₁ , obtain the embedding factor E _4i of the restored image sub-block B _4i : E _4i = E _3i - Dvalue ₁ = E _2i - Dvalue ₁ = E _0i ;

Step C40, according to the first low-frequency coefficient LL _3i (1,1)' after the second dithering modulation of the final watermark embedded image sub-block B _3i and the first low-frequency coefficient difference Dvalue ₂ , obtain the first low-frequency coefficient LL _4i (1,1) of the restored image sub-block B _4i : LL _4i (1,1) = LL _3i (1,1)'-Dvalue ₂ = LL _2i (1,1)'-Dvalue ₂ = LL _2i (1,1) = LL _0i (1,1);

Step C50, calculating the intermediate frequency coefficient matrix of the restored image sub-block B _4i by the embedding factor E _4i of the restored image sub-block B _4i , and using the intermediate frequency coefficient matrix of the restored image sub-block B _4i and the first low-frequency coefficient LL _4i (1,1), transforming the restored image sub-block B _4i from the frequency domain to the spatial domain to obtain the restored image sub-block B _4i in the spatial domain, and all the restored image sub-blocks B _4i constitute the restored image.

The present invention firstly eliminates the overflow problem caused by watermark embedding through anti-overflow processing, and through an anti-overflow jitter modulation method, synthesizes the change amount caused by watermark embedding and image overflow processing and the change amount caused by jitter modulation itself to restore information without overflow and embeds it into the image. Moreover, by controlling the restored information to be less than half the quantization step of jitter modulation, the restored information will not jump out of the jitter interval when added to the first low-frequency coefficient, thereby ensuring that the image is completely reversible and that the restoration does not require any additional information and will not cause other problems such as low embedding capacity, poor image quality, excessive additional information, and high computational complexity.

Further, the pixel matrix s of the image sub-block in the spatial domain is subjected to SLT transformation according to formula (1) to obtain the image sub-block coefficient matrix S in the frequency domain, and the coefficient matrix S includes the low-frequency coefficient matrix LL, the first intermediate frequency coefficient matrix LH, the second intermediate frequency coefficient matrix HL and the high-frequency coefficient matrix HH; the image sub-block coefficient matrix S in the frequency domain is subjected to inverse SLT transformation according to formula (2) to obtain the pixel matrix s of the image sub-block in the spatial domain:

Among them, s is the pixel matrix of the image sub-block, S is the transformed SLT coefficient matrix, N is the size of the matrix, and SLT _N is the transformation matrix calculated according to the SLT transformation algorithm.

The SLT transformation adopted in this scheme has better invisibility, so it can improve the robustness while ensuring invisibility when designing embedding.

Further, the embedding factor E _i is calculated according to the intermediate frequency coefficient matrix of the image sub-block as follows: the intermediate frequency coefficient matrix of the image sub-block in the frequency domain includes a first intermediate frequency coefficient matrix LH _i and a second intermediate frequency coefficient matrix HL _i , and the average values of the elements in the first intermediate frequency coefficient matrix LH _i and the second intermediate frequency coefficient matrix HL _i are calculated respectively: meanLH _i =mean(LH _i ), meanHL _i =mean(HL _i ); and then the embedding factor E _i is calculated according to the average value meanLH _i of the first intermediate frequency coefficient matrix and the average value meanHL _i of the second intermediate frequency coefficient matrix: E _i =meanLH _i -meanHL _i , wherein mean() indicates averaging;

The specific process of embedding the watermark bits into the intermediate frequency coefficient matrix of the preprocessed image sub-block B _0i is:

The three-segment mapping function is constructed as formula (7) and (8), and the embedding factor E _0i of the preprocessing sub-block B _0i is mapped to a judgment factor D _0i on a judgment domain according to formula (7):

Among them, Range1＝[-0.3R,0.3R], Range2＝[-0.7R,-0.3R)∪(0.3R,0.7R], Range3＝[-k1×0.3R,k1×0.3R], Range4＝[-k1×0.3R-k2×0.4R,-k1×0.3R)∪(k1×0.3R,k1×0.3R+k2×0.4R]; k1, k2, k3 are all slopes, and k1∈(0,1), k2∈[1,2], k3∈(10,+∞); R is the adjustment interval of the mapping function, and sign is the sign function;

When the watermark bit _wi = 1, the watermark bit _wi is embedded into the judgment factor _Di according to formula (9) to obtain the judgment factor _DEMi after embedding the watermark; when the watermark bit _wi = 0, the watermark bit _wi is embedded into the judgment factor _Di according to formula (10) to obtain the judgment factor _DEMi after embedding the watermark:

Where T represents the equilibrium threshold;

According to formula (8), the watermarked judgment factor _DEMi is inversely mapped to the watermarked embedding factor _E0EMi , and then the watermarked embedding factor _E0EMi is added to the first intermediate frequency coefficient matrix LH and the second intermediate frequency coefficient matrix HL of the preprocessed image subblock _B0i .

In this scheme, in order to ensure the watermark has strong robustness and invisibility, a three-segment embedding module is designed, and the robustness and invisibility of the watermark are improved through SLT transformation and binary embedding strategy.

Furthermore, before image restoration, the watermark extraction process is also included:

Step B10, calculating the embedding factor: transforming the final watermark embedded image sub-block B _3i from the spatial domain to the frequency domain, and calculating the embedding factor E _3i according to the intermediate frequency coefficient matrix of the final watermark embedded image sub-block B _3i ;

Step B20, extracting watermark bits: reconstructing the three-segment mapping function formula (7) and formula (8); mapping the embedding factor E _3i of the final watermark embedded image sub-block B _3i to the judgment factor D _3i on the judgment domain according to formula (7), and extracting the watermark bit w _i from the judgment factor D _3i according to formula (22):

Traverse all the final watermark embedded image sub-blocks B _3i , extract all watermark bits, and then combine them into a watermark.

This scheme can verify the copyright of the image by extracting the watermark from the image, effectively protecting the copyright of the image and preventing it from being illegally copied or used.

Furthermore, anti-overflow processing is performed on the watermark embedded image sub-block B _1i according to formula (11):

Wherein, Pixel is the pixel grayscale value of the watermark embedded image sub-block B _1i .

The anti-overflow processing method of the scheme for images can avoid the pixel overflow problem caused by embedding watermarks into images.

Furthermore, when the grayscale value of the first pixel s(1,1)≥127, the first dithering modulation function is formula (16),

When the gray value of the first pixel s(1,1) is less than 127, the first dither modulation function is formula (17),

The second jitter modulation function is formula (23),

Among them, floor() is the floor function, ceil() is the ceiling function, and sign() is the sign function.

Beneficial Effects

The present invention provides a watermark image restoration method based on SLT-DM. When embedding a watermark, firstly, the image is divided into non-overlapping sub-blocks, the copyright information of the image constitutes a watermark and is embedded into the intermediate frequency coefficient matrix of the frequency domain of each image sub-block, and then the image sub-block is transformed from the frequency domain to the space domain and overflow processing is performed; then the low-frequency coefficients in the frequency domain are jitter modulated; then the watermark is embedded and the change amount of the intermediate frequency coefficient caused by the overflow processing of the image sub-block and the change amount of the low-frequency information caused by the jitter modulation constitute restoration information, and are embedded in the low-frequency coefficients in the frequency domain; finally, the image sub-block is transformed from the frequency domain to the space domain, and each image sub-block in the space domain is spliced into an image. When restoring the image, the image is also divided into sub-blocks, and then after frequency domain transformation, the low-frequency coefficients are jitter modulated to obtain restoration information, and the restoration information is used to restore the low-frequency coefficients and the intermediate frequency coefficients, and finally the original image is restored. The present invention first eliminates the overflow problem caused by watermark embedding through anti-overflow processing, and uses an anti-overflow jitter modulation method to synthesize the change amount caused by watermark embedding and image overflow processing and the change amount caused by jitter modulation itself to restore information without overflow and embed it into the image. Moreover, by controlling the restored information to be less than half the quantization step of the jitter modulation, the restored information will not jump out of the jitter interval when added to the first low-frequency coefficient, thereby ensuring that the image is completely reversible. The restoration does not require any additional information and will not cause other problems such as reducing the embeddable capacity, affecting the image quality, and adding additional information.

BRIEF DESCRIPTION OF THE DRAWINGS

Fig. 1 is an overall flow chart of the algorithm of the present invention;

FIG2 is a flow chart of watermark embedding of the present invention;

FIG3 is a diagram of the sub-band division of the SLT coefficient matrix;

FIG4 is a schematic diagram of watermark embedding in an embodiment, wherein (a) is an original image, (b) is a watermark image, and (c) is a final watermark-embedded image;

FIG5 is a flow chart of watermark extraction of the present invention;

Fig. 6 is the extracted watermark image;

FIG7 is a flowchart of image restoration of the present invention;

FIG8 is a schematic diagram of restoration in the embodiment, wherein (a) is a restored image, and (b) is an absolute difference image between the restored image and the original image.

DETAILED DESCRIPTION

This embodiment takes into account the overflow problem faced by the robust reversible watermark algorithm and aims to effectively and simply avoid the overflow problem without causing other problems without destroying the invisibility and embedding capacity of the watermark.

The present invention designs an anti-overflow jitter modulation module and provides a robust reversible image watermarking method based on SLT-DM, as shown in FIG1 , including three processes: watermark embedding, watermark extraction and image restoration.

The watermark embedding process is shown in Figure 2, including:

Step A10: preprocessing of original image.

If the original image is a color image, the G channel layer of the original image is taken as the preprocessed image; if the original image is a grayscale image, the original image is taken as the preprocessed image; the preprocessed image is divided into non-overlapping preprocessed image sub-blocks B _0i of size N×N, where i represents the sequence number corresponding to the image sub-block.

First, we need to determine whether the image is a color image. If it is a color image, we take its G channel layer. If it is a grayscale image, we directly use it. Because the G channel of the three RGB channels shows better robustness and invisibility, as well as the limitation of generating restoration information, this algorithm can only select integer channels. The reason will be further described in the section of generating restoration information. Therefore, we use the G channel instead of the Y channel for color images. Then divide this layer into non-overlapping sub-blocks of size N×N, and each watermark bit will be embedded in a sub-block. After testing, this method sets N=32.

Step A20, traverse all pre-processed image sub-blocks B _0i and embed watermarks.

The preprocessed image sub-block B _0i is transformed from the spatial domain to the frequency domain, the embedding factor E _0i is calculated according to the intermediate frequency coefficient matrix of the preprocessed image sub-block B _0i , the watermark bit is embedded into the intermediate frequency coefficient matrix of the preprocessed image sub-block B _0i , and then the image sub-block after watermark embedding is transformed from the frequency domain to the spatial domain to obtain the watermark embedded image sub-block B _1i .

According to Formula 1, the preprocessed image sub-block B _0i in the spatial domain is subjected to SLT transformation to obtain the image sub-block coefficient matrix in the frequency domain, and the coefficient matrix includes a low-frequency coefficient matrix LL, a first intermediate frequency coefficient matrix LH, a second intermediate frequency coefficient matrix HL and a high-frequency coefficient matrix HH:

Where s is the pixel matrix of the image sub-block, S is the transformed SLT coefficient matrix, N is the size of the matrix, and the SLT transformation here is only for square matrices. SLT _N is the transformation matrix calculated according to the SLT transformation algorithm.

The SLT transform is an optimized discrete wavelet transform (DWT), which has better invisibility than the DWT and allows better robustness under similar invisibility by improving the embedding strength. According to the image transformation method explained by C. Mulc-ahy in "Image compression using the Haarwavelet transform", we use the SLT _N matrix to calculate the SLT coefficient matrix of the image block instead of using the traditional SLT transform. The SLT transform is shown in Formula 1, and its inverse transform is shown in Formula 2. According to Formula 3, the SLT coefficient matrix is divided into the low-frequency coefficient matrix LL, the first intermediate frequency coefficient matrix LH, the second intermediate frequency coefficient matrix LH, and the high-frequency coefficient matrix HH, as shown in Figure 3.

The embedding factor E _0i is calculated according to the intermediate frequency coefficient matrix of the preprocessed image sub-block B _0i as follows: the intermediate frequency coefficient matrix of the image sub-block in the frequency domain includes HL, and the average value of the elements in the first intermediate frequency coefficient matrix LH is calculated according to Formula 4 and the second intermediate frequency coefficient matrix is calculated according to Formula 5:

meanLH _i =mean(LH _i ) (4),

meanHL _i =mean(HL _i ) (5);

Then, the embedding factor E _i is calculated according to the average value meanLH _i of the first intermediate frequency coefficient matrix and the average value meanHL _i of the second intermediate frequency coefficient matrix according to Formula 6:

E _i =meanLH _i -meanHL _i (6),

Where mean() represents the averaging function. The watermark is embedded by the coefficient mean to obtain stronger robustness.

Then, the specific process of embedding the watermark bit _wi into the intermediate frequency coefficient matrix of the pre-processed image sub-block _B0i is:

The three-segment mapping function is constructed as Formula 7 and Formula 8. According to Formula 7, the embedding factor E _0i of the preprocessing sub-block B _0i is mapped to a judgment factor D _0i on a judgment domain:

Among them, Range1=[-0.3R,0.3R], Range2=[-0.7R,-0.3R)∪(0.3R,0.7R],

Range3＝[-k1×0.3R,k1×0.3R],

Range4＝[-k1×0.3R-k2×0.4R,-k1×0.3R)∪(k1×0.3R,k1×0.3R+k2×0.4R]; k1, k2, k3 are all slopes; R is the adjustment interval of the mapping function, and sign is the sign function.

The slope k1 is used to expand the change, so its value should be less than 1, but it cannot reverse the change, so the value range of k1 is k1∈(0,1); the slope k2 is used to ensure that the change in the middle is consistent, but small fluctuations will not affect the change, so the value range of k2 is k2∈[1,2]; the slope k3 is to reduce the change, so the value range is k3∈(10,+∞). In this embodiment, _k1 = 0.5, _k2 = 1, _k3 = 50, and R is the adjustment interval of the mapping function, which is determined to be 13.5 according to experiments.

Through this three-stage mapping function, the original embedded factor is mapped to a judgment domain for modification, so that the change in the judgment domain is large enough to ensure strong robustness, and the change in E _i after the inverse transformation is small enough to ensure high invisibility. At the same time, this three-stage mapping function controls the actual change after the inverse transformation through three different slopes k1, k2, and k3, so that it is large when close to the midpoint and far away from the midpoint, which is also to ensure strong robustness and high invisibility.

When the watermark bit _wi = 1, the watermark bit _wi is embedded into the judgment factor _Di according to formula 9 to obtain the judgment factor _DEMi after embedding the watermark; when the watermark bit _wi = 0, the watermark bit _wi is embedded into the judgment factor _Di according to formula 10 to obtain the judgment factor _DEMi after embedding the watermark:

Wherein, T represents the equilibrium threshold.

When embedding watermark bits, this scheme designs a binary positive and negative relationship embedding strategy to improve robustness. In the judgment domain, by linking the positive and negative relationship of the judgment factor _Di with the watermark bit _wi value of 0 and 1, it is set that when the watermark bit _wi is 1, the judgment factor _Di must be greater than or equal to 0; when the watermark bit _wi is 0, the judgment factor _Di must be less than 0; at the same time, in order to improve robustness, the algorithm also sets a threshold T, so that _Di not only meets the positive and negative relationship, but also requires its absolute value to be greater than T to ensure the strong robustness of the watermark, where T = k ₁ × 0.3R + k ₂ × 0.3R.

According to Formula 8, the watermarked judgment factor _DEMi is inversely mapped to the watermarked embedding factor _E0EMi , and then the watermarked embedding factor _E0EMi is added to the first intermediate frequency coefficient matrix LH _i and the second intermediate frequency coefficient matrix HL _i of the preprocessed image sub-block _B0i to obtain a new frequency domain coefficient matrix, that is, the watermarked coefficient matrix:

Mean _i =meanLH _i +meanHL _i ;

newLH _i =Mean _i +E _0EMi ;

newHL _i =Mean _i −E _0EMi ;

LH _EMi =LH _i +(newLH _i -meanLH _i );

HL _EMi =HL _i + (newHL _i -meanHL _i ).

Then, the coefficient matrix after embedding the watermark is inversely transformed by SLT according to Formula 2 to obtain the pixel matrix of the watermark embedded image sub-block B _1i in the spatial domain.

Step A30, traverse all watermark embedded image sub-blocks B _1i and perform anti-overflow processing.

The watermark is embedded in the image sub-block B _1i and anti-overflow processing is performed to obtain the anti-overflow watermark image sub-block B _2i .

After the watermark is embedded, the watermark embedded image sub-block B _1i may overflow. In order to ensure that there is no overflow during embedding, this paper performs anti-overflow processing on the watermark embedded image sub-block B _1i according to formula 11:

Wherein, Pixel is the pixel grayscale value of the watermark embedded image sub-block B _1i .

Step A40, traverse all anti-overflow watermark image sub-blocks B _2i and embed restoration information.

The present invention uses the transformation characteristics of jitter modulation to embed restoration information, that is, the values in the same range will return to the same value after each modulation, so the restoration information is added to the low-frequency coefficient after jitter modulation, so that when extracting, only one more jitter modulation is needed for the low-frequency coefficient to obtain the embedded restoration information. In this patent, the restoration information includes the change in the embedding factor caused by the embedded watermark and the anti-overflow processing and the difference between the original low-frequency coefficient and its jitter regression value during the first jitter modulation. In order to ensure that the image can be completely reversibly restored, it is necessary to ensure that the change in the embedding factor caused by the embedded watermark and the anti-overflow processing and the difference between the original low-frequency coefficient and its jitter regression value during the first jitter modulation can be separated during image restoration. The two values need to be processed to ensure that there is at least half an order of magnitude difference between them, and the number of decimal places of one of them must be fixed (or less than this fixed value). Next, it is explained why it is necessary to select integer channels and the measures for controlling overflow in this module mentioned above.

Here, the relationship between the change of the first low-frequency coefficient LL(1,1) and the change of the image pixels is first derived as follows:

The inverse SLT transform of the atomic block is shown in formula 12, and the inverse SLT transform after changing the low-frequency coefficient LL(1,1) is shown in formula 13, where S' is the low-frequency coefficient matrix after the first low-frequency coefficient LL(1,1) is increased by _ΔS , as shown in formula 14; according to the SLT _N matrix calculation method, it can be known that: SLT _N (1,1) = (1/2)∧(log ₂ N)/2), and then the change _Δs of the sub-block pixel matrix is calculated, as shown in formula 15.

After derivation, it can be found from formula 15 that the change of the first low-frequency coefficient LL(1,1) is in the same direction as the change of the image pixel, and the change of LL(1,1) will only affect the first pixel of the sub-block. Therefore, in order to control all changes so that the pixel grayscale value does not jump out of the [0,255] interval, the algorithm determines whether the grayscale value of the first pixel of the sub-block is greater than 127 and selects different dithering functions, namely DM functions, to control the direction of change.

When the gray value of the first pixel s(1,1)≥127, the dither modulation function is Formula 16; when the gray value of the first pixel s(1,1)＜127, the first dither modulation function is Formula 17:

Among them, floor() is the floor function, ceil() is the ceiling function, sign() is the sign function, H is the quantization step size, which is given empirically by the size of the first low-frequency coefficient LL(1,1), and NumLL is an intermediate variable, indicating the number of steps contained in the first low-frequency coefficient LL(1,1). In this algorithm, the quantization step size H is set to 20.

At the same time, since the number of decimal places of the change in the embedding factor is uncertain, the number of decimal places of the change in the low-frequency coefficient LL(1,1) needs to be finite. In order to ensure that the number of decimal places is fixed (or less than this fixed value), it is necessary to ensure that the low-frequency coefficient LL(1,1) after the original image transformation is an integer.

The relationship between the low-frequency coefficient LL(1,1) and the pixel gray value matrix is derived below. The SLT transform calculation is shown in formula 18. Only LL(1,1) is considered. The calculation of LL(1,1) is shown in formula 19. According to the SLT _N matrix calculation method, the first row of the SLT _N coefficient matrix is (1/2)^((log ₂ N)/2), so LL(1,1) can be calculated as shown in formula 20. When this algorithm sets N=32, LL(1,1) is 1/32 of the sum of the sub-block pixels. In summary, the image channel selected for embedding the watermark needs to be an integer channel.

Where si _,j is the grayscale value of the pixel in the i-th row and j-th column in the sub-block.

Specifically, the process of embedding and restoring information is as follows: the method of calculating the embedding factor for the preprocessed image sub-block B _0i is the same as that of performing SLT transformation on the anti-overflow watermark image sub-block B _2i from the spatial domain to the frequency domain, and the same method is used to calculate the embedding factor E _2i embedded with the watermark according to the intermediate frequency coefficient matrix of the anti-overflow watermark image sub-block B _2i .

According to the embedding factor E _0i of the preprocessed image sub-block B _0i and the embedding factor E _2i of the anti-overflow watermark image sub-block B ₂ embedded with the watermark, the embedding factor difference Dvalue ₁ is calculated as: Dvalue ₁ = E _2i - E _0i .

The first low-frequency coefficient LL _2i (1,1) of the anti-overflow watermark image sub-block B _2i is subjected to a first dither modulation process according to formula 16 or formula 17, depending on whether the grayscale value of the first pixel is less than 127, to obtain the first low-frequency coefficient LL _2i (1,1)' subjected to the first dither modulation process; according to the first low-frequency coefficient LL _2i (1,1) of the anti-overflow watermark image sub-block B _2i and the first low-frequency coefficient LL _2i (1,1)' subjected to the first dither modulation process, the first low-frequency coefficient difference Dvalue ₂ is calculated as: Dvalue ₂ =LL _2i (1,1)'-LL _2i (1,1).

Then the total difference Dvalue is synthesized by the embedding factor difference Dvalue ₁ and the first low-frequency coefficient difference Dvalue ₂ :

Wherein Dc1 is the control factor of the embedding factor difference, Dc2 is the control factor of the first low-frequency coefficient difference, Dc3 is the control factor of the total difference, and Dvalue ₂ ×Dc ₂ is an integer greater than 1, |Dvalue ₁ /Dc ₁ |＜0.5, Dvalue＜0.5H, H represents the quantization step size of the first dither modulation and the second dither modulation.

By setting the control factor Dc1 of the embedding factor difference, it is ensured that the adjusted embedding factor difference |Dvalue ₁ /Dc ₁ | is less than 0.5; by setting the control factor Dc2 of the first low-frequency coefficient difference, it is ensured that the adjusted first low-frequency coefficient difference Dvalue ₂ ×Dc ₂ is an integer greater than 1; by setting the control factor Dc3 of the total difference, the adjusted total difference Dvalue×Dc ₃ can be rounded off to obtain the adjusted first low-frequency coefficient difference Dvalue ₂ ×Dc ₂ , and then the adjusted total difference Dvalue is subtracted from the adjusted first low-frequency coefficient difference to obtain the adjusted embedding factor difference Dvalue ₁ /Dc _1. The control factor Dc ₃ of the total difference can make the synthesized total difference Dvalue less than half the quantization step, so as not to affect the jitter modulation interval.

Specifically, the present invention can infer the approximate distribution of the embedding factor Dvalue ₁ and the first low-frequency coefficient difference Dvalue ₂ through the distribution of the embedding factor E in multiple experiments and the jitter modulation function, thereby setting the values of the control factor Dc1 of the embedding factor difference, the first low-frequency coefficient difference Dc2 and the control factor Dc3 of the total difference. In this patent, because N=32, according to the derivation of the relationship between LL(1,1) and the sub-block pixel, Dc ₂ is set to 32, so that the adjusted first low-frequency coefficient difference Dvalue ₂ ×Dc ₂ is an integer. Since the maximum change of the embedding factor E will not exceed its distribution length, it can be assumed that its maximum change is its distribution length. In order to control |Dvalue ₁ /Dc ₁ |＜0.5, Dc1 is set to 2 times the embedding factor distribution length. In order to ensure that the setting of Dc1 is universal, according to a large number of experiments, it is concluded that the approximate distribution interval is (1,18), and in the algorithm we take the embedding factor distribution length as 25, so Dc1 is set to 50. Moreover, the total difference Dvalue needs to ensure that it does not affect the jitter modulation range, so Dvalue＜0.5H. Since Dvalue ₂ ×Dc ₂ is an integer greater than 1, and |Dvalue ₁ /Dc ₁ |＜0.5, the order of magnitude of the sum of the adjusted embedding factor difference Dvalue ₁ /Dc ₁ and the adjusted first low-frequency coefficient difference Dvalue ₂ ×Dc ₂ (Dvalue ₂ ×Dc ₂ +Dvalue ₁ /Dc ₁ ) only depends on the adjusted first low-frequency coefficient difference Dvalue ₂ ×Dc _2. According to Formula 16 and Formula 17, the maximum change value of Dvalue ₂ is 3H/2. Therefore, when the control factor Dc ₃ =3×Dc ₂ /2, the maximum value of the total difference Dvalue is almost equal to the quantization step H (because of the influence of the adjusted embedding factor difference). Therefore, Dc ₃ =3×Dc ₂ ×H/2=960 is set. In this way, the maximum change amount of Dvalue will not exceed 1.6, which is much smaller than H/2, and thus will not affect the jitter modulation range.

Then, the total difference Dvalue is embedded into the first low-frequency coefficient LL _2i (1,1)' after the first dither modulation process, and the first low-frequency coefficient LL _2i (1,1)' _EM embedded with the restored information is obtained: LL _2i (1,1)' _EM =LL _2i (1,1)'+Dvalue, and then the image after the total difference Dvalue is embedded is transformed from the frequency domain to the spatial domain to obtain the final watermark embedded image sub-block B _3i . The original image is shown in Figure 4(a), the watermark image is shown in Figure 4(b), and the final watermark embedded image is shown in Figure 4(c).

The watermark extraction process is shown in Figure 5, including:

Step B10, calculate the embedding factor: the final watermark embedded image sub-block B _3i is transformed from the spatial domain to the frequency domain by SLT transformation in the same way as the embedding factor calculation method for the pre-processed image sub-block B _0i , and the embedding factor E _3i is calculated according to the intermediate frequency coefficient matrix of the final watermark embedded image sub-block B _3i .

Step B20, extracting watermark bits: reconstructing the three-segment mapping function formula 7 and formula 8, and mapping the embedding factor E _3i of the final watermark embedded image sub-block B _3i to the judgment factor D _3i on the judgment domain according to formula 7, and extracting the watermark bit w _i from the judgment factor D _3i according to formula 22:

Traverse all the final watermark embedded image sub-blocks B _3i , extract all watermark bits, and combine them into a watermark. The result is shown in Figure 6. The bit error rate (BER) of the extracted watermark and the original watermark is calculated to be 0.

The image restoration process is shown in Figure 7, including:

For the image to be restored, that is, the image obtained by combining all the final watermark embedded image sub-blocks B _3i , firstly, the image to be restored is divided into non-overlapping image sub-blocks to be restored as the watermark embedding, which are the final watermark embedded image sub-blocks B _3i .

Step C10, traverse all final watermark embedded image sub-blocks B _3i , perform SLT transformation on the final watermark embedded image sub-block B _3i from the spatial domain to the frequency domain, and calculate the embedding factor E _3i according to the intermediate frequency coefficient matrix of the final watermark embedded image sub-block B _3i .

Step C20, calculating the restoration information, ie, the total difference Dvalue, and separating the embedding factor difference Dvalue ₁ and the first low-frequency coefficient difference Dvalue ₂ therefrom.

The first low-frequency coefficient LL _3i (1,1) of the final watermark embedded image sub-block B _3i is subjected to a second dither modulation according to formula 23 to return it to the dither regression value. It can be seen that the first low-frequency coefficient LL _3i (1,1)' after the second dither modulation is the same as the first low-frequency coefficient LL _2i (1,1)' after the first dither modulation: LL _3i (1,1)'＝LL _2i (1,1)'. Then the total difference Dvalue embedded in the first low-frequency coefficient LL _3i (1,1) is calculated according to formula 24:

Dvalue=LL _3i (1,1)-LL _3i (1,1)' (24).

The jitter modulation equation designed by the algorithm, when s(1,1) is greater than or equal to 127, formula 16 is to round down LL(1,1) and then reduce the half step size; when s(1,1) is less than 127, formula 17 is to round up LL _2i (1,1) and add half a step size, so that it can be guaranteed that the transformation of the first low-frequency coefficient LL _2i (1,1) will not cause s(1,1) to overflow. Therefore, regardless of whether the first jitter modulation uses formula 16 or formula 17 to perform jitter modulation on the first low-frequency coefficient LL _2i (1,1), when the second jitter modulation is performed on the image restoration, the first low-frequency coefficient LL _3i (1,1) of the final watermark embedded image sub-block B _3i can be rounded up and then reduced by half a step size to restore the jitter regression value, that is, the first low-frequency coefficient LL _3i (1,1)' after the second jitter modulation, as shown in formula 23.

Then, the total difference Dvalue and the setting values of the control factors Dc1, Dc2, and Dc3 are used to calculate the embedding factor difference Dvalue ₁ and the first low-frequency coefficient difference Dvalue ₂ according to formula 25:

Step C30, according to the embedding factor E _3i of the final watermark embedded image sub-block B _3i and the embedding factor difference Dvalue ₁ , the embedding factor E _4i of the restored image sub-block B _4i is calculated according to formula 26:

E _4i =E _3i -Dvalue ₁ (26). Since the carrier of the dither modulation and embedded restoration information is the first low-frequency coefficient, the carrier of the embedding factor used for watermark embedding is the intermediate frequency coefficient, and the processing of the low-frequency coefficient and the intermediate frequency coefficient is independent of each other and does not affect each other, the dither modulation processing of the first low-frequency coefficient of the anti-overflow watermark image sub-block B _2i will not affect the intermediate frequency coefficient, so E _3i =E _2i , and thus E _4i =E _3i -Dvalue ₁ =E _2i -Dvalue ₁ =E _0i , it can be obtained that the embedding factor E _4i of the restored image sub-block B _4i is the same as the embedding factor E _0i of the pre-processed image sub-block B _0i , and the image can be restored according to the embedding factor E _4i of the restored image sub-block B _4i .

Step C40, according to the first low-frequency coefficient LL _3i (1,1)' of the final watermark embedded image sub-block B _3i after the second dither modulation and the first low-frequency coefficient difference Dvalue ₂ , the first low-frequency coefficient LL _4i (1,1) of the restored image sub-block B ₄ is obtained according to formula (27):

LL _4i (1,1)=LL _3i (1,1)'-Dvalue ₂ (27).

Since the first low-frequency coefficient LL _3i (1,1)' after the second dither modulation is the same as the first low-frequency coefficient LL _2i (1,1)' after the first dither modulation: LL _3i (1,1)'=LL _2i (1,1)', it can be obtained that: LL _4i (1,1)=LL _3i (1,1)'-Dvalue ₂ =LL _2i (1,1)'-Dvalue ₂ =LL _2i (1,1). Because only the intermediate frequency coefficient of the image sub-block is processed before the dithering modulation processing is performed on the first low frequency coefficient of the anti-overflow watermark image sub-block B _2i, the low frequency coefficient and the intermediate frequency coefficient are independent of each other and are not affected. Therefore, the first low frequency coefficient LL _2i (1,1) of the anti-overflow watermark image sub-block B _2i is the same as the first low frequency coefficient LL _0i (1,1) of the pre-processed image sub-block B _0i : LL _2i (1,1) = LL _0i (1,1), so it can be obtained that: LL _4i (1,1) = LL _0i (1,1). Therefore, the image can be restored according to the first low frequency coefficient LL _4i (1,1) of the restored image sub-block B ₄ .

Step C50, calculate the intermediate frequency coefficient matrix of the restored image sub-block B _4i by the embedding factor E _4i of the restored image sub-block B _4i , and use the intermediate frequency coefficient matrix of the restored image sub-block B _4i and the first low-frequency coefficient LL _4i (1,1) to transform the restored image sub-block B _4i from the frequency domain to the spatial domain to obtain the restored image sub-block B _4i in the spatial domain. All the restored image sub-blocks B _4i constitute the restored image, as shown in Figure 8(a).

Since _{the embedding factor E 4i of} the restored image sub-block B _4i is the same as the embedding factor E _0i of the pre-processed image sub-block B _0i , and the first low-frequency coefficient LL _4i (1,1) of the restored image sub-block B ₄ is the same as the first low-frequency coefficient LL _0i (1,1) of the pre-processed image sub-block B _0i , the restored image sub-block B 4i is the same as the pre-processed image sub-block B _0i , so the original image can be completely reversibly restored. It can be verified by the absolute difference image between the restored image and the original image shown in Figure 8(b) that the restored image is the same as the original image, that is, the method of the present invention can achieve completely reversible restoration of the original image.

In this embodiment, firstly, in order to ensure that the watermark has strong robustness and invisibility, a three-segment mapping function is designed, and the robustness and invisibility of the watermark are improved through SLT transformation and binary embedding strategy. At this time, in order to restore the watermark, it is necessary to record the change caused by the three-segment mapping function processing embedding factor and anti-overflow processing, so as to completely reversibly restore the image, but this is a huge amount of additional information. Inspired by the reversible watermark algorithm based on the jitter modulation method, this information is embedded into the image through jitter modulation, which can greatly reduce the additional information. However, there are certain defects in the scheme based on jitter modulation alone. For example, jitter modulation has high requirements on the carrier, and the carrier itself needs to have a large value and high robustness, so the jitter modulation method is generally used at low frequency, but this has limitations on the application scenario, and jitter modulation can also cause overflow, which is not completely reversible. Therefore, the present invention designs an anti-overflow jitter modulation method, which first deals with the overflow problem caused by embedding, and then embeds this information into the SLT low-frequency coefficients in an anti-overflow manner, and only uses this method to reversibly restore the image, separating the restored information from the copyright information to improve robustness and expand the application scenarios. In this way, separating the restored information from the copyright information can further enhance robustness and invisibility.

Claims (6)

1. A watermark image restoration method based on SLT-DM, characterized by comprising the following steps: Watermark embedding process: Step A10, preprocessing the original image; If the original image is a color image, then the G channel layer of the original image is taken as the preprocessed image; if the original image is a grayscale image, then the original image is taken as the preprocessed image; the preprocessed image is divided into non-overlapping preprocessed image sub-blocks B _0i of size N×N, where i represents the sequence number corresponding to the image sub-block; Step A20, embedding a watermark; Traverse all pre-processed image sub-blocks B _0i , transform the pre-processed image sub-block B _0i from the spatial domain to the frequency domain, calculate the embedding factor E _0i according to the intermediate frequency coefficient matrix of the pre-processed image sub-block B _0i , embed the watermark bit into the intermediate frequency coefficient matrix of the pre-processed image sub-block B _0i , and then transform the image sub-block after watermark embedding from the frequency domain to the spatial domain to obtain the watermark embedded image sub-block B _1i ; Step A30, anti-overflow processing; Traverse all watermark embedded image sub-blocks B _1i , perform anti-overflow processing on the watermark embedded image sub-blocks B _1i , and obtain anti-overflow watermark image sub-blocks B _2i ; Step A40, embedding restoration information; Traverse all anti-overflow watermark image sub-blocks B _2i , transform the anti-overflow watermark image sub-block B _2i from the spatial domain to the frequency domain, and calculate the embedding factor E _2i embedded with the watermark according to the intermediate frequency coefficient matrix of the anti-overflow watermark image sub-block B _2i ; perform the first dithering modulation processing on the first low-frequency coefficient LL _2i (1,1) of the anti-overflow watermark image sub-block B _2i to obtain the first low-frequency coefficient LL _2i (1,1)' subjected to the first dithering modulation processing; calculate the embedding factor difference Dvalue ₁ according to the embedding factor E _0i of the pre-processed image sub-block B _0i and the embedding factor E _2i embedded with the watermark of the anti-overflow watermark image _sub -block B _2i as follows: Dvalue ₁ = E _2i -E _0i ; according to the first low-frequency coefficient LL _2i (1,1) of the anti-overflow watermark image sub-block B 2i and the first low-frequency coefficient LL _2i after the first dithering modulation processing (1,1)', the first low-frequency coefficient difference Dvalue ₂ is calculated as: Dvalue ₂ =LL _2i (1,1)'-LL _2i (1,1); the total difference Dvalue synthesized by the embedded factor difference Dvalue ₁ and the first low-frequency coefficient difference Dvalue ₂ is:

Dc1, Dc2, Dc3 are control factors, and Dvalue ₂ ×Dc ₂ is an integer greater than 1, |Dvalue ₁ /Dc ₁ |＜0.5, Dvalue＜0.5H, H represents the quantization step of the first dither modulation and the second dither modulation; the total difference Dvalue is embedded into the first low-frequency coefficient LL _2i (1,1)' after the first dither modulation process to obtain the first low-frequency coefficient LL _2i (1,1)' _EM embedded with restored information: LL _2i (1,1)' _EM ＝LL _2i (1,1)'+Dvalue, and then the image after the embedded restored information is transformed from the frequency domain to the spatial domain to obtain the final watermark embedded image sub-block B ₃ ; Image restoration process: Step C10, traverse all final watermark embedded image sub-blocks B _3i , transform the final watermark embedded image sub-block B _3i from the spatial domain to the frequency domain, and calculate the embedding factor E _3i according to the intermediate frequency coefficient matrix of the final watermark embedded image sub-block B _3i ; Step C20, performing a second dither modulation on the first low-frequency coefficient LL _3i (1,1) of the final watermark embedded image sub-block B _3i to obtain the first low-frequency coefficient LL _3i (1,1)' after the second dither modulation, and calculating the total difference Dvalue embedded in the first low-frequency coefficient LL _3i (1,1) according to formula (24), and then calculating the embedding factor difference Dvalue ₁ and the first low-frequency coefficient difference Dvalue ₂ according to formula (25) from the total difference Dvalue: Dvalue=LL _3i (1,1)-LL _3i (1,1)'(24);

Step C30, according to the embedding factor E _3i of the final watermark embedded image sub-block B _3i and the embedding factor difference Dvalue ₁ , obtain the embedding factor E _4i of the restored image sub-block B _4i : E _4i = E _3i - Dvalue ₁ = E _2i - Dvalue ₁ = E _0i ; Step C40, according to the first low-frequency coefficient LL _3i (1,1)' after the second dithering modulation of the final watermark embedded image sub-block B _3i and the first low-frequency coefficient difference Dvalue ₂ , obtain the first low-frequency coefficient LL _4i (1,1) of the restored image sub-block B _4i : LL _4i (1,1) = LL _3i (1,1)'-Dvalue ₂ = LL _2i (1,1)'-Dvalue ₂ = LL _2i (1,1) = LL _0i (1,1); Step C50, calculating the intermediate frequency coefficient matrix of the restored image sub-block B _4i by the embedding factor E _4i of the restored image sub-block B _4i , and using the intermediate frequency coefficient matrix of the restored image sub-block B _4i and the first low-frequency coefficient LL _4i (1,1), transforming the restored image sub-block B _4i from the frequency domain to the spatial domain to obtain the restored image sub-block B _4i in the spatial domain, and all the restored image sub-blocks B _4i constitute the restored image. 2. The method according to claim 1 is characterized in that, according to formula (1), the pixel matrix s of the image sub-block in the spatial domain is subjected to SLT transformation to obtain the image sub-block coefficient matrix S in the frequency domain, and the coefficient matrix S includes a low-frequency coefficient matrix LL, a first intermediate frequency coefficient matrix LH, a second intermediate frequency coefficient matrix HL and a high-frequency coefficient matrix HH; according to formula (2), the image sub-block coefficient matrix S in the frequency domain is subjected to inverse SLT transformation to obtain the pixel matrix s of the image sub-block in the spatial domain:

Among them, s is the pixel matrix of the image sub-block, S is the transformed SLT coefficient matrix, N is the size of the matrix, and SLT _N is the transformation matrix calculated according to the SLT transformation algorithm. 3. The method according to claim 1 is characterized in that the embedding factor E _i is calculated according to the intermediate frequency coefficient matrix of the image sub-block as follows: the intermediate frequency coefficient matrix of the image sub-block in the frequency domain includes a first intermediate frequency coefficient matrix LH _i and a second intermediate frequency coefficient matrix HL _i , and the average values of the elements in the first intermediate frequency coefficient matrix LH _i and the second intermediate frequency coefficient matrix HL _i are calculated respectively: meanLH _i =mean(LH _i ), meanHL _i =mean(HL _i ); and then the embedding factor E _i is calculated according to the average value meanLH _i of the first intermediate frequency coefficient matrix and the average value meanHL _i of the second intermediate frequency coefficient matrix: E _i =meanLH _i -meanHL _i , wherein mean() indicates averaging; The specific process of embedding the watermark bits into the intermediate frequency coefficient matrix of the preprocessed image sub-block B _0i is: The three-segment mapping function is constructed as formula (7) and (8), and the embedding factor E _0i of the preprocessing sub-block B _0i is mapped to a judgment factor D _0i on a judgment domain according to formula (7):

Among them, Range1 = [-0.3R, 0.3R], Range2 = [-0.7R, -0.3R)U(0.3R, 0.7R], Range3 = [-k1×0.3R, k1×0.3R], Range4 = [-k1×0.3R-k2×0.4R, -k1×0.3R)U(k1×0.3R, k1×0.3R+k2×0.4R]; k1, k2, k3 are all slopes, and k1∈(0,1), k2∈[1,2], k3∈(10,+∞); R is the adjustment interval of the mapping function, and sign is the sign function; When the watermark bit _wi = 1, the watermark bit _wi is embedded into the judgment factor _Di according to formula (9) to obtain the judgment factor _DEMi after embedding the watermark; when the watermark bit _wi = 0, the watermark bit _wi is embedded into the judgment factor _Di according to formula (10) to obtain the judgment factor _DEMi after embedding the watermark:

Where T represents the equilibrium threshold; According to formula (8), the watermarked judgment factor _DEMi is inversely mapped to the watermarked embedding factor _E0EMi , and then the watermarked embedding factor _E0EMi is added to the first intermediate frequency coefficient matrix LH and the second intermediate frequency coefficient matrix HL of the preprocessed image subblock _B0i . 4. The method according to claim 3 is characterized in that, before the image restoration, it also includes a watermark extraction process: Step B10, calculating the embedding factor: transforming the final watermark embedded image sub-block B _3i from the spatial domain to the frequency domain, and calculating the embedding factor E _3i according to the intermediate frequency coefficient matrix of the final watermark embedded image sub-block B _3i ; Step B20, extracting watermark bits: reconstructing the three-segment mapping function formula (7) and formula (8); mapping the embedding factor E _3i of the final watermark embedded image sub-block B _3i to the judgment factor D _3i on the judgment domain according to formula (7), and extracting the watermark bit w _i from the judgment factor D _3i according to formula (22):

Traverse all the final watermark embedded image sub-blocks B _3i , extract all watermark bits, and then combine them into a watermark. 5. The method according to claim 1 is characterized in that anti-overflow processing is performed on the watermark embedded image sub-block B _1i according to formula (11):

Wherein, Pixel is the pixel grayscale value of the watermark embedded image sub-block B _1i . 6. The method according to claim 1, characterized in that When the gray value of the first pixel s(1,1)≥127, the first dither modulation function is formula (16),

When the gray value of the first pixel s(1,1) is less than 127, the first dither modulation function is formula (17),

The second jitter modulation function is formula (23),

Among them, floor() is the floor function, ceil() is the ceiling function, and sign() is the sign function.

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