A Reversible Embedding Method Based on Adaptive Modification of Multiple Difference Histograms

Abstract

The present invention is applicable to the field of reversible information hiding, and provides a reversible embedding method based on adaptive modification of multiple difference histograms. Image difference calculation is performed on the original image to obtain a difference sequence; the differences are classified according to a pseudo-random sequence, the difference sequence is evenly divided into N parts, the number of differences is counted, and N difference histograms are generated; a pair of expansion points is selected for each difference histogram to embed the secret information, and the parameter N is obtained by exhaustive optimization to minimize the difference histogram offset; the modification parameter is obtained, fixed according to the pseudo-random sequence, and used as a fixed rule for each embedding to modify the pixels of the difference histogram image; the carrier image and the secret information are restored. The technical problem that most existing reversible hiding methods have is solved. After the secret information is embedded into the carrier, the difference histogram will have irregular changes, and the peak is no longer at the zero point position, and it is easy for an attacker to discover the existence of the secret information from the statistical features of its histogram.

Description

Technical Field

[0001] The invention belongs to the field of reversible information hiding, and in particular relates to a reversible embedding method based on adaptive modification of multiple difference histograms. Background Art

[0002] With the advent of the era of comprehensive informatization, the digital economy has developed rapidly. While information resources provide convenience to people, they also bring various information security issues such as information leakage, information resource copyright disputes, and difficulty in distinguishing the authenticity of information content. These problems have hindered the development of the digital economy, infringed on the rights and interests of individuals, and even threatened national security. How to properly handle the relationship between the massive growth of information and the development of the digital economy, strengthen the security protection of data resources throughout the life cycle, and ensure information security has become one of the key issues that need to be urgently addressed in social development.

[0003] As a key technology for protecting information security, information hiding can effectively hide secret information without affecting the use of the carrier. In recent years, it has attracted widespread attention from researchers at home and abroad. Among them, reversible information hiding aims to achieve lossless recovery of embedded secret information and original carriers with the help of certain auxiliary messages. It has important application value in some sensitive image processing fields that have high requirements for the recovery of the original carrier. In general, the performance of a hiding algorithm can be evaluated from several aspects, such as imperceptibility, visual quality of the embedded image, and embedding capacity. In order to improve the embedding capacity and visual quality of the embedded image, many scholars have proposed a large number of reversible hiding schemes, such as reversible hiding methods based on difference expansion and reversible hiding methods based on prediction error histogram shift. These methods generate corresponding histograms by counting certain features of the image, expand and shift some point values ​​of the generated histogram, and reversibly embed them in a way that does not overlap points. Since these methods only make minor changes to part of the image, they can achieve better visual quality of the embedded image. However, there are relatively few related studies on imperceptibility. In fact, for most existing reversible hiding methods, after the secret information is embedded into the carrier, the difference histogram will produce irregular changes and the peak will no longer be at the zero point. It is easy for attackers to discover the existence of secret information from the statistical characteristics of its histogram. In this case, if the algorithm cannot guarantee a certain degree of resistance to statistical feature detection, the advantages of its reversible hiding algorithm cannot be reflected, which is not conducive to the effective protection of secret information. Under the premise of ensuring reversibility, it is necessary to change the embedding method to further improve the imperceptibility of the reversible embedding algorithm. Summary of the invention

[0004] The purpose of the present invention is to provide a reversible embedding method based on adaptive modification of multiple difference histograms, aiming to solve the technical problem that in most existing reversible hiding methods, after embedding secret information into the carrier, the difference histogram will change irregularly, the peak is no longer at the zero position, and it is easy for attackers to discover the existence of secret information from its histogram statistical features.

[0005] The present invention is implemented as follows. A reversible embedding method based on adaptive modification of multiple difference histograms, the reversible embedding method includes the following steps:

[0006] Step S1: Calculate the image difference of the original image to obtain a difference sequence;

[0007] Step S2: Classify the differences according to the pseudo-random sequence, evenly divide the difference sequence into N parts, and count the number of differences to generate N difference histograms;

[0008] Step S3: Select a pair of expansion points for each difference histogram, embed the secret information, and use exhaustive search to find the parameter N to minimize the difference histogram offset;

[0009] Step S4: Obtain the modification parameter, fix it according to the pseudo-random sequence as the fixed rule for each embedding, and modify the pixels of the difference histogram image;

[0010] Step S5: Recover the carrier image and the secret information, that is, complete the reversible embedding and recovery.

[0011] A further technical solution of the present invention is: The specific steps of step S1 are as follows. First, assume an image I of size A×B. In the order from left to right and top to bottom, form pixel pairs (x 2i-1 , x 2i ) of non-overlapping adjacent pixels in the image, where 1≤i≤[A×B / 2], then the pixel pair difference can be calculated as:

[0012] d i =x 2i -x 2i-1

[0013] where, -255≤d i ≤255. The corresponding difference sequence is D={d 1 ,..., d A×B / 2}.

[0014] A further technical solution of the present invention is: The specific steps of step S2 are as follows. Through a fixed N -ary pseudo-random number sequence {s 1 ,..., s A×B / 2}, classify the differences, and s i is the difference d iThe corresponding category, thereby evenly dividing the difference sequence into N parts {D 0 ,..., D N-1}; for each 0 ≤ n ≤ N - 1, count the number of differences in D n to generate N histograms {h 0 ,..., h N-1}, where h n is defined as

[0015] h n (k) = #{1 ≤ i ≤ A × B / 2: d i = k, s i = n}

[0016] where # denotes the cardinality of the set.

[0017] A further technical solution of the present invention is: the specific steps of step S3 are to select a pair of expansion points (a n , b n ) for each difference histogram, and its embedding method is expressed as, for 0 ≤ n ≤ N - 1, 1 ≤ i ≤ [A × B / 2], then

[0018]

[0019] where m ∈ {0, 1} is the secret information, d i ' is the modified pixel difference. In fact, this embedding method is a generalization extension of the traditional difference expansion. The traditional difference expansion corresponds to the case of (a n , b n ) = (-1, 0), 0 ≤ n ≤ N - 1; among them, the difference histogram remains unchanged at point -1 or moves one unit to the left, remains unchanged at point 0 or moves one unit to the right, and other values move one unit to create space for reversible embedding. Define the total difference histogram of the image as:

[0020] H(k) = #{1 ≤ i ≤ [A × B / 2]: d i = k}

[0021] Taking the Lena image as an example, for the traditional difference histogram reversible scheme, comparing the difference histogram generated by the pre-embedded image with the difference histogram regenerated after embedding 10,000 bits, it can be obtained that after modifying the histogram, the distribution trend of the histogram has changed significantly. This is because the frequency of the selected expansion points is reduced to half of the original, and half of the numbers are moved to the adjacent points on the right or left, and the remaining points are moved one unit to the left or right, resulting in a different distribution from the original difference histogram;

[0022] Further select different (a n , b n) Further analyze the changes in the image difference histogram in this case. Consider full embedding of the image. For the modified difference histogram h n ', 0 ≤ n ≤ N - 1, there is

[0023]

[0024] And Actually, by selecting (a n , b n ) = (-n, n - 1), 0 ≤ n ≤ N - 1 for different difference histograms, the distribution difference between H(s) and H'(s) is greatly reduced. The specific embedding method can be expressed as follows. For 0 ≤ n ≤ N - 1, 1 ≤ i ≤ [A × B / 2], there is

[0025]

[0026] Under this embedding rule, when embedding 10,000 bits into the Lena image in the same way, the comparison between the image difference histogram before embedding and the difference histogram after embedding can be obtained. When the number of histograms N = 64, it can be seen that after modifying the difference histogram under this rule, the distribution gap between the difference histogram and the original difference histogram is significantly reduced. For the selection of the parameter N, further, the offset before and after embedding the image difference histogram is defined as:

[0027]

[0028] Since the embedding capacity EC n of the nth histogram h n can be calculated as

[0029] EC n = h n (-n) + h n (n - 1)

[0030] For a given embedding capacity P, an optimization equation can be established:

[0031]

[0032] According to this optimization equation, the optimal N can be determined by the exhaustive method, that is, to minimize the corresponding SD under the condition of meeting the embedding capacity.

[0033] A further technical solution of the present invention is: the specific steps of the step S4 are as follows. After obtaining the modification parameters, fix them according to the pseudo-random sequence as the fixed rule for each embedding, without using additional auxiliary information. Modify the pixels according to the embedding rule to achieve embedding. For 0 ≤ n ≤ N - 1, 1 ≤ i ≤ [A × B / 2], there is

[0034]

[0035] where x 2i ' is the pixel after embedding, and x 2i-1 remains unchanged. To ensure that the user can completely recover the embedded information and the carrier image at the extraction end, the selected parameter N needs to be embedded into the carrier as auxiliary information.

[0036] A further technical solution of the present invention is that the specific steps of step S5 for the recovery process of the carrier image and the secret information are as follows: First, extract the previous pixels to obtain the parameter N, pair the images in sequence, and then evenly divide the pixel pairs of the image into N parts according to the pseudo-random sequence, and calculate the difference d' of all pixel pairs i = x' 2i - x' 2i-1 , where the pixel x 2i-1 was not modified during embedding and can be directly restored to x 2i-1 = x 2i-1 ', corresponding to x 2i can be restored to

[0037]

[0038] and the embedded secret information m can be restored to

[0039]

[0040] The beneficial effect of the present invention is that, compared with the traditional reversible hiding method, the present invention designs an adaptive reversible embedding rule for the corresponding difference histogram by analyzing the statistical characteristics of multiple generated difference histograms under different embedding rules, and maximally maintains the statistical characteristics of the histogram after embedding. Under the same embedding capacity, the present invention can achieve a higher statistical characteristic maintenance performance. Description of the Drawings

[0041] Figure 1 is the overall block diagram of the embedding process provided by the embodiment of the present invention;

[0042] Figure 2 are multiple difference histograms generated by the image Lena provided by the embodiment of the present invention;

[0043] Figure 3 is the comparison between the difference histogram before embedding by the traditional method and the difference histogram after embedding 10,000 bits provided by the embodiment of the present invention;

[0044] Figure 4 is the comparison between the difference histogram before embedding by the present method and the difference histogram after embedding 10,000 bits provided by the embodiment of the present invention;

[0045] Figure 5It shows the trend of SD varying with N when different images are embedded with 10,000 bits in the embodiments of the present invention;

[0046] Figure 6 It shows the comparison of the change in the difference histogram before and after embedding an Airplane image with 40,000 bits by two methods in the embodiments of the present invention;

[0047] Figure 7 It shows the comparison of the change in the difference histogram before and after embedding a Baboon image with 40,000 bits by two methods in the embodiments of the present invention;

[0048] Figure 8 It shows the comparison of the change in the difference histogram before and after embedding a Barbara image with 40,000 bits by two methods in the embodiments of the present invention;

[0049] Figure 9 It shows the comparison of the change in the difference histogram before and after embedding a Lena image with 40,000 bits by two methods in the embodiments of the present invention;

[0050] Figure 10 It shows the comparison of the histogram offset SD before and after embedding by two methods in the embodiments of the present invention. Detailed implementation manners

[0051] Figures 1-10 It shows a reversible information hiding method for digital images that preserves the statistical characteristics of an image by adaptively modifying multiple difference histograms in the present invention. The reversible hiding based on the modification of the difference histogram mainly generates a difference histogram by statistically calculating the differences between adjacent two pixels in the image, and realizes reversible embedding by expanding and shifting the histogram. Different from the previous traditional method of modifying a single difference histogram, the present invention considers evenly dividing the image pixel pairs into N parts according to a pseudo-random sequence, calculating their difference statistics to generate N difference histograms. Based on the generated multiple difference histograms, the present invention further analyzes and designs a reversible embedding rule for preserving statistical characteristics, and adaptively optimizes to obtain the optimal parameter N under the condition of meeting the embedding capacity, and modifies the image pixels to realize the embedding of the final secret message image, thereby completing the reversible hiding of statistical characteristics preservation.

[0052] To achieve the above object, the method for reversible hiding of statistical characteristics preservation based on the modification of multiple difference histograms in the present invention mainly includes the following two parts: (1) evenly dividing the image pixel pairs into N parts and statistically generating N image difference histograms; (2) designing an adaptive embedding rule to modify the histogram and embed the secret information. The histogram modification and information embedding part includes the following steps: analyzing and designing the embedding rules of different difference histograms; establishing an optimization equation to optimize and obtain the optimal N; modifying the image pixels to realize reversible embedding.

[0053] The generation process of multiple image difference histograms is as follows: Combine all non-overlapping adjacent two pixels in the image to obtain a number of pixel pairs, and evenly divide the pixel pairs into N parts according to a fixed pseudo-random sequence, where N > 1. Then, calculate the difference of each group of pixel pairs, and count the differences of different categories of pixel pairs to generate N difference histograms. The selection of N is related to the embedding capacity and the embedding rule.

[0054] The adaptive modification process based on multiple image difference histograms is as follows: First, consider modifying each difference histogram using a pair of extension points, and each difference histogram can have different mapping rules. By analyzing different embedding rules, that is, the selection of different extension points, and aiming at the change of the statistical characteristics of the generated multiple difference histograms, design a reversible embedding rule that can keep the image difference histogram basically unchanged. Then, establish an optimization equation, and obtain N that minimizes the offset of the statistical characteristics of the histogram after embedding through an exhaustive method, so as to establish the entire embedding process. Finally, modify the image pixels correspondingly, and pre-embed the previously recorded parameter N into the carrier as auxiliary information to complete the reversible embedding.

[0055] As Figure 1 shown, a reversible embedding method based on adaptive modification of multiple difference histograms, the reversible embedding method includes the following steps:

[0056] Step S1: Calculate the difference sequence of the original image; the specific steps are as follows: First, assume an image I with a size of A×B. According to the order from left to right and from top to bottom, form pixel pairs (x 2i-1 , x 2i ) of non-overlapping adjacent two pixels in the image, where 1 ≤ i ≤ [A×B / 2], then the pixel pair difference can be calculated as:

[0057] d i = x 2i - x 2i-1

[0058] where -255 ≤ d i ≤ 255. The corresponding difference sequence is D = {d 1 ,..., d A×B / 2}.

[0059] Step S2: Classify the differences according to the pseudo-random sequence, evenly divide the difference sequence into N parts, and count the number of differences to generate N difference histograms; the specific steps are as follows: Through a fixed N -ary pseudo-random number sequence {s 1 ,..., s A×B / 2}, classify the differences, and s i is the corresponding category of the difference d i , thus evenly dividing the difference sequence into N parts {D0 ,..., D N-1}; For each 0 ≤ n ≤ N - 1, count the number of differences in D n to generate N histograms {h 0 ,..., h N-1}, where h n is defined as

[0060] h n (k) = #{1 ≤ i ≤ A × B / 2 : d i = k, s i = n}

[0061] where # denotes the cardinality of the set. Taking the 512×512 grayscale image Lena as an example, when N = 8, the corresponding 8 difference histograms {h 0 ,..., h 7} are as shown in Figure 2 . Since each histogram is generated by statistically analyzing randomly selected pixels, the distributions of different histograms are basically the same. Reversible hiding is achieved by modifying these generated difference histograms, that is, for each histogram, select the corresponding expansion points and perform expansion and shift on the histogram.

[0062] Step S3: Select a pair of expansion points for each difference histogram, embed the secret information, and use exhaustive search to find the parameter N to minimize the offset of the difference histogram; the specific steps are to select a pair of expansion points (a n , b n ) for each difference histogram, and its embedding method is expressed as, for 0 ≤ n ≤ N - 1, 1 ≤ i ≤ [A × B / 2], then

[0063]

[0064] where m ∈ {0, 1} is the secret information, d i ' is the modified pixel difference. In fact, this embedding method is a generalized extension of the traditional difference expansion. The traditional difference expansion corresponds to the case of (a n , b n ) = (-1, 0) for 0 ≤ n ≤ N - 1; where the difference histogram remains unchanged at point -1 or moves one unit to the left, remains unchanged at point 0 or moves one unit to the right, and other values move one unit to create space for reversible embedding. Define the total difference histogram of the image as:

[0065] H(k) = #{1 ≤ i ≤ [A × B / 2] : d i = k}

[0066] Taking the Lena image as an example, for the traditional differential histogram reversible scheme, comparing the differential histogram generated by the image before embedding with the differential histogram regenerated after embedding 10,000 bits, for example Figure 3 As shown, it can be obtained that after modifying the histogram, the distribution trend of the histogram has changed significantly. This is because the frequency of the selected expansion points is reduced to half of the original, and half of the numbers are moved to the adjacent points on the right or left, and the remaining points are moved one unit distance to the left or right, resulting in a distribution different from the original differential histogram;

[0067] Further select different (a n , b n ) cases to further analyze the changes in the image differential histogram. Considering full embedding of the image, for the modified differential histogram h n ', 0 ≤ n ≤ N - 1, there is

[0068]

[0069] And In fact, by selecting (a n , b n ) = (-n, n - 1), 0 ≤ n ≤ N - 1 for different differential histograms, the distribution difference between H(s) and H'(s) is greatly reduced. The specific embedding method can be expressed as, for 0 ≤ n ≤ N - 1, 1 ≤ i ≤ [A × B / 2], then there is

[0070]

[0071] Under this embedding rule, embedding 10,000 bits into the Lena image again, the comparison between the differential histogram of the image before embedding and the differential histogram after embedding can be obtained, as Figure 4 shown. In this example, when the number of histograms N = 64, it can be seen that after modifying the differential histogram under this rule, the distribution gap between the differential histogram and the original differential histogram is significantly reduced. For the selection of the parameter N, further, the offset before and after embedding the image differential histogram is defined as:

[0072]

[0073] Since the embedding capacity EC n of the nth histogram h n can be calculated as

[0074] EC n = h n (-n) + h n (n - 1)

[0075] For a given embedding capacity P, an optimization equation can be established:

[0076]

[0077] According to this optimized equation, the optimal N can be determined by the exhaustive method, that is, the corresponding SD is minimized under the condition of satisfying the embedding capacity.

[0078] Step S4: Obtain the modification parameter, which is fixed according to the pseudo-random sequence and used as the fixed rule for each embedding to modify the pixels of the difference histogram image. The specific steps are as follows: After obtaining the modification parameter, it is fixed according to the pseudo-random sequence and used as the fixed rule for each embedding. Without additional auxiliary information, the pixels are modified according to the embedding rule to achieve embedding. For 0 ≤ n ≤ N - 1, 1 ≤ i ≤ [A × B / 2], there is

[0079]

[0080] where x 2i ' is the pixel after embedding, while x 2i-1 remains unchanged. To ensure that the user can completely recover the embedded information and the carrier image at the extraction end, the selected parameter N needs to be embedded into the carrier as auxiliary information.

[0081] Step S5: Recover the carrier image and the secret information, that is, complete the reversible embedding recovery. The specific steps are as follows: For the recovery process of the carrier image and the secret information, first, extract the previous pixels to obtain the parameter N, pair the images in sequence, and then evenly divide the pixel pairs of the image into N parts according to the pseudo-random sequence, and calculate the difference d' i = x' 2i - x' 2i-1 , where the pixel x 2i-1 was not modified during embedding and can be directly restored to x 2i-1 = x 2i-1 ', corresponding to x 2i can be restored to

[0082]

[0083] and the embedded secret information m can be restored to

[0084]

[0085] To effectively illustrate the performance of the present invention, the experimental results are presented and analyzed below using the accompanying drawings and tabular data to prove that the present invention has excellent performance.

[0086] Such as Figure 5They are the changing trends of the histogram offset SD before and after embedding for 4 different images, namely Airplane, Baboon, Barbara, and Lena, when embedding 10,000 bits. These four images are commonly used for testing in reversible hiding of images and are quite representative. In the experiment, the present invention sets the value range of N as [1, 128]. It can be seen that the determined optimal parameter N changes according to the image content, but the trend is generally the same, that is, the offset first decreases and then levels off as N increases, and the optimal value is obtained between 100 and 128.

[0087] Such as Figure 6 , 7 , 8, 9 are the comparison of the change of the difference histogram before and after embedding when Airplane, Baboon, Barbara, and Lena are respectively embedded with 40,000 bits by two methods. It can be seen that after embedding by the original method, the histogram changes significantly, especially for the intermediate values. This is because the traditional difference expansion method selects the same expansion points (-1, 0) for different histograms, reducing their frequencies, moving half of the numbers of the capacity size to the adjacent points on the right (left), and moving the remaining points one unit distance to the left (right), resulting in a distribution significantly different from the original difference histogram. While the proposed method can well maintain the distribution characteristics of the difference histogram after embedding. After embedding by selecting different expansion points for different difference histograms, its histogram characteristics can basically remain unchanged.

[0088] Such as Figure 10 Appendix 1 is the specific numerical comparison of the histogram offset SD before and after embedding obtained for different images under different embedding capacities. It can be seen that for any image and embedding capacity, the proposed method can obtain significantly smaller offsets, and the advantage is significant, that is, the proposed method can well maintain the distribution characteristics of the difference histogram after embedding.

[0089] Therefore, the reversible hiding method based on maintaining the statistical characteristics by modifying multiple difference histograms proposed by the present invention can well protect the histogram statistical characteristics at different embedding capacities and different carrier images, still ensure the invariance of the image statistical characteristics after embedding reversible messages, thereby improving the imperceptibility of the algorithm, fully protecting the security of the embedded information, and relatively ideally realizing the embedding work of reversible information hiding with maintained statistical characteristics.

[0090] Compared with the traditional reversible hiding method, the present invention designs an adaptive reversible embedding rule for the corresponding difference histogram by analyzing the statistical characteristics of the generated multiple difference histograms under different embedding rules, and maximally maintains the histogram statistical characteristics after embedding. Under the same embedding capacity, the present invention can achieve higher performance in maintaining statistical characteristics.

[0091] The above are only the preferred embodiments of the present invention and are not intended to limit the present invention. Any modifications, equivalent replacements, improvements, etc. made within the spirit and principle of the present invention shall be included within the protection scope of the present invention.

Claims

1. A reversible embedding method based on adaptive modification of multiple difference histograms, characterized in that, the reversible embedding method comprises the following steps: Step S1: Calculate the image difference of the original image to obtain a difference sequence; the specific steps are as follows. First, assume an image I of size A×B. In the order from left to right and top to bottom, form pixel pairs (x 2i-1 , x 2i ) of two adjacent non-overlapping pixels in the image, where 1 ≤ i ≤ [A×B / 2]. Then, the pixel pair difference can be calculated as: d i = x 2i - x 2i-1 where, -255 ≤ d i ≤ 255, and the corresponding difference sequence is D = {d 1 ,..., d A×B / 2}; Step S2: Classify the differences according to the pseudo-random sequence, evenly divide the difference sequence into N parts, and count the number of differences to generate N difference histograms; Step S3: For each difference histogram, select a pair of extension points to embed the secret information, and use exhaustive search to find the parameter N to minimize the difference histogram offset; the specific steps are as follows: for each difference histogram, select a pair of extension points (a n , b n ), and its embedding method is expressed as, for 0 ≤ n ≤ N - 1, 1 ≤ i ≤ [A × B / 2], then where m ∈ {0, 1} is the secret information, d i ' is the modified pixel difference, s i is the corresponding category of the difference d i . In fact, this embedding method is a generalized extension of the traditional difference expansion. The traditional difference expansion corresponds to the case of (a n , b n ) = (-1, 0), 0 ≤ n ≤ N - 1 in this method; where the difference histogram remains unchanged at point -1 or moves one unit to the left, remains unchanged at point 0 or moves one unit to the right, and other values move one unit to create space for reversible embedding. The total difference histogram of the image is defined as: H(k) = #{1 ≤ i ≤ [A × B / 2]: d i = k}; Further select the changes in the image difference histogram under different (a n , b n ) cases for further analysis. Consider full embedding of the image. For the modified difference histogram h n ', For 0 ≤ n ≤ N - 1, there is where h n is defined as h n (k) = #{1 ≤ i ≤ A × B / 2 : d i = k, s i = n} where # represents the cardinality of the set, and In fact, by selecting different difference histograms (a n , b n ) = (-n, n - 1), 0 ≤ n ≤ N - 1, the distribution difference between H(s) and H'(s) is greatly reduced. The specific embedding method can be expressed as follows: for 0 ≤ n ≤ N - 1, 1 ≤ i ≤ [A × B / 2], there is Regarding the selection of the parameter N, further, define the offset before and after embedding the image difference histogram as: Since the embedding capacity EC n of the n-th histogram h n can be calculated as EC n = h n (-n) + h n (n - 1) For a given embedding capacity P, an optimization equation can be established: Determine the optimal N by using the exhaustive method according to this optimization equation, that is, to minimize the corresponding SD under the condition of meeting the embedding capacity; Step S4: Obtain the modification parameter, fix it according to the pseudo-random sequence, as the fixed rule for each embedding, and modify the pixels of the difference histogram image; Step S5: Recover the carrier image and the secret information, that is, complete the reversible embedding recovery.

2. The reversible embedding method according to claim 1, characterized in that, The specific steps of step S2 are to classify the differences through a fixed N - ary pseudo - random number sequence {s 1 ,..., s A×B / 2}, where s i is the corresponding category of the difference d i . Thus, the difference sequence is evenly divided into N parts {D 0 ,..., D N-1}; for each 0 ≤ n ≤ N - 1, count the number of differences in D n and generate N histograms {h 0 ,..., h N-1}, where h n is defined as h n (k) = #{1 ≤ i ≤ A × B / 2 : d i = k, s i = n} where # represents the cardinality of the set.

3. The reversible embedding method according to claim 2, characterized in that, The specific steps of step S4 are as follows: after obtaining the modification parameter, fix it according to the pseudo-random sequence, as the fixed rule for each embedding, without using additional auxiliary information, and modify the pixels according to the embedding rule to achieve embedding. For 0 ≤ n ≤ N - 1, 1 ≤ i ≤ [A × B / 2], then there is where x 2i ' is the pixel after embedding, and x 2i-1 remains unchanged. In order to ensure that the user can completely recover the embedded information and the carrier image at the extraction end, the selected parameter N needs to be embedded into the carrier as auxiliary information.

4. The reversible embedding method according to claim 3, characterized in that, The specific steps of step S5 are for the recovery process of the carrier image and the secret information. First, extract the previous pixels to obtain the parameter N, pair the images sequentially, and then evenly divide the pixel pairs of the image into N parts according to the pseudo-random sequence, and calculate the difference d of all pixel pairs i ' = x' 2i -x' 2i-1 , where the pixel is x 2i-1 without modification during embedding and can be directly restored to x 2i-1 = x 2i-1 ', corresponding to x 2i can be restored to and the embedded secret information m can be recovered as

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