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

Watermark image restoration method based on SLT-DM Download PDF

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CN109493270B
CN109493270B CN201811321674.6A CN201811321674A CN109493270B CN 109493270 B CN109493270 B CN 109493270B CN 201811321674 A CN201811321674 A CN 201811321674A CN 109493270 B CN109493270 B CN 109493270B
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CN109493270A (en
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刘熙尧
王一帆
楼杰挺
张雅云
廖胜辉
邹北骥
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Central South University
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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

Watermark image restoration method based on SLT-DM
Technical Field
The invention belongs to the technical field of image digital watermarking, and particularly relates to a watermark image restoration method based on SLT-DM and aiming at the application fields with high nondestructive requirements such as medical image systems, military image systems and the like.
Background
With the development of internet technology and the innovation of new media technology, the digital media technology has made breakthrough progress, changes the dominant pattern of the traditional media in the information dissemination process, and simultaneously, a series of problems about the digital media also appear as the digital media is more abundant. Among them, how to effectively protect the copyright of the digital media, and prevent the digital media from being illegally copied or used has become an important aspect. Digital Rights Management (DRM) is a main means for protecting the rights of Digital media transmitted in a network, and Digital watermarking is increasingly regarded as an important technology of DRM. Watermarking is also increasingly combined with copyright protection in various digital media application scenarios, such as video and audio photographs, medical images, 3D images, videos, and the like.
Unlike traditional digital watermarking methods, in some fields such as medical imaging systems, military imaging systems, and remote sensing applications, any change in the original digital content may affect the final decision making process, thus requiring the watermark to be lossless for the operation of the original digital content. A watermarking scheme that meets such lossless requirements is called a lossless watermarking scheme. The lossless watermark includes a reversible watermark and a zero watermark.
Reversible watermarking schemes expect that after the embedded data is retrieved, the digital content can be recovered completely lossless. Most lossless watermarking schemes require a lossless environment to transmit the watermarked media, since small changes like channel noise or JPEG compression destroy the hidden watermark. In practical application, non-malicious attacks and malicious illegal attacks such as channel noise and lossy compression often occur, and even if a watermark medium experiences the attacks, a lossless watermark scheme also has the copyright protection capability, so that robustness is of practical significance to lossless watermarking. A lossless watermarking scheme that is effective against attacks against digital media is called a robust lossless watermarking scheme.
The design of the robust reversible watermarking algorithm often has a series of problems: the robustness, invisibility, embedding capacity and reversibility of the watermark need to be considered in design, however, the four requirements are not only a series of challenges in themselves, but also mutually toggle, which requires that the design of the watermark cannot only consider one requirement individually, but also needs to consider each requirement comprehensively. Robustness, invisibility and embedding capacity of the watermark are classic triangles of the watermarking algorithm, and how to improve and balance the robustness, invisibility and embedding capacity are always pursued by the watermarking algorithm. The robust reversible watermark adds a reversibility corner to the classical triangle, but the robust reversible watermark has a serious challenge: overflow, which often destroys reversibility, results in the watermark operation not being fully reversible.
To address the overflow problem, robust reversible watermarking algorithms often employ local-map based solutions for recording sub-blocks that can be watermarked without causing overflow or that require special handling to avoid overflow. However, the embedding capacity is greatly reduced, the calculation complexity is increased, and the invisibility is weakened by some methods; some algorithms adopt a method of directly recording overflow information, but the method can cause huge additional information; some algorithms directly ignore the overflow problem, but such watermarking operations are not fully reversible. These approaches, while suppressing overflow, often lead to new problems: 1) Excessive additional information; 2) The embedding capacity is reduced; 3) Invisibility is reduced; 4) The computational complexity increases and this problem is not completely solved.
Disclosure of Invention
In consideration of the problem that the existing image reversible methods cannot well solve the image overflow problem, the invention provides a watermark image restoration method based on SLT (Slantlet transform) -DM (Dither Modulation), wherein the change caused by watermark embedding and anti-overflow processing is embedded into the frequency domain of an image, so that the image can be completely restored reversibly after watermark embedding and anti-overflow processing, and no additional information is needed.
In order to achieve the technical purpose, the invention adopts the following technical scheme:
a watermark image restoration method based on SLT-DM includes the following steps:
and (3) watermark embedding process:
step A10, preprocessing an original image;
if the original image is a color image, taking a G channel image layer of the original image as a preprocessing image; if the original image is a gray image, the original image is used as a pre-processing image; dividing the pre-processed image into non-overlapping pre-processed image sub-blocks B of size NxN 0i Wherein i represents a serial number corresponding to the image subblock;
step A20, embedding a watermark;
traversing all preprocessed image sub-blocks B 0i Preprocessing the image sub-block B 0i Transformation from the spatial domain into the frequency domain, according to a preprocessed image sub-block B 0i Calculating an embedding factor E of the intermediate frequency coefficient matrix 0i Embedding watermark bits into pre-processed image sub-block B 0i Then the image sub-block after watermark embedding is converted from the frequency domain to the space domain to obtain the watermark embedding image sub-block B 1i ；
Step A30, anti-overflow treatment;
traversing all watermarksEmbedding image sub-block B 1i Embedding a watermark into an image sub-block B 1i Performing anti-overflow processing to obtain anti-overflow watermark image sub-block B 2i ；
Step A40, embedding reduction information;
traversing all anti-overflow watermark image sub-blocks B 2i The anti-overflow watermark image sub-block B 2i Converting from space domain to frequency domain according to anti-overflow watermark image sub-block B 2i Calculating an embedding factor E embedded with a watermark by using the intermediate frequency coefficient matrix 2i (ii) a For anti-overflow watermark image sub-block B 2i First low frequency coefficient LL of 2i (1, 1) carrying out a first dithering modulation processing to obtain a first low-frequency coefficient LL of the first dithering modulation processing 2i (1, 1)'; from pre-processed image sub-block B 0i Embedding factor E of 0i And anti-overflow watermark image sub-block B 2 Embedded with watermark embedding factor E 2i Calculating an embedding factor difference Dvalue 1 Comprises the following steps: dvalue 1 ＝E 2i -E 0i (ii) a According to the anti-overflow watermark image sub-block B 2i First low frequency coefficient LL of 2i (1, 1) and a first low-frequency coefficient LL after the first dither modulation processing 2i (1, 1)', calculating a first low frequency coefficient difference Dvalue 2 Comprises the following steps: dvalue 2 ＝LL 2i (1,1)'-LL 2i (1, 1); by the difference Dvalue of the embedding factor 1 And the first low-frequency coefficient difference Dvalue2, the total difference Dvalue is:
Figure BDA0001857674580000031
dc1, dc2, dc3 are control factors, and Dvalue 2 ×Dc 2 Is an integer greater than 1, | Dvalue 1 /Dc 1 I is less than 0.5, dvalue is less than 0.5H, H represents the quantization step size of the first time jitter modulation and the second time jitter modulation; embedding the total difference Dvalue into the first low-frequency coefficient LL after the first jitter modulation processing 2i (1, 1)', obtaining a first low frequency coefficient LL in which the restoration information is embedded 2i (1,1)' EM ：LL 2i (1,1)' EM ＝LL 2i (1, 1)' + Dvalue, and then the image embedded with the reduction information is transformed from the frequency domain to the space domain to obtain the final watermarkEmbedding image sub-block B 3 ；
And (3) image restoration process:
step C10, traversing all final watermark embedding image sub-blocks B 3i Embedding the final watermark into a sub-block B of the image 3i Transforming from spatial domain to frequency domain, embedding into image sub-block B according to final watermark 3i Calculating an embedding factor E of the intermediate frequency coefficient matrix 3i ；
Step C20, embedding the final watermark into the image sub-block B 3i First low frequency coefficient LL of 3i (1, 1) carrying out second jitter modulation to obtain a first low-frequency coefficient LL after the second jitter modulation 3i (1, 1)', calculated according to the formula (24) and embedded in the first low frequency coefficient LL 3i (1, 1), and calculating the embedding factor difference Dvalue according to the formula (25) by using the total difference Dvalue 1 And a first low frequency coefficient difference value Dvalue 2 ：
Dvalue＝LL 3i (1,1)-LL 3i (1,1)' (24)；
Figure BDA0001857674580000032
Step C30, embedding the image sub-block B according to the final watermark 3i Embedding factor E of 3i And the embedding factor difference Dvalue 1 To obtain a restored image sub-block B 4i Embedding factor E of 4i ：E 4i ＝E 3i -Dvalue 1 ＝E 2i -Dvalue 1 ＝E 0i ；
Step C40, embedding the image sub-block B according to the final watermark 3i Second dither modulated first low frequency coefficient LL 3i (1, 1)' and a first low frequency coefficient difference Dvalue 2 To obtain a restored image sub-block B 4i First low frequency coefficient LL of 4i (1,1)：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, restoring the image sub-block B 4i Embedding factor E of 4i ComputingRestoring image sub-block B 4i And using the restored image sub-block B 4i And the first low-frequency coefficient LL 4i (1, 1) restoring the image sub-block B 4i Transforming the image block into a space domain from a frequency domain to obtain a restored image sub-block B of the space domain 4i All restored image sub-blocks B 4i And forming a restored image.
The invention firstly eliminates the overflow problem caused by watermark embedding through the anti-overflow treatment, synthesizes the change quantity caused by watermark embedding and image overflow treatment and the change quantity caused by jitter modulation into the restored information and embeds the restored information into the image without overflow through the anti-overflow jitter modulation method, and controls the restored information to be smaller than the quantization step length of half jitter modulation, so that the restored information can not jump out of the jitter interval when being added on the first low-frequency coefficient, thereby ensuring the complete reversible restoration of the image, and the restoration does not need any additional information, and can not cause other problems of low embedding capacity, poor image quality, excessive additional information, high calculation complexity and the like.
Further, performing SLT transformation on a pixel matrix S of an image subblock in a spatial domain according to formula (1) to obtain an image subblock coefficient matrix S in a frequency domain, where 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; and (3) carrying out inverse SLT (simultaneous localization) transformation on the image subblock coefficient matrix S in the frequency domain according to a formula (2) to obtain a pixel matrix S of the image subblock in the spatial domain:
Figure BDA0001857674580000041
Figure BDA0001857674580000042
Figure BDA0001857674580000043
where s is the pixel matrix of the image sub-blockS is the transformed SLT coefficient matrix, N is the size of the matrix, SLT N Is a transformation matrix calculated according to the SLT transformation algorithm.
The SLT transformation adopted by the scheme has better invisibility, so that the robustness can be improved under the condition of ensuring the invisibility during design embedding.
Further, calculating an embedding factor E according to the intermediate frequency coefficient matrix of the image subblocks i The method specifically comprises the following steps: the intermediate frequency coefficient matrix of the image sub-block in the frequency domain comprises a first intermediate frequency coefficient matrix LH i And a second IF coefficient matrix HL i Separately calculating a first intermediate frequency coefficient matrix LH i And a second IF coefficient matrix HL i Average value of the elements in (1): meanLH i ＝mean(LH i )，meanHL i ＝mean(HL i ) (ii) a Then, the mean value meanLH of the first intermediate frequency coefficient matrix is used i And the average value meanHL of the second intermediate frequency coefficient matrix i Calculating an embedding factor E i ：E i ＝meanLH i -meanHL i Where mean () represents the average;
embedding watermark bits into pre-processed image sub-block B 0i The specific process in the intermediate frequency coefficient matrix is as follows:
constructing three-segment mapping functions as formulas (7) and (8), and preprocessing the sub-block B according to the formula (7) 0i Embedding factor E of 0i Decision factor D mapped onto a decision field 0i ：
Figure BDA0001857674580000051
Figure BDA0001857674580000052
Wherein, 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) (k 1 × 0.3R, k1 × 0.3R + k2 × 0.4R ]; k1, k2, k3 are slopes, and k1 ∈ (0, 1), k2 ∈ [1,2], k3 ∈ (10, + ∞); r is the adjustment interval of the mapping function, and sign is a sign function;
when the watermark bit w i If =1, watermark bit w is expressed by equation (9) i Is embedded into the judgment factor D i Obtaining the judgment factor D after embedding the watermark EMi (ii) a When the watermark bit w i If =0, watermark bit w is converted according to equation (10) i Is embedded into the judgment factor D i Obtaining the judgment factor D after embedding the watermark EMi ：
Figure BDA0001857674580000053
Figure BDA0001857674580000054
Wherein T represents an equilibrium threshold;
judging factor D after embedding watermark according to formula (8) EMi Inverse mapping to embedded factor E after embedding watermark 0EMi Then embedding factor E after embedding the watermark 0EMi Adding to a preprocessed image sub-block B 0i And the first and second midrange coefficient matrices LH and HL.
In the scheme, in order to ensure that the watermark has strong robustness and invisibility, a three-section embedding module is designed, and the robustness and the invisibility of the watermark are improved through SLT (slow scale time) conversion and a binary embedding strategy.
Further, before the image restoration, the method also comprises a watermark extraction process:
step B10, calculating an embedding factor: embedding the final watermark into the image sub-block B 3i Transforming from spatial domain to frequency domain, embedding into image sub-block B according to final watermark 3i Calculating an embedding factor E of the intermediate frequency coefficient matrix 3i ；
Step B20, extracting watermark bits: reconstructing a three-segment mapping function formula (7) and a three-segment mapping function formula (8); embedding the final watermark into the image sub-block B according to equation (7) 3i Embedding factor E of 3i Decision factor D mapped onto decision field 3i And determining the factor D from the equation (22) 3i In which watermark bit w is extracted i ：
Figure BDA0001857674580000061
Traversing all final watermark embedding image sub-blocks B 3i All watermark bits are extracted and combined to form the watermark.
According to the scheme, the watermark is extracted from the image, the copyright of the image can be verified, the copyright of the image is effectively protected, and illegal copying or use is avoided.
Further, the watermark is embedded into the image sub-block B according to equation (11) 1i And (3) performing anti-overflow treatment:
Figure BDA0001857674580000062
wherein Pixel is a watermark-embedded image sub-block B 1i The pixel gray value of (c).
The anti-overflow processing method for the image can avoid the pixel overflow problem caused by embedding the watermark into the image.
Further, when the gray-level value s (1, 1) ≧ 127 of the first pixel, the first-time dither modulation function is formula (16),
Figure BDA0001857674580000063
when the gray value s (1, 1) < 127 of the first pixel, the first-time dither modulation function is formula (17),
Figure BDA0001857674580000064
the second dither modulation function is equation (23),
Figure BDA0001857674580000071
wherein, floor () is a floor function, ceil () is a ceiling function, and sign () is a sign function.
Advantageous effects
The invention provides a watermark image restoration method based on SLT-DM, when the watermark is embedded, firstly dividing the image into non-overlapping sub-blocks, forming the watermark by the copyright information of the image and embedding the watermark into the intermediate frequency coefficient matrix of the frequency domain of each image sub-block, then transforming the image sub-blocks from the frequency domain to the space domain and carrying out overflow treatment; then, carrying out jitter modulation on the low-frequency coefficient of the frequency domain; then, the watermark is embedded, and the change quantity of the intermediate frequency coefficient caused by the overflow processing of the image sub-blocks and the change quantity of the low frequency information caused by the jitter modulation form restoration information and are embedded into the low frequency coefficient of the frequency domain; and finally, transforming the image sub-blocks from the frequency domain to the space domain, and splicing the image sub-blocks in the space domain into an image. When the image is restored, the image is divided into sub-blocks, then the low-frequency coefficient is subjected to jitter modulation to obtain restoration information after frequency domain transformation, and the low-frequency coefficient and the intermediate-frequency coefficient are restored by using the restoration information, and finally the original image is restored. The invention firstly eliminates the overflow problem caused by watermark embedding through the anti-overflow treatment, and synthesizes the change quantity caused by watermark embedding and image overflow treatment and the change quantity caused by jitter modulation into the restored information through the anti-overflow jitter modulation method, and embeds the restored information into the image without overflow, and controls the restored information to be smaller than the quantization step length of half jitter modulation, so that the restored information will not jump out of the jitter interval when being added on the first low-frequency coefficient, thereby ensuring the complete reversible restoration of the image, and the restoration does not need any additional information, and other problems of reducing the embeddable capacity, influencing the image quality, increasing the additional information, and the like can not be caused.
Drawings
FIG. 1 is a general flow chart of the algorithm of the present invention;
FIG. 2 is a watermark embedding flow diagram of the present invention;
FIG. 3 is a diagram of SLT coefficient matrix subband partitioning;
fig. 4 is a schematic diagram of watermark embedding in an embodiment, where (a) is an original image, (b) is a watermark image, and (c) is a final watermark-embedded image;
fig. 5 is a watermark extraction flow diagram of the present invention;
fig. 6 is an extracted watermark image;
FIG. 7 is a flow chart of image restoration of the present invention;
fig. 8 is a schematic diagram of restoration in an embodiment, in which (a) is a restored image and (b) is an absolute difference image of the restored image and an original image.
Detailed Description
The embodiment considers the overflow problem faced by the robust reversible watermark algorithm, and aims to effectively and simply avoid the overflow problem without causing other problems under the condition of not destroying the invisibility and the embedding capacity of the watermark.
The invention designs an anti-overflow jitter modulation module, and provides an SLT-DM-based robust reversible image watermarking method, which comprises three processes of watermark embedding, watermark extraction and image restoration as shown in figure 1.
The watermark embedding process is shown in fig. 2, and includes:
and step A10, preprocessing an original image.
If the original image is a color image, taking a G channel image layer of the original image as a preprocessing image; if the original image is a gray image, the original image is used as a pre-processing image; dividing the pre-processed image into non-overlapping pre-processed image sub-blocks B of size NxN 0i Where i represents the sequence number corresponding to the image sub-block.
Firstly, whether an image is a color image or not needs to be judged, if so, a G channel layer is taken, and if so, the G channel layer is directly adopted. Because the G channel in the three RGB channels shows more excellent robustness and invisibility and the limitation of generating the reduction information, the algorithm can only select the integral type channel, and the G channel is adopted in the color image instead of the Y channel because the generation of the reduction information is further detailed. This layer is then divided into non-overlapping sub-blocks of size nxn, into which each bit of watermark bits is to be embedded. Through testing, the method sets N =32.
Step A20, traversing all the preprocessed image sub-blocks B 0i And embedding a watermark.
Pre-processing image sub-block B 0i Transformation from the spatial domain into the frequency domain, according to a preprocessed image sub-block B 0i Calculating an embedding factor E of the intermediate frequency coefficient matrix 0i Embedding watermark bits into pre-processed image sub-block B 0i Then the image sub-block after watermark embedding is converted from the frequency domain to the space domain to obtain the watermark embedding image sub-block B 1i 。
Preprocessing image sub-block B in spatial domain according to equation 1 0i Performing SLT conversion to obtain an image subblock coefficient matrix of a frequency domain, wherein the coefficient matrix comprises 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:
Figure BDA0001857674580000081
Figure BDA0001857674580000082
Figure BDA0001857674580000091
where S is the pixel matrix of the image sub-block, S is the transformed SLT coefficient matrix, and N is the size of the matrix, where the SLT transform is only for the square matrix. SLT N Is a transformation matrix calculated from the SLT transformation algorithm.
The SLT transform is an optimized Discrete Wavelet Transform (DWT) that possesses better invisibility than DWT, allowing for better robustness under similar invisibility performance by increasing embedding strength. According to the Image transformation method explained by C.Mulc-ahy in Image compression using the Haarwave transform, we let us makeBy SLT N The matrix is used to calculate the SLT coefficient matrix for the image block instead of using the conventional SLT transform. The SLT transform is shown in equation 1, and the inverse transform is shown in equation 2. The SLT coefficient matrix is then divided into a low frequency coefficient matrix LL, a first intermediate frequency coefficient matrix LH, a second intermediate frequency coefficient matrix LH, and a high frequency coefficient matrix HH according to equation 3, as shown in fig. 3.
From pre-processed image sub-block B 0i Calculating an embedding factor E of the intermediate frequency coefficient matrix 0i The method specifically comprises the following steps: the intermediate frequency coefficient matrix of the image subblock in the frequency domain comprises HL, and the average value of elements in the first intermediate frequency coefficient matrix LH is calculated according to a formula 4 and the average value of elements in the second intermediate frequency coefficient matrix is calculated according to a formula 5 respectively:
meanLH i ＝mean(LH i ) (4)，
meanHL i ＝mean(HL i ) (5)；
then, the mean value meanLH of the first intermediate frequency coefficient matrix is used i And the average value meanHL of the second intermediate frequency coefficient matrix i Calculating the embedding factor E according to equation 6 i ：
E i ＝meanLH i -meanHL i (6)，
Where mean () represents the averaging function. The watermark is embedded by coefficient averaging to achieve greater robustness.
Then, watermark bit w i Embedding into a preprocessed image sub-block B 0i The specific process in the intermediate frequency coefficient matrix is as follows:
constructing three-segment mapping functions as formula 7 and formula 8, and preprocessing the sub-block B according to formula 7 0i Embedding factor E of 0i Decision factor D mapped onto a decision field 0i ：
Figure BDA0001857674580000092
Figure BDA0001857674580000101
/>
Wherein 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 (k 1 × 0.3R, k1 × 0.3R + k2 × 0.4R ]; k1, k2 and k3 are all slopes; r is the adjustment interval of the mapping function, and sign is a sign function.
The slope k1 is used for expanding the variation, so the value of the slope k1 is less than 1, but the variation cannot be reversed, and the value range of k1 belongs to (0, 1); the slope k2 is used to ensure that the variation in the middle is consistent, but small fluctuations will not affect the variation, so the value range of k2 is k2 ∈ [1,2]](ii) a The slope k3 is set to a value in the range of k3 ∈ (10, + ∞) in order to reduce the amount of change. In the present embodiment, k 1 ＝0.5,k 2 ＝1,k 3 =50, r is the adjustment interval of the mapping function, which is determined to be 13.5 according to the experiment.
The original embedding factor is mapped to a judgment domain through the three-segment mapping function to be changed, so that the variation of the judgment domain is large enough to ensure strong robustness, and meanwhile E is inversely transformed i Is small enough to ensure high invisibility. Meanwhile, the three-segment mapping function controls the real change amount after inverse transformation through three different slopes k1, k2 and k3, so that the real change amount is large when the real change amount is close to the midpoint and is far when the real change amount is far away from the midpoint, which also aims to ensure strong robustness and high invisibility.
When the watermark bit w i If =1, watermark bit w is expressed by equation 9 i Is embedded into the judgment factor D i Obtaining the judgment factor D after embedding the watermark EMi (ii) a When the watermark bit w i If =0, watermark bit w is mapped according to equation 10 i Is embedded into the judgment factor D i Obtaining the judgment factor D after embedding the watermark EMi ：
Figure BDA0001857674580000102
Figure BDA0001857674580000103
Where T represents the equilibrium threshold.
When watermark bits are embedded, a binary positive-negative relation embedding strategy is designed by the scheme so as to improve robustness. In the judgment domain, by a judgment factor D i Positive and negative relation of (d) to the watermark bit w i The values are 0 and 1, and the watermark bit w is set i When the value is 1, the factor D is judged i It is required to be 0 or more; when the watermark bit w i When 0, the factor D is judged i Needs to be less than 0; meanwhile, in order to improve robustness, the algorithm also sets a threshold value T to enable D i Not only must satisfy the positive-negative relation, but also the absolute value thereof must be greater than T to ensure the strong robustness of the watermark, where T = k 1 ×0.3R+k 2 ×0.3R。
Judging factor D after embedding watermark according to formula 8 EMi Inverse mapping to embedding factor E after embedding watermark 0EMi Then embedding factor E after embedding the watermark 0EMi Adding to a preprocessed image sub-block B 0i First intermediate frequency coefficient matrix LH of i And a second IF coefficient matrix HL i In the method, a new coefficient matrix of the frequency domain is obtained, namely the coefficient matrix after the watermark is embedded:
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, according to the formula 2, the coefficient matrix after embedding the watermark is subjected to inverse SLT transformation to obtain a spatial domain watermark embedded image subblock B 1i A matrix of pixels of (1).
Step A30, traversing all watermark embedding image sub-blocks B 1i And performing anti-overflow treatment.
Embedding a watermark into an image sub-block B 1i To prevent overflowPerforming output processing to obtain an anti-overflow watermark image sub-block B 2i 。
After watermark embedding, the watermark is embedded into image sub-block B 1i There is a possibility of overflow, and in order to ensure that there is no overflow during embedding, we apply equation 11 to embed the watermark into the image sub-block B 1i And (3) performing anti-overflow treatment:
Figure BDA0001857674580000111
wherein Pixel is the watermark embedded image sub-block B 1i The pixel gray scale value of (2).
Step A40, traversing all the anti-overflow watermark image sub-blocks B 2i And embedding restoring information.
The invention utilizes the conversion characteristic of the jitter modulation to embed the reduction information, namely, the value in the same range returns to the same value after being modulated each time, so that the reduction information is added into the low-frequency coefficient after the jitter modulation, and the embedded reduction information can be obtained only by carrying out the jitter modulation on the low-frequency coefficient once during extraction. In this patent, the restoration information includes the amount of change of the embedding factor caused by embedding the watermark and performing the anti-overflow processing, and the difference between the original low-frequency coefficient and the jitter regression value thereof during the first jitter modulation. In order to restore the image completely and reversibly, it is necessary to ensure that the amount of change of the embedding factor caused by the watermark embedding and the anti-overflow processing and the difference between the original low-frequency coefficient and the jitter regression value thereof during the first jitter modulation can be separated during the image restoration, the difference between the two values needs to be ensured to be at least half order of magnitude, and the number of small bits of one of the two values needs to be fixed (or smaller than the fixed value). The following is a description of how the integer type of channel needs to be selected and how this module controls overflow.
The relationship of the change of the first low-frequency coefficient LL (1, 1) to the change of the image pixels is derived here first as follows:
the inverse SLT transform of the original block is shown in equation 12, and the inverse SLT transform after changing the low frequency coefficient LL (1, 1) is shown in equation 13, where S' is the first low frequency systemNumber LL (1, 1) increased by Δ S The latter low frequency coefficient matrix, as shown in equation 14; according to SLT N The matrix calculation method can know that: SLT N (1,1)＝(1/2)∧(log 2 N)/2), then calculating the change delta of the sub-block pixel matrix s As shown in equation 15.
Figure BDA0001857674580000121
Figure BDA0001857674580000122
Figure BDA0001857674580000123
Figure BDA0001857674580000124
By derivation, it can be found from equation 15 that the amount of change of the first low frequency coefficient LL (1, 1) is in the same direction as the amount of change of the image pixel, and the change of LL (1, 1) affects only the first pixel of the sub-block. So to control that all changes do not cause the pixel's gray value to jump out of the [0,255] interval, the algorithm selects a different dithering function, i.e. DM function, to control the direction of change by determining whether the gray value of the first pixel of the sub-block is greater than 127.
When the gray value s (1, 1) of the first pixel is equal to or more than 127, the dithering modulation function is formula 16; when the gray value s (1, 1) < 127 of the first pixel, the first-time dither modulation function is formula 17:
Figure BDA0001857674580000125
Figure BDA0001857674580000126
where floor () is a floor function, ceil () is a ceiling function, sign () is a sign function, H is a quantization step, empirically given by the size of the first low frequency coefficient LL (1, 1), and NumLL is an intermediate variable representing the number of steps that the first low frequency coefficient LL (1, 1) contains. In the present algorithm, the quantization step H is set to 20.
Meanwhile, since the number of small digits of the amount of change of the embedding factor is uncertain, the small digits of the amount of change of the low-frequency coefficient LL (1, 1) need to be guaranteed to be limited. In order to ensure that the number of decimal places is fixed (or less than the 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 of the low frequency coefficient LL (1, 1) to the pixel gray value matrix is derived below. SLT transform calculation is shown in equation 18, considering only LL (1, 1), LL (1, 1) calculation is shown in equation 19, based on SLT N Known as the matrix calculation method, SLT N The first row of the coefficient matrix is (1/2) ^ (log) 2 N)/2), so LL (1, 1) can be calculated as in equation 20. When the present algorithm sets N =32, LL (1, 1) is 1/32 of the sub-block pixel sum. In summary, the image channel to be selected for embedding the watermark is required to be an integer channel.
Figure BDA0001857674580000131
Figure BDA0001857674580000132
Figure BDA0001857674580000133
Wherein s is i,j Is the gray value of the pixel in the ith row and j column in the sub-block.
Specifically, the process of embedding the restore information is as follows: e.g. for pre-processed image sub-block B 0i The same method for calculating the embedding factor is adopted, and the anti-overflow watermark image sub-block B is obtained 2i Performing an SLT transformation from the spatial domain to the frequency domain, anThe same method is adopted to carry out the anti-overflow watermark image sub-block B 2i Calculating an embedding factor E embedded with a watermark by using the intermediate frequency coefficient matrix 2i 。
According to the pre-processed image sub-block B 0i Embedding factor E of 0i And anti-overflow watermark image sub-block B 2 Embedded with watermark embedding factor E 2i Calculating an embedding factor difference Dvalue 1 Comprises the following steps: dvalue 1 ＝E 2i -E 0i 。
For anti-overflow watermark image sub-block B 2i First low frequency coefficient LL of 2i (1, 1) according to whether the gray value of the first pixel is less than 127, carrying out the first time jitter modulation processing according to the formula 16 or the formula 17 to obtain a first low-frequency coefficient LL of the first time jitter modulation processing 2i (1, 1)'; according to the anti-overflow watermark image sub-block B 2i First low frequency coefficient LL of 2i (1, 1) and the first low frequency coefficient LL after the first dither modulation processing 2i (1, 1)', calculating a first low frequency coefficient difference Dvalue 2 Comprises the following steps: dvalue 2 ＝LL 2i (1,1)'-LL 2i (1,1)。
Then the difference Dvalue of the embedding factor 1 And a first low frequency coefficient difference value Dvalue 2 Synthesizing a total difference Dvalue:
Figure BDA0001857674580000141
/>
where Dc1 is the control factor for the embedding factor difference, dc2 is the control factor for the first low frequency coefficient difference, dc3 is the control factor for the total difference, and Dvalue 2 ×Dc 2 Is an integer greater than 1, | Dvalue 1 /Dc 1 And | is less than 0.5, dvalue is less than 0.5H, and H represents the quantization step size of the first time jitter modulation and the second time jitter modulation.
Ensuring the adjusted embedding factor difference value | Dvalue by setting the control factor Dc1 of the embedding factor difference value 1 /Dc 1 Less than 0.5; the adjusted first low-frequency coefficient difference Dvalue is ensured by setting a control factor Dc2 of the first low-frequency coefficient difference 2 ×Dc 2 Is an integer greater than 1(ii) a The adjusted total difference Dvalue multiplied by Dc is set by the control factor Dc3 of the total difference 3 The adjusted first low-frequency coefficient difference Dvalue can be determined by rounding 2 ×Dc 2 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 . And the control factor Dc of the total difference 3 The resultant total difference Dvalue can be made smaller than half the quantization step size so as not to affect the dither modulation interval.
In particular, the invention can deduce the embedding factor Dvalue through the distribution of the embedding factor E in a plurality of experiments and the jitter modulation function 1 Difference Dvalue with first low frequency coefficient 2 The values of the embedding factor difference control factor Dc1, the first low-frequency coefficient difference value Dc2, and the total difference control factor Dc3 are set accordingly. In this patent, since N =32, dc is derived from the relationship of LL (1,1) to the sub-block pixels 2 Is set to 32 so that the adjusted first low frequency coefficient difference Dvalue 2 ×Dc 2 Are integers. Since the variation of the embedding factor E does not exceed the distribution length at the maximum, it can be assumed that the maximum variation thereof is the distribution length thereof in order to control | Dvalue 1 /Dc 1 If | is less than 0.5, so Dc1 is set to 2 times the embedding factor distribution length, to ensure the universality of the setting of Dc1, it is found out from a large number of experiments that the approximate distribution interval is (1, 18), and in the algorithm we take the embedding factor distribution length to be 25, so Dc1=50 is set. Moreover, the total difference Dvalue needs to be guaranteed not to affect the jitter modulation range, so Dvalue < 0.5H. And due to Dvalue 2 ×Dc 2 Is an integer greater than 1, and | Dvalue 1 /Dc 1 | is less than 0.5, so the adjusted embedding factor difference Dvalue 1 /Dc 1 And the adjusted first low-frequency coefficient difference Dvalue 2 ×Dc 2 Sum (Dvalue) 2 ×Dc 2 +Dvalue 1 /Dc 1 ) Is only dependent on the adjusted first low frequency coefficient difference Dvalue 2 ×Dc 2 Dvalue can be known from the equations 16 and 17 2 Has a maximum variation value of 3H/2, soTo control the factor Dc 3 ＝3×Dc 2 At/2, the maximum value of the total difference Dvalue is almost equal to the quantization step H (since there is also an effect of the adjusted embedding factor difference), so set Dc 3 ＝3×Dc 2 X H/2=960 so that the maximum variation of the Dvalue does not exceed 1.6 and is much smaller than H/2, thereby not affecting the jitter modulation range.
Then, the total difference Dvalue is embedded into the first low frequency coefficient LL after the first dither modulation processing 2i (1, 1)', obtaining a first low frequency coefficient LL embedding the reproduction information 2i (1,1)' EM ：LL 2i (1,1)' EM ＝LL 2i (1, 1)' + Dvalue, and then the image embedded with the total difference Dvalue is transformed from the frequency domain to the space domain to obtain the final watermark embedded image sub-block B 3i . The original image is shown in fig. 4 (a), the watermark image is shown in fig. 4 (b), and the final watermark-embedded image is shown in fig. 4 (c).
The watermark extraction process is shown in fig. 5 and includes:
step B10, calculating an embedding factor: e.g. for pre-processing image sub-block B 0i The same method is used for calculating the embedding factor, and the final watermark is embedded into the image sub-block B 3i SLT transform from spatial domain to frequency domain, embedding in image sub-block B according to final watermark 3i Calculating an embedding factor E of the intermediate frequency coefficient matrix 3i 。
Step B20, extracting watermark bits: reconstructing three-segment mapping function formula 7 and formula 8, and embedding the final watermark into the image sub-block B according to formula 7 3i Embedding factor E of 3i Decision factor D mapped onto decision field 3i And determining the factor D from the equation 22 3i In which watermark bit w is extracted i ：
Figure BDA0001857674580000151
Traversing all final watermark embedding image sub-blocks B 3i All watermark bits are extracted and combined to form the watermark. The result is shown in fig. 6, and the Bit Error Rate (BER) calculation of the extracted watermark and the original watermark0 is obtained.
The image restoration process is shown in fig. 7 and includes:
for the image to be restored, i.e. all final watermarks embedded in the image sub-block B 3i Combining the obtained images, dividing the images to be restored into non-overlapping image sub-blocks to be restored according to the same watermark embedding, namely, the final watermark embedding image sub-block B 3i 。
Step C10, traversing all final watermark embedding image sub-blocks B 3i Embedding the final watermark into the image sub-block B 3i SLT transform from spatial domain to frequency domain, embedding in image sub-block B according to final watermark 3i Calculating an embedding factor E of the intermediate frequency coefficient matrix 3i 。
Step C20, calculating reduction information, namely a total difference Dvalue, and separating an embedding factor difference Dvalue from the reduction information 1 And a first low frequency coefficient difference value Dvalue 2 。
Embedding the final watermark into an image sub-block B 3i First low-frequency coefficient LL of 3i (1, 1) performing a second dither modulation according to the formula 23 to return to a dither regression value, thereby obtaining a first low frequency coefficient LL after the second dither modulation 3i (1, 1)' and the first low-frequency coefficient LL after the first time jitter modulation 2i (1, 1)' same: LL (LL) 3i (1,1)'＝LL 2i (1,1)'. Then calculating according to formula 24 to obtain the embedded low-frequency coefficient LL 3i Total difference Dvalue of (1, 1):
Figure BDA0001857674580000161
Dvalue＝LL 3i (1,1)-LL 3i (1,1)' (24)。
when s (1, 1) is greater than or equal to 127, formula 16 is to round down LL (1, 1) and then reduce by half step size; when s (1, 1) is less than 127, equation 17 is for LL 2i (1, 1) rounding up and then half step length, so that the first low-frequency coefficient LL can be ensured 2i The transformation of (1, 1) does not cause s (1, 1) to overflow up and down. Therefore, whether the first dither modulation uses equation 16 or equation 16Using equation 17 to pair the first low frequency coefficient LL 2i (1, 1) carrying out dithering modulation, and embedding the final watermark into the image subblock B when carrying out second dithering modulation on image restoration 3i First low frequency coefficient LL of 3i (1, 1) rounding up and reducing by half step length to obtain a jitter regression value, namely a first low-frequency coefficient LL after second jitter modulation 3i (1, 1)', as shown in equation 23.
Then, the total difference Dvalue and the setting values of the control factors Dc1, dc2 and Dc3 are calculated according to the formula 25 to obtain the embedding factor difference Dvalue 1 And a first low frequency coefficient difference value Dvalue 2 ：
Figure BDA0001857674580000162
Step C30, embedding the image sub-block B according to the final watermark 3i Embedding factor E of 3i And the embedding factor difference Dvalue 1 The restored image sub-block B is calculated according to the formula 26 4i Embedding factor E of 4i ：
E 4i ＝E 3i -Dvalue 1 (26). Because the carrier for jitter modulation and embedding reduction information is the first low-frequency coefficient, the carrier for the embedding factor of watermark embedding is the intermediate-frequency coefficient, and the processing of the low-frequency coefficient and the intermediate-frequency coefficient are independent and do not influence each other, the overflow-preventing watermark image sub-block B is processed 2i Does 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 Thus, the image sub-block B can be restored 4i Embedding factor E of 4i And pre-processing image sub-block B 0i Embedding factor E of 0i Similarly, image sub-block B may be restored from 4i Embedding factor E of 4i And restoring the image.
Step C40, embedding the image sub-block B according to the final watermark 3i First low-frequency coefficient LL after second time jitter modulation 3i Difference between (1, 1)' and the first low-frequency coefficientDvalue 2 Obtaining a restored image sub-block B according to the formula (27) 4 First low frequency coefficient LL of 4i (1,1)：
LL 4i (1,1)＝LL 3i (1,1)'-Dvalue 2 (27)。
The first low-frequency coefficient LL after the second time of jitter modulation 3i (1, 1)' and the first low-frequency coefficient LL after the first time jitter modulation 2i (1, 1)' same: LL (LL) 3i (1,1)'＝LL 2i (1, 1)', available: LL (LL) 4i (1,1)＝LL 3i (1,1)'-Dvalue 2 ＝LL 2i (1,1)'-Dvalue 2 ＝LL 2i (1,1). Due to the fact that the anti-overflow watermark image sub-block B is paired 2i Before the first low-frequency coefficient is subjected to jitter modulation processing, only the intermediate-frequency coefficient of the image subblock is processed, and the low-frequency coefficient and the intermediate-frequency coefficient are independent from each other and are not influenced, so that the anti-overflow watermark image subblock B 2i First low frequency coefficient LL of 2i (1, 1) and Pre-processed image sub-Block B 0i First low frequency coefficient LL of 0i (1, 1) the same: LL (LL) 2i (1,1)＝LL 0i (1, 1), thus obtaining: LL (LL) 4i (1,1)＝LL 0i (1,1). So that the sub-block B of the image can be restored according to the restored image 4 First low frequency coefficient LL of 4i (1, 1) restoring the image.
Step C50, restoring the image sub-block B 4i Embedding factor E of 4i Computing restored image sub-block B 4i And using the restored image sub-block B 4i And the first low-frequency coefficient LL 4i (1, 1) restoring the image sub-block B 4i Transforming the image block B into a space domain from a frequency domain to obtain a restored image sub-block B of the space domain 4i All restored image sub-blocks B 4i The restored image is constructed as shown in fig. 8 (a).
Since the image sub-block B is restored 4i Embedding factor E of 4i And pre-processing image sub-block B 0i Embedding factor E of 0i Same, and restoring image sub-block B 4 First low frequency coefficient LL of 4i (1, 1) and Pre-processed image sub-Block B 0i First low frequency coefficient LL of 0i (1, 1) same, so that the image sub-block B is restored 4i And pre-processing image sub-block B 0i And (b) verifying the restored image shown in fig. 8 (b) and the absolute difference image of the original image to obtain the restored image, wherein the restored image is the same as the original image, namely the method realizes the completely reversible restoration of the original image.
In this embodiment, first, 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 by SLT transformation and a binary embedding strategy. In order to restore the watermark, it is necessary to record the amount of change caused by the embedding factor and the anti-overflow processing in the three-segment mapping function process, so as to restore the image completely and reversibly, but this is a huge additional information. This information is embedded in the image by dither modulation, which is inspired by reversible watermarking algorithms based on dither modulation methods, which can reduce the additional information by a large amount. However, the scheme based on the pure dither modulation has certain defects, for example, the dither modulation has high requirements on the carrier, and the carrier itself needs to have a large value and high robustness, so the method of the dither modulation is generally used at a low frequency, but the application scenario is limited, and the dither modulation causes overflow and is not completely reversible. Therefore, the invention designs an anti-overflow jitter modulation method, firstly, the overflow problem caused by embedding is processed, then, the information is embedded into the SLT low-frequency coefficient in an anti-overflow mode, and the image can be restored reversibly only by using the method, the restored information is separated from the copyright information so as to improve the robustness and widen the application scene, so that the robustness and the invisibility can be enhanced again by separating the restored information from the copyright information.

Claims (6)

1. A watermark image restoration method based on SLT-DM is characterized by comprising the following steps:
and (3) watermark embedding process:
step A10, preprocessing an original image;
if the original image is a color image, taking a G channel image layer of the original image as a preprocessing image; if the original image is a gray image, the original image is used as a pre-processing image;dividing the pre-processed image into non-overlapping pre-processed image sub-blocks B of size NxN 0i Wherein i represents a serial number corresponding to the image subblock;
step A20, embedding a watermark;
traversing all pre-processed image sub-blocks B 0i Preprocessing the image sub-block B 0i Transformation from the spatial domain into the frequency domain, according to a preprocessed image sub-block B 0i Calculating an embedding factor E of the intermediate frequency coefficient matrix 0i Embedding watermark bits into the pre-processed image sub-block B 0i Then the image sub-block after watermark embedding is converted from the frequency domain to the space domain to obtain the watermark embedding image sub-block B 1i ；
Step A30, anti-overflow treatment;
traversing all watermark embedding image sub-blocks B 1i Embedding a watermark into an image sub-block B 1i Performing anti-overflow treatment to obtain anti-overflow watermark image sub-block B 2i ；
Step A40, embedding reduction information;
traversing all anti-overflow watermark image sub-blocks B 2i The anti-overflow watermark image sub-block B 2i Transforming from space domain to frequency domain, and watermarking the image sub-block B according to the overflow prevention 2i Calculating an embedding factor E embedded with a watermark by using the intermediate frequency coefficient matrix 2i (ii) a For anti-overflow watermark image sub-block B 2i First low frequency coefficient LL of 2i (1, 1) carrying out a first dithering modulation processing to obtain a first low-frequency coefficient LL of the first dithering modulation processing 2i (1, 1)'; from pre-processed image sub-block B 0i Embedding factor E of 0i And anti-overflow watermark image sub-block B 2 Embedded with watermark embedding factor E 2i Calculating an embedding factor difference Dvalue 1 Comprises the following steps: dvalue 1 ＝E 2i -E 0i (ii) a According to the anti-overflow watermark image sub-block B 2i First low frequency coefficient LL of 2i (1, 1) and the first low frequency coefficient LL after the first dither modulation processing 2i (1, 1)', calculating a first low frequency coefficient difference Dvalue 2 Comprises the following steps: dvalue 2 ＝LL 2i (1,1)'-LL 2i (1, 1); by the difference Dvalue of the embedding factor 1 And a first low frequency coefficient difference value Dvalue 2 The total difference Dvalue is synthesized as:
Figure FDA0003979829740000011
dc1, dc2, dc3 are control factors, and Dvalue 2 ×Dc 2 Is an integer greater than 1, | Dvalue 1 /Dc 1 I is less than 0.5, dvalue is less than 0.5H, H represents the quantization step size of the first time jitter modulation and the second time jitter modulation; embedding the total difference Dvalue into the first low-frequency coefficient LL after the first jitter modulation processing 2i (1, 1)', obtaining a first low frequency coefficient LL in which the restoration information is embedded 2i (1,1)' EM ：LL 2i (1,1)' EM ＝LL 2i (1, 1)' + Dvalue, and then the image embedded with the reduction information is transformed from the frequency domain to the space domain to obtain the final watermark embedded image sub-block B 3 ；
And (3) image restoration process:
step C10, traversing all final watermark embedding image sub-blocks B 3i Embedding the final watermark into a sub-block B of the image 3i Transforming from spatial domain to frequency domain, embedding into image sub-block B according to final watermark 3i Calculating the embedding factor E of the intermediate frequency coefficient matrix 3i ；
Step C20, embedding the final watermark into the image sub-block B 3i First low frequency coefficient LL of 3i (1, 1) carrying out second jitter modulation to obtain a first low-frequency coefficient LL after the second jitter modulation 3i (1, 1)', calculated according to the formula (24) and embedded in the first low frequency coefficient LL 3i (1, 1), and calculating the embedding factor difference Dvalue according to a formula (25) by using the total difference Dvalue 1 And a first low frequency coefficient difference value Dvalue 2 ：
Dvalue＝LL 3i (1,1)-LL 3i (1,1)' (24)；
Figure FDA0003979829740000021
Step C30, embedding the image sub-block B according to the final watermark 3i Embedding factor E of 3i And the embedding factor difference Dvalue 1 To obtain a restored image sub-block B 4i Embedding factor E of 4i ：E 4i ＝E 3i -Dvalue 1 ＝E 2i -Dvalue 1 ＝E 0i ；
Step C40, embedding the image sub-block B according to the final watermark 3i Second dither modulated first low frequency coefficient LL 3i (1, 1)' and a first low frequency coefficient difference Dvalue 2 To obtain a restored image sub-block B 4i First low frequency coefficient LL of 4i (1,1)：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, restoring the image sub-block B 4i Embedding factor E of 4i Computing restored image sub-block B 4i And using the restored image sub-block B 4i And the first low-frequency coefficient LL 4i (1, 1) restoring the image sub-block B 4i Transforming the image block into a space domain from a frequency domain to obtain a restored image sub-block B of the space domain 4i All restored image sub-blocks B 4i And forming a restored image.
2. The method of claim 1, wherein the SLT transform is performed on a pixel matrix S of the image subblock in the spatial domain according to formula (1), so as to obtain an image subblock coefficient matrix S in the frequency domain, wherein 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; carrying out inverse SLT transformation on the image subblock coefficient matrix S in the frequency domain according to a formula (2) to obtain a pixel matrix S of the image subblock in the spatial domain:
Figure FDA0003979829740000031
Figure FDA0003979829740000032
Figure FDA0003979829740000033
wherein S is the pixel matrix of the image subblock, S is the transformed SLT coefficient matrix, N is the size of the matrix, SLT N Is a transformation matrix calculated according to the SLT transformation algorithm.
3. Method according to claim 1, characterized in that the embedding factor E is calculated from a matrix of intermediate frequency coefficients of image sub-blocks i The method comprises the following specific steps: the intermediate frequency coefficient matrix of the image sub-block in the frequency domain comprises a first intermediate frequency coefficient matrix LH i And a second IF coefficient matrix HL i Separately calculating a first intermediate frequency coefficient matrix LH i And a second IF coefficient matrix HL i Average value of the elements in (1): meanLH i ＝mean(LH i )，meanHL i ＝mean(HL i ) (ii) a Then, the mean value meanLH of the first intermediate frequency coefficient matrix is used i And the average value meanHL of the second intermediate frequency coefficient matrix i Calculating an embedding factor E i ：E i ＝meanLH i -meanHL i Where mean () represents the average;
embedding watermark bits into pre-processed image sub-block B 0i The specific process in the intermediate frequency coefficient matrix is as follows:
constructing three-segment mapping functions as formulas (7) and (8), and preprocessing the sub-block B according to the formula (7) 0i Embedding factor E of 0i Decision factor D mapped onto a decision field 0i ：
Figure FDA0003979829740000034
Figure FDA0003979829740000035
Wherein, 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 (k 1 × 0.3R, k1 × 0.3R + k2 × 0.4R ]; k1, k2, k3 are slopes, and k1 ∈ (0, 1), k2 ∈ [1,2], k3 ∈ (10, + ∞); r is the adjustment interval of the mapping function, and sign is a sign function;
when the watermark bit w i If =1, watermark bit w is expressed by equation (9) i Is embedded into the judgment factor D i Obtaining the judgment factor D after embedding the watermark EMi (ii) a When the watermark bit w i If =0, watermark bit w is converted according to equation (10) i Is embedded into the judgment factor D i Obtaining the judgment factor D after embedding the watermark EMi ：
Figure FDA0003979829740000041
Figure FDA0003979829740000042
Wherein T represents an equilibrium threshold;
judging factor D after embedding watermark according to formula (8) EMi Inverse mapping to embedding factor E after embedding watermark 0EMi Then embedding factor E after embedding the watermark 0EMi Adding to a preprocessed image sub-block B 0i And the first and second midrange coefficient matrices LH and HL.
4. The method of claim 3, further comprising, prior to image restoration, a watermark extraction process:
step B10, calculating an embedding factor: embedding the final watermark into the image sub-block B 3i Transforming from spatial domain to frequency domain, embedding into image sub-block B according to final watermark 3i Calculating an embedding factor E of the intermediate frequency coefficient matrix 3i ；
Step B20, extracting watermark bits: reconstructing a three-segment mapping function formula (7) and a three-segment mapping function formula (8); embedding the final watermark into the image according to equation (7)Image block B 3i Embedding factor E of 3i Decision factor D mapped onto decision field 3i And determining the factor D from the equation (22) 3i In which watermark bit w is extracted i ：
Figure FDA0003979829740000043
Traversing all final watermark embedding image sub-blocks B 3i All watermark bits are extracted and combined to form the watermark.
5. Method according to claim 1, characterized in that the watermark is embedded in the image sub-block B according to equation (11) 1i And (3) performing anti-overflow treatment:
Figure FDA0003979829740000044
wherein Pixel is a watermark-embedded image sub-block B 1i The pixel gray value of (c).
6. The method of claim 1,
when the gray value s (1, 1) ≧ 127 of the first pixel, the first-time dither modulation function is formula (16),
Figure FDA0003979829740000051
when the gray scale value s (1, 1) < 127 of the first pixel, the first-time dithering modulation function is formula (17),
Figure FDA0003979829740000052
the second dither modulation function is equation (23),
Figure FDA0003979829740000053
wherein, floor () is a floor function, ceil () is a ceiling function, and sign () is a sign function.
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