CN113507547B - Reversible information hiding method combining self-adaptive coefficient multi-histogram with high-dimensional histogram - Google Patents
Reversible information hiding method combining self-adaptive coefficient multi-histogram with high-dimensional histogram Download PDFInfo
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Abstract
The invention relates to a reversible information hiding method combining a self-adaptive coefficient multi-histogram with a high-dimensional histogram. Comprising the following steps: step 1, calculating a weighted smoothness value of each position according to DCT coefficients quantized by a JPEG image, adjusting a block sequence according to a descending order of the block smoothness, and taking the middle-low frequency band AC coefficients to construct a plurality of histograms; step 2, connecting non-0 coefficients of each histogram into pairs to construct a plurality of high-dimensional histograms; step 3, adaptively determining an optimal embedding parameter pair and a smoothness threshold T of each high-dimensional histogram; and step 4, embedding the secret information into DCT coefficient pairs of each histogram meeting the threshold limit according to the determined optimal modification parameter pairs and the corresponding two-dimensional histogram mapping rules to obtain the marked JPEG image. The invention can realize high rate distortion performance, and the memory space of the image containing the dense JPEG is not greatly increased.
Description
Technical Field
The invention relates to the technical field of reversible information hiding, in particular to a reversible information hiding method combining a self-adaptive coefficient multi-histogram with a high-dimensional histogram.
Background
With the rapid development of computer networks and digital media information, the storage, propagation and acquisition of information are easier and easier. In the big data age, the mobile terminal equipment is used everywhere, the digital media forms are more diversified, the carrying information amount is larger, the propagation speed is faster, and the requirements on information security are higher and higher. However, the copyright of media, authenticity of content, security of information content and the like are accompanied while enjoying convenience of technological achievements. The information hiding technology is to hide some secret information in the information carrier, and can not lead to the information carrier not being used normally, the reversible watermark technology is to embed the secret information by using the redundancy of the digital carrier, and recover the original carrier and the secret information without distortion during detection.
In the prior art, a plurality of reversible information hiding methods exist, but most of the reversible information hiding methods are designed for uncompressed images, only a few of the reversible information hiding methods based on JPEG images exist, and the JPEG image format is widely applied in daily life and has great significance for innovation and optimization of the reversible information hiding algorithm of the JPEG images. Therefore, it is required to minimize the increase in the size of the JPEG file and improve the visual quality on the basis of securing the embedding capacity.
Disclosure of Invention
The invention aims to provide a reversible information hiding method combining a self-adaptive coefficient multi-histogram with a high-dimensional histogram, which utilizes block smoothness and frequency band smoothness to calculate weighted smoothness values, sets a smoothness threshold value, selects non-0 alternating current coefficient pairs of smooth positions of smooth blocks in low and medium 35 frequency bands to construct a plurality of high-dimensional histograms, and adaptively selects embedding parameter pairs and embedding rules of each high-dimensional histogram, thereby effectively improving embedding performance and greatly reducing the increase of file size on the basis of ensuring embedding capacity.
In order to achieve the above purpose, the technical scheme of the invention is as follows: a reversible information hiding method combining self-adaptive coefficient multi-histogram with high-dimensional histogram, selecting non-0 alternating current coefficient of low-medium k frequency bands to connect, constructing k high-dimensional histograms, each high-dimensional histogram self-adaptively selecting embedding parameter pair and embedding rule, satisfying high embedding capacity, simultaneously maintaining good visual effect and realizing small file growth, comprising the following steps:
In one embodiment of the present invention, to ensure that the embedded information can be extracted losslessly and the embedded image can be restored losslessly, for k histograms, the parameter set (2 kbits) and the smoothness threshold t (6 bits) and the payload length (18 bits) of the 512×512 image should be embedded in LSB manner into the DC coefficient as the auxiliary information.
In one embodiment of the present invention, step 1 specifically comprises:
dividing an original 512×512 carrier image from left to right and from top to bottom into 4096 image blocks with non-overlapping size of 8×8, forming a 64×1 column matrix by Z-shaped scanning each image block, and sequentially arranging the column matrices formed by each image block to form a 64×4096 matrix A;
second, each 8×8 image block includes 1 DC coefficient and 63 AC coefficients, forming 64 frequency channels, i.e., 64 frequency bands, the DC coefficient frequency bands are denoted as 0 channels, the 63 AC coefficient frequency bands are denoted as 1-63 channels, and the block smoothness TB is calculated based on the number of 0 coefficients of each small block k Calculating the band smoothness TF according to the number of 0 coefficients in each channel i Based on block smoothness and band smoothnessCalculating a weighted smoothness value T for each location k,i ：
Wherein TF is i Band smoothness value, TB, for the ith band k Block smoothness for the kth block, α is the weighting factor, T k,i A smoothness value T representing a coefficient at the ith sub-block and the ith band position k,i The larger, the smoother;
third step, per block smoothness TB k And (5) reducing the order, adjusting the column order, and taking channel numbers 1-k in the matrix A to construct k histograms.
In one embodiment of the present invention, step 2 specifically comprises: the coefficients in the k histograms are scanned sequentially from left to right, DCT coefficients which are not 0 and have a smoothness value less than the threshold t are connected in pairs, k two-dimensional histograms (H 1 ,H 2 ,…,H k )。
In one embodiment of the present invention, step 3 specifically comprises:
information is embedded into the data by translating and maintaining the original position in the two-dimensional histogram, H i Expressed in the form of a plane rectangular coordinate system, c 1 Is the horizontal axis, c 2 Is a longitudinal axis;
first step, each two-dimensional histogram H i Three embedding rules exist, non-0 coefficient pairs to be embedded in each two-dimensional histogram are divided into A, B, C, D four types of points, and the three embedding rules are used for embedding; since the embedded secret information is represented by a randomly generated 0-1 sequence, the probability of 0, 1 occurrence is each
For class A points (N Ai ) When the embedded information bit is 0, the position is unchanged, and the 1bit secret information is embedded, then the embedded capacity is +.>
The embedding distortion is 0, when the embedded information bit is 1, then considerThe next information bit, at this time, the embedded information bit has two possibilities of 10 and 11, and the occurrence probability is +.>
2bit secret information is respectively embedded, shift operation is carried out along the coordinate axis direction, and the corresponding embedding capacity is +.>
The embedding distortion is +.>
So the total embedded capacity of class A dots is +.>
Total embedded distortion is +.>
For class B points (N Bi ) When the embedded information bit is 0, the position is unchanged, 1bit secret information is embedded, and the embedded capacity is +.>
When the embedded information bit is 1, shifting operation is performed along the diagonal direction, and 1bit secret information is embedded, wherein the embedded capacity is +.>
Embedded distortion of N Bi So the total embedding capacity of the B-class point is N Bi Total embedded distortion is N Bi The method comprises the steps of carrying out a first treatment on the surface of the For class C points (N Ci ) When the embedded information bit is 0, shift operation is performed along the coordinate axis direction, 1bit secret information is embedded, and the embedded capacity is
Embedding distortion is +.>
When the embedded information bit is 1, shift operation is performed in the diagonal direction, 1bit secret information is embedded, and the embedded capacity is +.>
Embedded distortion of N Ci So the total embedding capacity of the C class point is N Ci Total embedded distortion is
For class D points (N Di ) The shift operation was performed in the diagonal direction without embedding the secret information, the embedding capacity at this time was 0, and the embedding distortion was 2N Di The method comprises the steps of carrying out a first treatment on the surface of the Through the above analysis, the capacity and distortion of each histogram are the sum of the capacity distortions of the A, B, C, D four types of points, respectively, that is,
wherein N is Ai 、N Bi 、N Ci 、N Di Respectively is a histogram H i In the mapping rule M i The number of the lower A, B, C, D four types of points;
from this, class A point (c 1 ,c 2 ) The value condition, the modification direction, the corresponding relation between the bit b to be embedded and the changed value and the capacity distortion;
setting a smoothness threshold t e {1,2, …,63} iterates in turn, calculating k=35 two-dimensional histograms (H 1 ,…,H i ,…H j ,…,H 35 ) Generating a 35 multiplied by 4 matrix by taking a capacity distortion matrix corresponding to the four embedding parameter pairs, wherein each position of the matrix is a { EC, ED } cell array calculated by taking different embedding parameters according to 35 histograms under the limit of a threshold t; two histograms are selected at a time (H i ,H j ) Is the same as the 16 coefficient pairs of parameters, all combinations are reservedThe other 33 histogram parameters are unchanged, and are all set to 1 initially; on the premise of meeting the capacity requirement, selecting all
Group { M } of minimum rate distortion values in seed parameter combinations 1 ,...,M 35 Is the current optimal embedding parameter, will (H) i ,H j ) The selected optimal parameters are retained to the next generation, replacing all (H i ,H j ) The position is then arbitrarily selected from the 35 histograms (H i2 ,H j2 ) And will be in addition to (H) i ,H j )、(H i2 ,H j2 ) All other histogram parameters of (1) are set to 1, the iteration is completed, and (H i2 ,H j2 ) Until the rate-distortion value is no longer reduced, determining the parameter set corresponding to the rate-distortion minimum value as the optimal embedded parameter set { M ] 1 ,...,M 35 The corresponding threshold value at this time is the optimal embedded threshold value T; for 35 two-dimensional histograms { H 1 ,...,H 35 The two-dimensional embedding rule finally selected by each histogram is an optimal embedding parameter set { M } 1 ,...,M 35 Embedding rule corresponding to the computation complexity is +.>
Wherein 63 is the value number of the threshold t, 50 represents the iteration number of selecting two histograms under each threshold, calculating the embedding capacity of each histogram under the corresponding embedding rule and the modification quantity of the DCT coefficient, and calculating the embedding distortion according to the modification quantity of the DCT coefficient and the quantization step length, and the rate distortion optimization problem is as follows:
wherein ED (H) i ,M i ) Representing histogram H i At embedding rule M i Under embedded distortion, EC (H) i ,M i ) Representing histogram H i At embedding rule M i The lower embedding capacity, P, is the given embedding capacity;
considering the influence of quality factors of different frequency bands, the distortion of 35 histograms is proportional to the square of the quality factor corresponding to the frequency band, and then the rate distortion optimization model is that,
wherein Q is i For the histogram H i Quantization factors of the corresponding quantization table.
In one embodiment of the present invention, the extraction operation is also included, which is the inverse of the embedding process of steps 1-4.
In an embodiment of the present invention, the extracting operation specifically includes: firstly, entropy decoding is carried out on a JPEG image to obtain quantized DCT coefficients, embedding parameters including auxiliary information and a smoothness threshold T are extracted, non-0 AC coefficient pairs meeting the smoothness requirement position in a channel 1-k are taken to form k two-dimensional histograms, and opposite translation or unchanged operation is carried out according to two-dimensional histogram mapping rules of corresponding histograms in the embedding parameters; and sequentially extracting the secret information from the coefficient pairs selected by each histogram, and after all k pieces of histogram secret information are extracted, performing entropy coding on the restored DCT coefficients to obtain a restored JPEG image, thereby recovering the original image after the embedded secret information is extracted.
Compared with the prior art, the invention has the following beneficial effects: the invention calculates the weighted smoothness value by using the block smoothness and the frequency band smoothness, sets the smoothness threshold value, selects the non-0 alternating current coefficient pairs of the smooth positions of the smooth blocks in the low-medium 35 frequency bands, constructs a plurality of high-dimensional histograms, and adaptively selects the embedding parameter pairs and the embedding rules of each high-dimensional histogram, thereby effectively improving the embedding performance and greatly reducing the increase of the file size on the basis of ensuring the embedding capacity. The following three advantages are shared:
(1) The invention provides a reversible information hiding method combining a plurality of histograms with high-dimensional histograms in consideration of correlation among adjacent coefficients.
(2) Aiming at the problem of unnecessary distortion caused by the selection of single parameter embedding, the invention adaptively selects the embedded parameters of each high-dimensional histogram to minimize the distortion.
(3) The invention firstly uses the block smoothness to adjust the sub-block position, then uses the block smoothness and the frequency band smoothness to calculate the smoothness value of each coefficient position, and selects the smooth position of the flat sliding block to be embedded with secret information preferentially by the method, thereby greatly reducing the increase of the file size.
Drawings
Fig. 1 is a flow chart of a reversible information hiding method of combining multiple histograms of adaptive coefficient selection with a multi-dimensional histogram.
Fig. 2 shows three values of each histogram class a coefficient pair.
Fig. 3 is a two-dimensional mapping rule corresponding to 3 embedding parameter pairs according to the present invention.
Fig. 4 shows an example of embedding rule of A, B, C, D four kinds of points whose a-kind point is (1, 1).
FIG. 5 shows the PSNR comparison of the method of the present invention with the yellow et al, shore et al methods.
FIG. 6 shows the result of comparing the file size increase of the method of the present invention with that of yellow et al, shore et al.
Detailed Description
The technical scheme of the invention is specifically described below with reference to the accompanying drawings.
In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings that are needed in the description of the embodiments will be briefly described below, in which the drawings are only some embodiments of the present invention, and other drawings can be obtained according to these drawings without inventive effort for a person skilled in the art.
The invention relates to a reversible information hiding method combining a self-adaptive coefficient multi-histogram with a high-dimensional histogram, which selects AC coefficients of low-medium frequency bands to be connected, constructs a plurality of high-dimensional histograms, adaptively selects an embedding parameter pair and an embedding rule of each high-dimensional histogram, can still keep a better visual effect and realize smaller file growth while meeting high embedding capacity, and comprises the following steps:
The following is a specific embodiment of the present invention.
A reversible information hiding method based on two-dimensional histogram of adaptive coefficient selection, select and link to pair with non-0 alternating current coefficient of low-medium k frequency bands, construct k high-dimensional histograms, each high-dimensional histogram adaptively selects embedding parameter pair and embedding rule, can still keep better visual effect and realize smaller file growth while meeting the high embedding capacity, comprising the following steps:
dividing an original 512×512 carrier image from left to right and from top to bottom into 4096 image blocks with non-overlapping size of 8×8, forming a 64×1 column matrix by Z-shaped scanning each image block, and sequentially arranging the column matrices formed by each image block to form a 64×4096 matrix A;
second, each 8×8 image block includes 1 DC coefficient and 63 AC coefficients, forming 64 frequency channels, i.e., 64 frequency bands, the DC coefficient frequency bands are denoted as 0 channels, the 63 AC coefficient frequency bands are denoted as 1-63 channels, and the block smoothness TB is calculated based on the number of 0 coefficients of each small block k Calculating the band smoothness TF according to the number of 0 coefficients in each channel i Calculating a weighted smoothness value T for each position based on the block smoothness and the band smoothness k,i ：
Wherein TF is i Band smoothness value, TB, for the ith band k Block smoothness for the kth block, α is the weighting factor, T k,i A smoothness value T representing a coefficient at the ith sub-block and the ith band position k,i The larger, the smoother;
third step, per block smoothness TB k And (5) reducing the order, adjusting the column order, and taking channel numbers 1-k in the matrix A to construct k histograms.
the coefficients in 35 histograms are scanned sequentially from left to right, DCT coefficients which are not 0 and have a smoothness value smaller than the threshold t are connected in pairs, and 35 two-dimensional histograms (H 1 ,H 2 ,…,H 35 )。
information is embedded into the data by translating and maintaining the original position in the two-dimensional histogram, H i Expressed in the form of a plane rectangular coordinate system, c 1 Is the horizontal axis, c 2 Is the vertical axis. Class a point in two-dimensional histogram H i Three values are shown in figure 2 in four quadrantsThe different parameters correspond to the three embedding rules shown in fig. 3 (a), (b) and (c), and when the embedding parameters are adaptively selected, the histogram with larger distortion is discarded when the maximum embedding capacity is reached, and is not selected to embed secret information, in which case we will note that the histogram is selected (4, 4), which represents that the histogram does not perform any operation, so that the capacity and distortion of the histogram selected as the (4, 4) coefficient are both 0.
In the first step, the values of the three a-type parameters (a, b) corresponding to the first quadrant are (1, 1), (2, 2), (3, 3), and when the histogram is (4, 4), the capacity and distortion are all set to 0, and the four values are respectively recorded as {1,2,3,4}. The values of class a points and the corresponding B, C, D points are shown in table 1 below.
Table 1 corresponding to the four types of points A and B, C, D
The non-0 coefficient pairs to be embedded in each two-dimensional histogram are divided into A, B, C, D four types of points, and are embedded according to the embedding rule of fig. 3. Since the embedded secret information is generally represented by a randomly generated 0-1 sequence, the probability of 0, 1 occurrence is each
Fig. 4 shows an example of embedding rule of four types A, B, C, D points with type a points (1, 1). For class A points (N Ai ) When the embedded information bit is 0, the position is unchanged, and the 1bit secret information is embedded, then the embedded capacity is +.>
The embedding distortion is 0, when the embedded information bit is 1, the next information bit is considered, at this time, the embedded information bit has two possibilities of 10 and 11 respectively, and the occurrence probability is +.>
Respectively embedding 2bit secret information, and proceeding along the coordinate axis directionThe row shift operation has the embedding capacities of
The embedding distortion is +.>
So the total embedded capacity of class A dots is +.>
Total embedded distortion is +.>
For class B points (N Bi ) When the embedded information bit is 0, the position is unchanged, 1bit secret information is embedded, and the embedded capacity is +.>
When the embedded information bit is 1, shifting operation is performed along the diagonal direction, and 1bit secret information is embedded, wherein the embedded capacity is +.>
Embedded distortion of N Bi So the total embedding capacity of the B-class point is N Bi Total embedded distortion is N Bi The method comprises the steps of carrying out a first treatment on the surface of the For class C points (N Ci ) When the embedded information bit is 0, shift operation is performed along the coordinate axis direction, 1bit secret information is embedded, and the embedded capacity is +.>
Embedding distortion is +.>
When the embedded information bit is 1, shift operation is performed in the diagonal direction, 1bit secret information is embedded, and the embedded capacity is +.>
Embedded distortion of N Ci So the total embedding capacity of the C class point is N Ci Total embedded distortion is +.>
For class D points (N Di ) The shift operation was performed in the diagonal direction without embedding the secret information, the embedding capacity at this time was 0, and the embedding distortion was 2N Di . Through the above analysis, the capacity and distortion of each histogram are the sum of the capacity distortions of the A, B, C, D four types of points, respectively, that is,
wherein N is Ai 、N Bi 、N Ci 、N Di Respectively is a histogram H i In the mapping rule M i The number of the lower A, B, C, D four types of points.
According to the above, the class a point (c 1 ,c 2 ) The value condition, the modification direction, the corresponding relation between the bit b to be embedded and the changed value and the capacity distortion are calculated as shown in the following table 2,
table 2A class point embedding and corresponding value change condition table
Setting a smoothness threshold t E {1,2, …,63} iterates in order, and 35 two-dimensional histograms (H) are calculated from Table 2 above 1 ,…,H i ,…H j ,…,H 35 ) And generating a 35 multiplied by 4 matrix by taking the capacity distortion matrix corresponding to the four embedding parameter pairs, wherein each position of the matrix is a { EC, ED } cell array calculated by taking different embedding parameters according to 35 histograms under the limit of a threshold t. Two histograms are selected at a time (H i ,H j ) All combinations are reserved for the 16 coefficient pair parameters of (2), while the other 33 histogram parameters are unchanged, and are all set to 1 initially. On the premise of meeting the capacity requirement, selecting all
Group { M } of minimum rate distortion values in seed parameter combinations 1 ,...,M 35 Is the current optimal embedding parameter, will (H) i ,H j ) The selected optimal parameters are retained to the next generation, replacing all (H i ,H j ) The position is then arbitrarily selected from the 35 histograms (H i2 ,H j2 ) And will be in addition to (H) i ,H j )、(H i2 ,H j2 ) All other histogram parameters of (1) are set to 1, the iteration is completed, and (H i2 ,H j2 ) Until the rate-distortion value is no longer reduced, determining the parameter set corresponding to the rate-distortion minimum value as the optimal embedded parameter set { M ] 1 ,...,M 35 And the corresponding threshold value is the optimal embedded threshold value T. For 35 two-dimensional histograms { H 1 ,...,H 35 The two-dimensional embedding rule finally selected by each histogram is an optimal embedding parameter set { M } 1 ,...,M 35 The rule is embedded as shown in FIG. 3, so that the computational complexity of our method is +.>
Wherein 63 is the value number of the threshold t, 50 represents the iteration number of selecting two histograms under each threshold, calculating the embedding capacity of each histogram under the corresponding embedding rule and the modification quantity of the DCT coefficient, and calculating the embedding distortion according to the modification quantity of the DCT coefficient and the quantization step length, and the rate distortion optimization problem is as follows:
wherein ED (H) i ,M i ) Representing histogram H i At embedding rule M i Under embedded distortion, EC (H) i ,M i ) Representing histogram H i At embedding rule M i The embedding capacity below, P, is the given embedding capacity.
Considering the influence of quality factors of different frequency bands, the distortion of 35 histograms is proportional to the square of the quality factor corresponding to the frequency band, and then the rate distortion optimization model is that,
wherein Q is i For the histogram H i Quantization factors of the corresponding quantization table.
In order to ensure that the embedded information can be extracted losslessly and that the embedded image can be restored losslessly, for k histograms, the parameter set (2 kbits) and the smoothness threshold t (6 bits) and the payload length (18 bits) of the 512 x 512 image should be embedded in LSB fashion in the DC coefficients as side information.
Regarding the extraction operation, it is the inverse of the embedding process. Firstly, entropy decoding is carried out on a JPEG image to obtain quantized DCT coefficients, information such as embedding parameters of auxiliary information, smoothness threshold t and the like is extracted, non-0 AC coefficient pairs meeting the smoothness requirement position in channels 1-35 are taken to form 35 two-dimensional histograms, and opposite translation or unchanged operation is carried out according to embedding rules of the histograms corresponding to the extracted embedding parameters.
The reversible information extraction operation is described as follows by taking the embedding method in fig. 3 as an example. When AC coefficient pair (a=1, b=1), 1-bit secret information 0 is extracted, and the coefficient pair position is unchanged and still is (1, 1); when the AC coefficient pair is (a=2, b=1), 2-bit secret information 10 is extracted, and (2, 1) is changed to (1, 1); when the AC coefficient pair is (a=1, b=2), 2-bit secret information 11 is extracted, and (1, 2) is changed to (1, 1); when the AC coefficient pair is (a=2, b=2), 1-bit secret information 0 is extracted, and the position of the coefficient pair is unchanged and is still (2, 2); when the coefficient pair is (a=3, b=3), 1-bit secret information 1 is extracted, and (3, 3) is changed to (2, 2); when the coefficient pair is (a=1, b > 2), 1-bit secret information 0 is extracted, and (a, b) is changed to (a, b-1); when the coefficient pair is (a=2, b > 2), 1-bit secret information 1 is extracted, and (a, b) is changed to (a-1, b-1); when the coefficient pair is (a > 2, b=1), 1-bit secret information 0 is extracted, and (a, b) is changed to (a-1, b); when the coefficient pair is (a > 2, b=2), 1-bit secret information 1 is extracted, and (a, b) is changed to (a-1, b-1); when the coefficient pair does not belong to the above various possible coefficient pair combinations, the secret information is not extracted, and only the coefficient pair (a, b) is changed to (a-1, b-1).
And sequentially extracting the secret information from the coefficient pairs selected by each histogram in the mode, and after all 35 pieces of histogram secret information are extracted, performing entropy coding on DCT coefficients at the recovery position to obtain a recovered JPEG image, thereby recovering the original image in a lossless manner after the embedded secret information is extracted.
The following fig. 5 is a comparison chart of PSNR results of different images by the method of the present invention and Huang Deng, xiao, etc. when the quality factors are 70, 80, 90, respectively, and fig. 6 is a comparison chart of file size increase results of different images by the method of the present invention and Huang Deng, xiao, etc. when the quality factors are 70, 80, 90, respectively, and the test results show that the present invention can not only meet the requirement of embedding capacity, but also greatly reduce the increase of file size on the basis of ensuring embedding performance, so as to facilitate transmission and storage.
In summary, the invention provides excellent embedding performance, has great advantages in embedding capacity, and ideally realizes the reversible embedding work of JPEG domain.
The above is a preferred embodiment of the present invention, and all changes made according to the technical solution of the present invention belong to the protection scope of the present invention when the generated functional effects do not exceed the scope of the technical solution of the present invention.
Claims (4)
1. A reversible information hiding method combining a self-adaptive coefficient multi-histogram with a high-dimensional histogram is characterized in that non-0 alternating current coefficient pairs of low-medium k frequency bands are selected to construct k high-dimensional histograms, each high-dimensional histogram adaptively selects an embedding parameter pair and an embedding rule, high embedding capacity is met, meanwhile, a good visual effect can be kept, and small file growth is realized, and the method comprises the following steps:
step 1, calculating a weighted smoothness value of each position according to DCT coefficients quantized by a JPEG image, adjusting a block sequence according to a descending order of the block smoothness, and taking a middle-low k frequency band to construct k histograms;
step 2, setting a smoothness threshold t, and connecting non-0 coefficients of each histogram meeting the requirement of the smoothness threshold t to form a plurality of high-dimensional histograms;
step 3, adaptively determining an optimal embedded parameter pair of each high-dimensional histogram, a corresponding two-dimensional histogram mapping rule and a smoothness threshold T;
step 4, embedding the secret information into DCT coefficient pairs of each histogram meeting the limit of the smoothness threshold T according to the determined optimal embedded coefficient pairs and the corresponding two-dimensional histogram mapping rule, and performing entropy coding on the coefficients to obtain a dense JPEG image; in order to ensure that the embedded information can be extracted in a lossless manner and the embedded image can be recovered in a lossless manner, the optimal parameter set and the smoothness threshold T are used as auxiliary information to be embedded into the carrier image;
the step 1 specifically comprises the following steps:
dividing an original 512×512 carrier image from left to right and from top to bottom into 4096 image blocks with non-overlapping size of 8×8, forming a 64×1 column matrix by Z-shaped scanning each image block, and sequentially arranging the column matrices formed by each image block to form a 64×4096 matrix A;
in a second step, each 8 x 8 image block comprises 1 DC coefficient and 63 AC coefficients, forming 64 frequency channels, i.e. 64 frequency bands, to beThe DC coefficient band is recorded as 0 channel, the 63 AC coefficient bands are recorded as 1-63 channels, and the block smoothness TB is calculated according to the number of 0 coefficients of each small block k Calculating the band smoothness TF according to the number of 0 coefficients in each channel i Calculating a weighted smoothness value T for each position based on the block smoothness and the band smoothness k,i ：
Wherein TF is i Band smoothness value, TB, for the ith band k Block smoothness for the kth block, α is the weighting factor, T k,i A smoothness value T representing a coefficient at the ith sub-block and the ith band position k,i The larger, the smoother;
third step, per block smoothness TB k Decreasing the order, adjusting the sequence, and taking channel serial numbers 1-k in the matrix A to construct k histograms;
the step 2 is specifically as follows: the coefficients in the k histograms are scanned sequentially from left to right, DCT coefficients which are not 0 and have a smoothness value less than the threshold t are connected in pairs, k two-dimensional histograms (H 1 ,H 2 ,...,H k )；
The step 3 is specifically as follows:
information is embedded into the data by translating and maintaining the original position in the two-dimensional histogram, H i Expressed in the form of a plane rectangular coordinate system, c 1 Is the coordinate of the transverse axis, c 2 Is the vertical axis coordinate;
first step, each two-dimensional histogram H i Three embedding rules exist, non-0 coefficient pairs to be embedded in each two-dimensional histogram are divided into A, B, C, D four types of points, and the three embedding rules are used for embedding; since the embedded secret information is represented by a randomly generated 0-1 sequence, the probability of 0, 1 occurrence is each
For the class A point, when the embedded information bit is 0, the position is unchanged, and the 1bit secret information is embedded, thenEmbedding capacity of +.>
The embedding distortion is 0, when the embedded information bit is 1, the next information bit is considered, at this time, the embedded information bit has two possibilities of 10 and 11 respectively, and the occurrence probability is +.>
2bit secret information is respectively embedded, shift operation is carried out along the coordinate axis direction, and the corresponding embedding capacity is +.>
The embedding distortion is +.>
So the total embedded capacity of class A dots is +.>
Total embedded distortion is +.>
For the B-type point, when the embedded information bit is 0, the position is unchanged, 1bit secret information is embedded, and the embedded capacity is +.>
When the embedded information bit is 1, shifting operation is performed along the diagonal direction, and 1bit secret information is embedded, wherein the embedded capacity is +.>
Embedded distortion of N Bi So the total embedding capacity of the B-class point is N Bi Total embedded distortion is N Bi The method comprises the steps of carrying out a first treatment on the surface of the For the C-type point, when the embedded information bit is 0, shifting operation is performed along the coordinate axis direction, 1bit secret information is embedded, and the embedded capacity is +.>
Embedding distortion as
When the embedded information bit is 1, shift operation is performed in the diagonal direction, 1bit secret information is embedded, and the embedded capacity is +.>
Embedded distortion of N Ci So the total embedding capacity of the C class point is N Ci Total embedded distortion is +.>
For class D points, no secret information is embedded, and shift operation is performed in the diagonal direction, where the embedding capacity is 0 and the embedding distortion is 2N Di The method comprises the steps of carrying out a first treatment on the surface of the Through the above analysis, the capacity and distortion of each histogram are the sum of the capacities of the four types of A, B, C, D points and the sum of the distortions, respectively, that is,
wherein N is Ai 、N Bi 、N Ci 、N Di Respectively is a histogram H i In the mapping rule M i The number of the lower A, B, C, D four types of points;
from this, class A point (c 1 ,c 2 ) The value condition, the modification direction, the corresponding relation between the bit b to be embedded and the changed value and the capacity distortion;
the smoothness threshold t e {1,2,.. 1 ,…,H i ,…H j ,…,H 35 ) Generating a 35 multiplied by 4 matrix by taking a capacity distortion matrix corresponding to the four embedding parameter pairs, wherein each position of the matrix is a { EC, ED } cell array calculated by taking different embedding parameters according to 35 histograms under the limit of a threshold t; two histograms are selected at a time (H i ,H j ) All combinations are reserved for the parameters of the 16 coefficient pairs, and the parameters of the other 33 histograms are unchanged, and are all set to be 1 initially; on the premise of meeting the capacity requirement, selecting all
Group { M } of minimum rate distortion values in seed parameter combinations 1 ,...,M 35 Is the current optimal embedding parameter, will (H) i ,H j ) The selected optimal parameters are retained to the next generation, replacing all (H i ,H j ) The position is then arbitrarily selected from the 35 histograms (H i2 ,H j2 ) And will be in addition to (H) i ,H j )、(H i2 ,H j2 ) All other histogram parameters of (1) are set to 1, the iteration is completed, and (H i2 ,H j2 ) Until the rate-distortion value is no longer reduced, determining the parameter set corresponding to the rate-distortion minimum value as the optimal embedded parameter set { M ] 1 ,...,M 35 The corresponding threshold value at this time is the optimal embedded threshold value T; for 35 two-dimensional histograms { H 1 ,...,H 35 The two-dimensional embedding rule finally selected by each histogram is an optimal embedding parameter set { M } 1 ,...,M 35 Embedding rule corresponding to the computation complexity is +.>
Wherein 63 is the value number of the threshold t, 50 represents the iteration number of selecting two histograms under each threshold, calculating the embedding capacity of each histogram under the corresponding embedding rule and the modification quantity of the DCT coefficient, and calculating the embedding distortion according to the modification quantity of the DCT coefficient and the quantization step length, and the rate distortion optimization problem is as follows:
wherein ED (H) i ,M i ) Representing histogram H i At embedding rule M i Under embedded distortion, EC (H) i ,M i ) Representing histogram H i At embedding rule M i The lower embedding capacity, P, is the given embedding capacity;
considering the influence of quality factors of different frequency bands, the distortion of 35 histograms is proportional to the square of the quality factor corresponding to the frequency band, and then the rate distortion optimization model is that,
wherein Q is i For the histogram H i Quantization factors of the corresponding quantization table.
2. The reversible information hiding method of the adaptive coefficient multi-histogram combined with the high-dimensional histogram according to claim 1, wherein, in order to ensure that the embedded information can be extracted losslessly and the embedded image can be restored losslessly, for k histograms, the parameter set and the smoothness threshold t and the payload length of 512 x 512 images should be embedded in the DC coefficient in LSB manner as auxiliary information.
3. The reversible information hiding method of adaptive coefficient multi-histogram combined with high-dimensional histogram according to claim 1, further comprising an extraction operation, which is an inverse of the embedding process of steps 1-4.
4. A reversible information hiding method according to claim 3, wherein said extracting operation is specifically: firstly, entropy decoding is carried out on a JPEG image to obtain quantized DCT coefficients, embedding parameters including auxiliary information and a smoothness threshold T are extracted, non-0 AC coefficient pairs meeting the smoothness requirement position in a channel 1-k are taken to form k two-dimensional histograms, and opposite translation or unchanged operation is carried out according to two-dimensional histogram mapping rules of corresponding histograms in the embedding parameters; and sequentially extracting the secret information from the coefficient pairs selected by each histogram, and after all k pieces of histogram secret information are extracted, performing entropy coding on the restored DCT coefficients to obtain a restored JPEG image, thereby recovering the original image after the embedded secret information is extracted.
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