CN112132731A - DWT-SVD domain adaptive robust watermarking algorithm adopting preset PSNR - Google Patents

DWT-SVD domain adaptive robust watermarking algorithm adopting preset PSNR Download PDF

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CN112132731A
CN112132731A CN202010948552.0A CN202010948552A CN112132731A CN 112132731 A CN112132731 A CN 112132731A CN 202010948552 A CN202010948552 A CN 202010948552A CN 112132731 A CN112132731 A CN 112132731A
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watermark
blocks
embedded
image
block
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CN112132731B (en
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王文冰
桑永宣
毛艳芳
张玲
杨华
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Zhengzhou University of Light Industry
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    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
    • G06T1/00—General purpose image data processing
    • G06T1/0021—Image watermarking
    • G06T1/005—Robust watermarking, e.g. average attack or collusion attack resistant
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
    • G06T2201/00—General purpose image data processing
    • G06T2201/005—Image watermarking
    • G06T2201/0202—Image watermarking whereby the quality of watermarked images is measured; Measuring quality or performance of watermarking methods; Balancing between quality and robustness

Abstract

The invention belongs to the technical field of image information processing, and particularly relates to a DWT-SVD domain adaptive robust watermarking algorithm adopting a preset PSNR. The method utilizes the anti-aggressivity of discrete wavelet transform and the stability of singular value decomposition, embeds watermarks by modifying the size relation between the first column elements of the left singular matrix of the image and modifies the right singular matrix to realize quality compensation. The method is different from other algorithms which use fixed embedding parameters or obtain the embedding parameters by repeated experiments, the embedding strength of the watermark depends on the embedding parameters, the invention not only establishes the correlation among the embedding parameters, the carrier image and the watermark information, but also does not need to sacrifice the time complexity of the algorithm, and the pixel overflow and the correction after the embedding are finished enhance the reliability of the algorithm.

Description

DWT-SVD domain adaptive robust watermarking algorithm adopting preset PSNR
Technical Field
The invention belongs to the technical field of image information processing, and particularly relates to a DWT-SVD domain adaptive robust watermarking algorithm adopting a preset PSNR.
Background
The network is opened to bring convenience to the multimedia circulation, and simultaneously, the intellectual property protection of various content information faces unprecedented challenges. Among various electronic information protection means, electronic watermarks having characteristics such as concealment and security attract attention of students. Electronic watermarking refers to the secret embedding of electronic information called watermark in carrier information such as images, videos, audios and the like, and the carrier ownership, integrity and the like are indicated by the accuracy of watermark extraction at an extractor.
Conventional image watermarks are classified into two categories according to function: and the robust watermark and the fragile watermark are respectively used for protecting the image copyright and the image content integrity. The robust watermark is the watermark embedded by modifying the content of the carrier, and the recognizable watermark information can still be extracted after the image is attacked. The modification of the carrier information by the embedding necessarily causes a degradation of the image quality. Therefore, the robust watermark performance measurement indexes are mainly three: capacity, robustness, visibility. These three indexes are eliminated, and when the watermark capacity is determined, the watermark method needs to sacrifice the image quality after watermark embedding for the purpose of pursuing robustness, and vice versa. The information load capacity of the carrier, the quality of the watermark image and the integrity of the watermark extracted after the carrier is attacked are optimized as much as possible, and the design aim of the robust watermark method is always achieved.
The watermark embedding process can be divided into a spatial domain watermark and a frequency domain watermark according to an embedding domain. The spatial domain watermark directly modifies spatial domain pixels to embed the watermark, and although the computation complexity is low, the pixel interference is large in image processing, so that the robustness is reduced. By utilizing the advantages of energy gathering capability and multiple analysis capability of frequency domain conversion and embodying time domain or frequency domain characteristics of the image, the algorithm based on the frequency domain has stronger robustness and image quality, thereby being widely applied to a watermarking algorithm. In the frequency domain algorithm, DCT, DWT, RDWT and FrFT are common conversion modes, and multiple conversions enable the algorithm to integrate the advantages of different conversions, so that the aim of improving the performance of the algorithm is finally achieved, and the method becomes a research hotspot of the watermarking algorithm in recent years.
Besides considering the design of the embedding and extracting process, the robust watermark design also has important parameter selection means. More and more algorithms use artificial intelligence techniques such as evolutionary algorithms, neural networks, etc. to select parameters. Compared with the traditional watermarking algorithm using fixed parameters, the artificial intelligence technology is used for selecting parameters, and the connection among the parameters, the watermark and the carrier can be established, for example, the Particle Swarm Optimization (PSO), the Firefly Algorithm (FA) and the artificial bee colony optimization (ABC) are used for selecting embedding parameters, so that the quality of the watermark image and the embedding strength of robustness can be balanced, but the technologies cannot ensure that the watermark image reaches the preset quality.
Disclosure of Invention
Aiming at the defects and problems of the existing SVD-based robust watermarking algorithm, the invention provides the DWT-SVD domain adaptive robust watermarking algorithm which does not depend on an experimental feedback result and can ensure the quality of a watermark image and adopts the preset PSNR.
The technical scheme adopted by the invention for solving the technical problems is as follows: a DWT-SVD domain adaptive robust watermarking algorithm adopting a preset PSNR comprises the following steps:
step one, selecting an embedded block: let the carrier image be A ∈ RM×NM, N is even, and W is { W ═ W }rR is more than or equal to 1 and less than or equal to m, and m is the watermark length; dividing the carrier image into non-overlapping blocks, calculating entropy values of the blocks and calculating weighted average sum of entropy values of the blocks and adjacent blocks, sequencing the entropy values, and selecting the blocks with the same number as watermark bits as embedded blocks.
Step two, determining the self-adaptive quantization step size: dividing the embedded block into blocks wr1 and
Figure BDA0002676124220000031
when and whenrIs equal to 0 and
Figure BDA0002676124220000032
the embedded blocks of the two types are respectively marked as sequences S1And S2Calculating S according to the singular value of each block of the DWT low frequency domain of the carrier image and the difference value of the second element and the third element of the first column of the left singular vector1And S2Square error Ls of image pixel before and after embedding of subsequence watermark1And Ls2According to the carrier image, the watermark and the preset PSNR value, by formula
Figure BDA0002676124220000033
And calculating to obtain the self-adaptive quantization step size t.
Step three, embedding the watermark: performing first-level haar wavelet transform on a carrier image, dividing low-frequency sub-bands into non-overlapping blocks, performing SVD (singular value decomposition) on embedded blocks, and modulating difference quantization indexes between second and third elements in a first row of a left singular vector to embed a watermark;
step four, constructing a watermark image: carrying out reverse SVD decomposition and reverse haar wavelet transformation on the modified embedded block to obtain a watermark image;
step five, watermark extraction: and carrying out SVD on low-frequency sub-bands of the watermark image which can be modified, and comparing the size relation of second and third elements in the first column of the odd-difference vector to extract the watermark.
The first step of the DWT-SVD domain adaptive robust watermarking algorithm adopting the preset PSNR comprises the following steps:
(1) dividing the carrier image into non-overlapping blocks, each block comprising 8 x 8 pixels, and denoting a set of blocks as
Figure BDA0002676124220000034
To round up the symbol, the number of blocks is
Figure BDA0002676124220000035
(2) Calculating the blocks l in turni,jEntropy of
Figure BDA0002676124220000036
And
Figure BDA0002676124220000037
respectively representing the visual entropy and the edge entropy of the block, and calculating the weighted average sum of the block and the adjacent block:
Figure BDA0002676124220000038
wherein max and min respectively represent the maximum value and the minimum value of the variables;
(3) will Ei,jSorting from small to large, selecting the first m blocks as embedded blocks, and recording the sequence number set of the embedded blocks as a sequence
Figure BDA0002676124220000041
S will be used as side information for the extraction process.
In the DWT-SVD domain adaptive robust watermarking algorithm adopting the preset PSNR, the calculation process of t in the second step is as follows:
to the embedded block
Figure BDA0002676124220000042
After the watermark is embedded, the mark is recorded as
Figure BDA0002676124220000043
Figure BDA0002676124220000044
And
Figure BDA0002676124220000045
the SVD decomposition form of (a) may be expressed as:
Figure BDA0002676124220000046
Figure BDA0002676124220000047
the modified embedded blocks are divided into two categories:
1) when w isr1 and
Figure BDA0002676124220000048
an embedded block;
2) when w isrIs equal to 0 and
Figure BDA0002676124220000049
the insert when in use.
This embodiment records the sequence numbers of the second type of embedded blocks as the sequence S1And S2，S1And S2Are subsequences of S and do not intersect with each other. Corresponding to the first and second type of embedded blocks
Figure BDA00026761242200000411
In contrast, it is specifically defined as:
Figure BDA00026761242200000410
the difference between the embedded blocks before and after embedding is:
Figure BDA0002676124220000051
after the modification amplitude of the embedded block element is obtained, a corresponding relation is further established between the embedded block difference value and the square error of the LL subband coefficient after the first-level haar wavelet transform, and the square error of the LL subband coefficient is calculated:
Figure BDA0002676124220000052
knowing that the square error between LL subband coefficient of haar wavelet transform and image pixel satisfies
Figure BDA0002676124220000053
The calculation formula of the known PSNR is:
Figure BDA0002676124220000054
Figure BDA0002676124220000055
wherein, MAXAIs the maximum of the matrix a elements.
Can obtain the product
Figure BDA0002676124220000061
Namely:
Figure BDA0002676124220000062
namely, it is
Figure BDA0002676124220000063
And calculating to obtain the self-adaptive quantization step length t through a formula according to the determined image, the watermark and the preset PSNR value.
The third step of the DWT-SVD domain adaptive robust watermarking algorithm adopting the preset PSNR comprises the following steps:
(1) performing first-level haar wavelet transform on the carrier image, and dividing LL sub-band into non-overlapping 4 × 4 blocks to obtain
Figure BDA0002676124220000064
A block, in which a set of embedded blocks is denoted as
Figure BDA0002676124220000065
(2) To the embedded block
Figure BDA0002676124220000066
Performing SVD decomposition to obtain left singular vector
Figure BDA0002676124220000067
Is noted as the first column vector
Figure BDA0002676124220000068
Wherein the difference between the second and the third element is recorded as
Figure BDA0002676124220000069
(3) To the embedded block
Figure BDA00026761242200000610
Difference of (2)
Figure BDA00026761242200000611
Quantisation to embed a watermark wrThe corresponding modification modes of the second and the third elements are as follows:
if wr＝1
Figure BDA00026761242200000612
Figure BDA00026761242200000613
if wr＝0
Figure BDA0002676124220000071
Figure BDA0002676124220000072
wherein t is an adaptive quantization step size of the quantization index modulation strategy.
The DWT-SVD domain adaptive robust watermarking algorithm adopting the preset PSNR comprises the following five steps:
(1) partitioning the LL subband after performing primary haar wavelet transform on the watermark image, and determining the blocks for extracting the watermark as extraction blocks according to the embedded block sequence number set S;
(2) SVD decomposition is carried out on each extraction block, and left singular vectors U are recorded*The first column vector of
Figure BDA0002676124220000073
The difference between the second and third elements is
Figure BDA0002676124220000074
Wherein s isr∈S；
(3) Sequentially extracting 1-bit watermark from each extraction block by the method of
Figure BDA0002676124220000075
Finally, the complete watermark is synthesized.
The invention has the beneficial effects that: the method obtains the relationship between the PSNR value and the quantization step length as well as the image characteristics, under the condition of determining the carrier image and the watermark, the optimal quantization step length is obtained by calculation according to the preset PSNR value, the corresponding relationship between the image quality and the quantization step length is clarified, the quantization step length which ensures the image quality to reach the preset value can be obtained without repeatedly embedding and extracting processes, the DWT conversion enhances the anti-noise, compression and other common image processing capabilities of the watermark algorithm, and the SVD decomposition increases the anti-geometric attack capability of the watermark algorithm; the stability of the singular vector element relation is utilized in the proposed algorithm, and the robustness is further enhanced, so that the actual watermark image can be ensured to reach the preset image quality, and the time complexity of the algorithm is not required to be sacrificed; the pixel overflow and correction after the embedding are finished also enhance the reliability of the algorithm, the invisibility and the robustness of the algorithm are superior to those of other similar algorithms, and the algorithm has practical value in application occasions such as copyright protection.
Drawings
Fig. 1 is a flow chart of a watermarking algorithm based on an adaptive quantization step size according to the present invention.
FIG. 2 is a flow chart of the embedding process of the present invention.
Fig. 3 is a list of images and watermarks according to the present invention.
Fig. 4 is a corresponding relationship between the parameter t-mean value of the test image and the preset PSNR mean value and the actual PSNR mean value.
Fig. 5 shows the test images after embedding the watermark, and their embedding parameters t and actual PSNR, under the premise that the PSNR is preset to be 40 db.
Detailed Description
The invention is further illustrated with reference to the following figures and examples.
Example 1: the embodiment provides a DWT-SVD domain adaptive robust watermarking algorithm adopting a preset PSNR, which mainly comprises the following contents, and the flow is shown in FIG. 1.
Step one, setting a gray level image Lena with carrier images of 512 multiplied by 512 and 32 multiplied by 32 watermarks to be embeddedBinary image, denoted as W ═ WrR is more than or equal to 1 and less than or equal to 1024. The specific embedding steps are as follows:
step 1: dividing the carrier image into non-overlapping blocks, each block comprising 8 x 8 pixels; record the set of blocks as L ═ Li,j|I is more than or equal to 1 and less than or equal to 64, j is more than or equal to 1 and less than or equal to 64, and the number of blocks is 4096.
Step 2: calculating the blocks l in turni,jEntropy of
Figure BDA0002676124220000081
And
Figure BDA0002676124220000082
respectively representing the visual entropy and the edge entropy of the block; calculating a weighted average sum of entropy values of the partitions and the neighboring blocks:
Figure BDA0002676124220000083
wherein max and min represent the maximum and minimum values of the variable, respectively.
Step 3: will Ei,jSorting from small to large, selecting the first 32 multiplied by 32 blocks as embedded blocks, and recording the sequence number set of the embedded blocks as a sequence S ═ Sr|1≤r≤1024，1≤sr4096 or less, and S is used as side information of the extraction process.
Is provided with
Figure BDA0002676124220000091
Respectively representing LL, LH, HL and HH sub-band coefficients of the image A after the first-level haar wavelet transform.
The low frequency sub-band coefficients after watermarking embedding are
Figure BDA0002676124220000092
Original spatial domain pixel is marked as ak,lK is more than or equal to 1 and less than or equal to M, l is more than or equal to 1 and less than or equal to N, and the pixel of the watermark image is marked as ak,l', the relationship between them is shown in FIG. 2.
The squared error of the LL subband coefficients from the image pixels satisfies the following equation:
Figure BDA0002676124220000093
the method shows that the square error of the image pixel before and after the watermark is embedded has an equivalent relation with the square error of the low-frequency subband coefficient of the haar wavelet transform.
Step 4: performing one-level haar wavelet transform on the carrier image, dividing LL sub-band into non-overlapping 4 × 4 blocks to obtain 4096 blocks, wherein the embedded block set is recorded as
Figure BDA0002676124220000094
Step 5: to the embedded block
Figure BDA0002676124220000095
Performing SVD decomposition to obtain left singular vector
Figure BDA0002676124220000096
Is noted as the first column vector
Figure BDA0002676124220000097
Wherein the difference between the second and the third element is recorded as
Figure BDA0002676124220000098
Step 6: to the embedded block
Figure BDA0002676124220000099
Difference of (2)
Figure BDA00026761242200000910
Quantising to embed an r-th bit watermark wrThe corresponding modification of the second and third elements is as follows:
if wr＝1
Figure BDA00026761242200000911
Figure BDA0002676124220000101
if wr＝0
Figure BDA0002676124220000102
Figure BDA0002676124220000103
in the expressions (3) to (6), t is the adaptive quantization step size of the quantization index modulation strategy, and the quantization step size t can be determined by the formula
Figure BDA0002676124220000104
The dichotomy is fast solved, wherein the quantization step t is specifically selected as follows.
To the embedded block
Figure BDA0002676124220000105
After the watermark is embedded, the mark is recorded as
Figure BDA0002676124220000106
And
Figure BDA0002676124220000107
the SVD decomposition form of (a) may be expressed as:
Figure BDA0002676124220000108
Figure BDA0002676124220000109
the modified inserts can be divided into two categories:
1) when w isr1 and
Figure BDA00026761242200001010
an embedded block;
2) when w isrIs equal to 0 and
Figure BDA00026761242200001011
the insert when in use.
This embodiment records the sequence numbers of the second type of embedded blocks as the sequence S1And S2，S1And S2Are subsequences of S and do not intersect with each other. Corresponding to the first and second type of embedded blocks
Figure BDA00026761242200001012
In contrast, it is specifically defined as:
Figure BDA0002676124220000111
as can be seen from equations (7) to (9), the difference between the embedding blocks before and after embedding is:
Figure BDA0002676124220000112
after the modification amplitude of the embedded block element is known, a corresponding relation is further established between the embedded block difference value and the square error of the LL subband coefficient after the first-level haar wavelet transform, namely the square error of the LL subband coefficient is calculated according to the formula (10):
Figure BDA0002676124220000113
namely:
Figure BDA0002676124220000114
it is illustrated that there is a relationship between the squared error of the low frequency subband coefficients and the magnitude of the embedded block modification.
The calculation formula of the known PSNR is:
Figure BDA0002676124220000121
Figure BDA0002676124220000122
wherein, MAXAIs the maximum of the matrix a elements.
Can obtain the product
Figure BDA0002676124220000123
Namely:
Figure BDA0002676124220000124
namely, it is
Figure BDA0002676124220000125
It can be known that the left side of the equal sign is related to the maximum singular value of the embedded block, the difference value of two elements of the singular vectors in the first column, the watermark and the quantization step length t, and when the image, the watermark and the PSNR value are determined, the quantization step length t meeting the equation (16) can be rapidly solved through a dichotomy. The quantization step selection strategy combines a PSNR (Peak Signal to noise ratio) calculation formula and an embedding mode of a watermark algorithm based on singular vector robustness to obtain a corresponding relation between a quantization step t and preset image quality, so that the quantization step ensuring that the image quality reaches a preset value can be obtained without repeatedly embedding and extracting processes.
Step 7: and carrying out reverse SVD on the modified embedded block.
Step 8: all embedded blocks repeat Step5 to Step 7; and after the blocks are combined, replacing the original LL sub-band, and then performing reverse haar wavelet conversion to obtain a watermark image.
Watermark extraction
Step 1: firstly, performing one-level haar wavelet transform on a watermark image, partitioning an LL subband, and selecting a partition for extracting a watermark as an extraction block according to an embedded block sequence number set S;
step 2: performing SVD on each extraction block, and remembering ZuoqiDifferential vector U*The first column vector of
Figure BDA0002676124220000131
The difference between the second and third elements is
Figure BDA0002676124220000132
Wherein s isr∈S。
Step 3: and (4) sequentially extracting 1-bit watermarks from each extraction block, wherein the extraction method is shown as a formula (18), and finally synthesizing the complete watermark.
Figure BDA0002676124220000133
Example 2: in order to verify the effect of the algorithm of the invention, the embodiment compares the method of the invention with three algorithms, i.e. one, two and three, which are based on SVD and have the same watermark capacity from two angles of watermark image quality and watermark robustness; the parameters of the four algorithms are detailed in table 1.
Table 1 parameter summary table of four algorithms
Figure BDA0002676124220000134
The 10 sets of 512 × 512 classical test images in fig. 3 are selected as carrier images, and the binary images of 32 × 32, 48 × 48, and 64 × 64 are selected as watermarks to be embedded. When the experimental result is quantitatively analyzed, PSNR and Bit Error Rate (BER) are respectively adopted as the measuring mechanisms of watermark image quality and algorithm robustness,
Figure BDA0002676124220000135
representing a bitwise xor operator.
Figure BDA0002676124220000141
(1) Invisibility
Minimizing the impact on the original image is one of the goals pursued by invisible watermarking algorithms. Unlike other algorithms which balance the relationship between image quality and robustness through embedding parameters, the watermarking algorithm of the invention uses the preset PSNR value as a parameter to reversely deduce the embedding parameter, and tests the corresponding relationship between the parameter t mean value of the image, the preset PSNR mean value and the actual PSNR mean value, as shown in FIG. 4.
As can be seen from fig. 4, when the preset PSNR is 30, 35, 40, 45, or 50, the mean values of the embedding parameters of the ten test images and the mean values of the actual PSNR substantially coincide, which proves that the method can ensure that the quality of the obtained watermark image reaches the preset value.
Generally speaking, the difference between the original image and the watermark image is measured by using subjective and objective methods. On the premise that the preset PSNR is 40db, and the test images with embedded watermarks, their embedding parameters t and the actual PSNR are 40db, six watermark images, their embedding parameters t and the actual PSNR are shown in fig. 5.
As can be seen from FIG. 5, the algorithm ensures that the PSNR of the watermark image is not lower than 40db, which not only proves the effectiveness of the adaptive parameter selection strategy of the invention, but also indicates that the watermark image quality of the algorithm of the invention can meet the application requirements from both subjective and objective aspects. And the correlation between the PSNR and the watermark length is simultaneously shown, and theoretically, when the watermark length is not more than 64 multiplied by 64, the watermark image quality of the watermark method can be ensured.
To verify this conclusion, this example was experimentally verified with different size watermarks on Lena images, with the results as in table 2.
Table 2 PSNR comparison of different watermark sizes fixed embedding parameters with the method of the invention (Lena images)
Figure BDA0002676124220000151
As can be seen from table 2, when the size of the watermark is 32 × 32, 32 × 48, 48 × 48, and 64 × 64, respectively, the PSNR of the watermark image can reach 40db, which cannot be achieved by the method using the fixed embedding parameter.
(2) Robustness
Robustness is another measure of the watermarking algorithm. The invention uses BER as the index for measuring the watermark robustness, the smaller the BER value is, the higher the similarity between the extracted watermark and the original watermark is, namely, the higher the watermark robustness is. In order to verify the robustness of the algorithm, the present invention selects 13 representative attack modes, which include common image processing means such as compression, filtering, noise, etc., and also include geometric attacks such as scaling and rotation operations, as shown in table 3 specifically.
TABLE 3 robustness of the algorithm of the present invention to different attacks
Figure BDA0002676124220000161
From the BER results of extracting the watermark after 13 attacks when the 32 × 32 watermark is embedded in the six-fu test image shown in table 3, it can be seen that from the robustness exhibited by different images, Peppers and Man images exhibit weaker attack resistance when subjected to image processing such as jpeg compression and median filtering with lower quality factors, which is related to that the algorithm preferentially selects a block with a small entropy value as an embedded block and the smooth region of the image itself is relatively less. However, in general, the algorithm has certain robustness in the face of common attacks, and particularly, the algorithm presents excellent robustness for histogram equalization, contrast enhancement, reduction and rotation attacks.
The present embodiment compares the robustness of the four watermarking methods on the premise that their PSNR values are all set to around 41 db. Tables 4 and 5 show PSNR values of four watermarking methods obtained herein for images Lena and Peppers, respectively, and watermark ber values after 13 attacks, when the watermark size is 32 × 32.
TABLE 4 comparison of robustness of the algorithm of the invention with the same type of algorithm (Lena image)
Figure BDA0002676124220000171
TABLE 5 comparison of robustness of the algorithm of the invention with the same algorithm (Peppers images)
Figure BDA0002676124220000172
In tables 4 and 5, although the PSNR preset for both the two test images is 41db, the t values obtained by the algorithm of the present invention are different (0.041 and 0.045), which indicates the necessity of adaptive embedding parameters. From the comparison results, although the four algorithms embed watermarks by changing the relationship between two elements, the two comparison elements in the second algorithm are taken from the maximum singular values of two matrixes formed by DCT intermediate frequency coefficients, and the two comparison elements are not as similar as the elements in the first column of the block singular matrix, so that the first algorithm and the third algorithm are better in robustness in the face of most attacks, especially noise attacks, than the second algorithm under the same embedding capacity as shown in tables 4 and 5. The algorithm of the first algorithm embeds the watermark in the RIDWT domain, although the watermark can resist continuous 90-degree rotation and line-column inversion attacks, the RIDWT conversion comprises a pixel position replacement step, so that the close characteristic of adjacent pixel values of an image is damaged, and the algorithm cannot resist JPEG compression, median filtering, mean filtering, size reduction and Gaussian filtering operation. The comparison of the known algorithm three is insufficient: the embedding parameters can not be dynamically selected according to different carriers, so that the situation that the quality of the watermark image is unstable needs to be faced when the algorithm is applied to different images. In addition, the algorithm provided by the invention is superior to the algorithm three, and is applied to the optimization of entropy block selection, which is reflected in the face of jpeg compression.
(3) Run time
To verify the advantage of the quantization step size selection strategy proposed herein in terms of time complexity, this section uses the ACO-based quantization step size selection strategy and the proposed adaptive quantization step size selection strategy, respectively, in the singular vector robustness-based watermarking algorithm and compares their running times. The experiment uses hardware to exchange the main frequency of 2.90GHz and the internal memory of 8GB, and the software environment is Microsoft Windows 10 flagship edition and MATLAB 2018. Table 6 compares the running time average values consumed by the two selection strategies used by Lena and Peppers of the test image, and in the selection strategy based on the ACO, the iteration number of the ACO is set to be 50 and the ant colony size is set to be 10; the results are shown in Table 6.
TABLE 6 run-time comparison of two quantization step selection strategies
Figure BDA0002676124220000191
As can be seen from table 6, the execution time of the two selection strategies is proportional to the size of the watermark, but the execution time of the adaptive quantization step size selection strategy of the present invention is much smaller than that of the ACO-based selection strategy, which indicates that the selection strategy proposed herein has significant advantages in time complexity.
The above description is only for the purpose of illustrating the preferred embodiments of the present invention and is not to be construed as limiting the invention, and any modifications, equivalents and improvements made within the spirit and scope of the present invention are intended to be covered thereby.

Claims (5)

1. A DWT-SVD domain self-adaptive robust watermarking algorithm adopting a preset PSNR is characterized in that: the method comprises the following steps:
step one, selecting an embedded block: let the carrier image be A ∈ RM×NM, N is even, and W is { W ═ W }rR is more than or equal to 1 and less than or equal to m, and m is the watermark length; dividing the carrier image into non-overlapping blocks, calculating entropy values of the blocks and calculating weighted average sum of entropy values of the blocks and adjacent blocks, sorting the entropy values, selecting the blocks with the same number as watermark bits as embedded blocks, and recording sequence number sets of the embedded blocks as a sequence S;
step two, determining the self-adaptive quantization step size: dividing the embedded block into blocks wr1 and
Figure FDA0002676124210000011
when and whenrIs equal to 0 and
Figure FDA0002676124210000012
two types of insertion blocks in time, the order of the two types of insertion blocksThe numbers are respectively marked as the sequence S1And S2Calculating S according to the singular value of each block of the DWT low frequency domain of the carrier image and the difference value of the second element and the third element of the first column of the left singular vector1And S2Square error Ls of image pixel before and after embedding of subsequence watermark1And Ls2According to the carrier image, the watermark and the preset PSNR value, by formula
Figure FDA0002676124210000013
Calculating to obtain a self-adaptive quantization step length t;
step three, embedding the watermark: performing first-level haar wavelet transform on a carrier image, dividing low-frequency sub-bands into non-overlapping blocks, performing SVD (singular value decomposition) on embedded blocks, and modulating difference quantization indexes between second and third elements in a first row of a left singular vector to embed a watermark;
step four, constructing a watermark image: carrying out reverse SVD decomposition and reverse haar wavelet transformation on the modified embedded block to obtain a watermark image;
step five, watermark extraction: and carrying out SVD on low-frequency sub-bands of the watermark image which can be modified, and comparing the size relation of second and third elements in the first column of the odd-difference vector to extract the watermark.
2. The DWT-SVD domain adaptive robust watermarking algorithm with preset PSNR of claim 1, wherein: the first step comprises the following steps:
(1) dividing the carrier image into non-overlapping blocks, each block comprising 8 x 8 pixels, and denoting a set of blocks as
Figure FDA0002676124210000021
Figure FDA0002676124210000022
To round up the symbol, the number of blocks is
Figure FDA0002676124210000023
(2) In accordance withSub-calculation block li,jEntropy of
Figure FDA0002676124210000024
Figure FDA0002676124210000025
And
Figure FDA0002676124210000026
respectively representing the visual entropy and the edge entropy of the block, and calculating the weighted average sum of the block and the adjacent block:
Figure FDA0002676124210000027
wherein max and min respectively represent the maximum value and the minimum value of the variables;
(3) will Ei,jSorting from small to large, selecting the first m blocks as embedded blocks, and recording the sequence number set of the embedded blocks as a sequence
Figure FDA0002676124210000028
S will be used as side information for the extraction process.
3. The DWT-SVD domain adaptive robust watermarking algorithm with preset PSNR of claim 1, wherein: the calculation process of t in the second step is as follows:
to the embedded block
Figure FDA0002676124210000029
After the watermark is embedded, the mark is recorded as
Figure FDA00026761242100000210
Figure FDA00026761242100000211
And
Figure FDA00026761242100000212
the SVD decomposition form of (a) may be expressed as:
Figure FDA00026761242100000213
Figure FDA00026761242100000214
the modified embedded block is divided into when wr1 and
Figure FDA00026761242100000215
when and whenrIs equal to 0 and
Figure FDA00026761242100000216
the sequence number of the two kinds of embedded blocks is respectively marked as a sequence S1And S2，S1And S2Are subsequences of S and do not intersect with each other, and the first and second types of embedded blocks correspond to
Figure FDA00026761242100000217
In contrast, it is specifically defined as:
Figure FDA0002676124210000031
the difference between the embedded blocks before and after embedding is
Figure FDA0002676124210000032
After the modification amplitude of the embedded block element is obtained, a corresponding relation is further established between the embedded block difference value and the square error of the LL subband coefficient after the first-level haar wavelet transform, and the square error of the LL subband coefficient is calculated:
Figure FDA0002676124210000033
knowing that the square error between LL subband coefficient of haar wavelet transform and image pixel satisfies
Figure FDA0002676124210000034
Then:
Figure FDA0002676124210000041
the calculation formula of the known PSNR is:
Figure FDA0002676124210000042
Figure FDA0002676124210000043
wherein, MAXAIs the maximum of the matrix a elements.
Can obtain the product
Figure FDA0002676124210000044
Namely:
Figure FDA0002676124210000045
namely, it is
Figure FDA0002676124210000046
And calculating to obtain the self-adaptive quantization step length t through a formula according to the determined image, the watermark and the PSNR value.
4. The DWT-SVD domain adaptive robust watermarking algorithm with preset PSNR of claim 1, wherein: the third step comprises the following steps:
(1) performing first-level haar wavelet transform on the carrier image, and dividing LL sub-band into non-overlapping 4 × 4 blocks to obtain
Figure FDA0002676124210000047
A block, in which a set of embedded blocks is denoted as
Figure FDA0002676124210000048
(2) To the embedded block
Figure FDA0002676124210000049
Performing SVD decomposition to obtain left singular vector
Figure FDA00026761242100000410
Is noted as the first column vector
Figure FDA00026761242100000411
Wherein the difference between the second and the third element is recorded as
Figure FDA00026761242100000412
(3) To the embedded block
Figure FDA00026761242100000413
Difference of (2)
Figure FDA00026761242100000414
Quantisation to embed a watermark wrThe corresponding modification modes of the second and the third elements are as follows:
if wr＝1
Figure FDA0002676124210000051
Figure FDA0002676124210000052
if wr＝0
Figure FDA0002676124210000053
Figure FDA0002676124210000054
wherein t is an adaptive quantization step size of the quantization index modulation strategy.
5. The DWT-SVD domain adaptive robust watermarking algorithm with preset PSNR of claim 1, wherein: the fifth step comprises the following steps:
(1) partitioning the LL subband after performing primary haar wavelet transform on the watermark image, and determining the blocks for extracting the watermark as extraction blocks according to the embedded block sequence number set S;
(2) SVD decomposition is carried out on each extraction block, and left singular vectors U are recorded*The first column vector of
Figure FDA0002676124210000055
The difference between the second and third elements is
Figure FDA0002676124210000056
Wherein s isr∈S；
(3) Sequentially extracting 1-bit watermark from each extraction block by the method of
Figure FDA0002676124210000057
Finally, the complete watermark is synthesized.
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