CN111464717A - Reversible information hiding framework with contrast pull-up using histogram translation - Google Patents
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Abstract
The invention discloses a reversible information hiding frame with contrast ratio pull-up by utilizing histogram translation, designs an improved optimal coding RDH (remote data link) based on a prediction error histogram, and expands a main algorithm into an efficient hiding frame with double embedding capability. Compared with many previous contrast-based pull-up RDH technologies, the framework provided by the invention not only has higher information embedding rate, but also can generate a high-quality confidential image, and in addition, the security test also proves that the framework can effectively resist many famous steganalysis technologies (such as an Ensemble classifier and the like). Moreover, the frame has a dual embedding function, and copyright information such as image identification, serial numbers, characters and the like is embedded into the carrier on the premise of ensuring the original appearance of the digital carrier, so that the purposes of copyright protection, integrity check and the like of the carrier are realized.
Description
Technical Field
The invention relates to a reversible information hiding frame, in particular to a reversible information hiding frame with contrast ratio pull-up by utilizing histogram translation, and belongs to the technical field of reversible information hiding.
Background
Reversible information hiding (RDH) is proposed as a special information hiding technique. The use of reversible concealment not only allows the extraction of the embedded information from the dense carrier, but also allows the lossless recovery of the original carrier from the dense carrier. Unlike two traditional information hiding technologies, namely digital watermarking and steganography, reversible hiding mainly focuses on the reversibility of an embedding algorithm and a distortion measure between a secret carrier and an original carrier.
Reversible information hiding can be extended to many new fields of applications, such as reversible storage and reversible image processing. Reversible storage differs from traditional storage in that this technique hides the secret document in a natural document, such as a natural image, so that the secret document is imperceptible, these natural carrier documents being referred to as covert storage space. And the application of covert storage naturally requires that information hiding has reversibility, so that the covert storage space can be recycled, and the expansion and maintenance are easy. In addition, most of the current image processing algorithms are irreversible, i.e. the processed image cannot be restored to its original state. The irreversible image processing brings great inconvenience to users, users and enterprises need to realize reversible recovery of the original image by a method of storing the whole original image, so that the cost is almost doubled by storage resources, and the reversible image processing can greatly save the storage space of the original image.
At present, the embedding performance of the RDH algorithm is well improved, but most reversible hiding technology algorithms seek to ensure that the secret-carrying image has the peak signal-to-noise ratio as high as possible. Furthermore, in recent years, academic research has gradually applied RDH technology to more fields, such as designing reversible information hiding (RDH-CE) with contrast pull-up to realize reversible image processing, and efficient reversible information hiding (RDH-EI) of Encrypted Images. The reversible image processing technology researched by the invention is developed mainly for further improving the embedding performance of the RDH algorithm and expanding the application scene of the RDH.
Disclosure of Invention
To overcome the disadvantages of the prior art, an object of the present invention is to provide a reversible information hiding (RDH) framework with contrast pull-up, which can improve the contrast of a carrier image while embedding information, and also has a dual embedding function. The technology mainly acts on gray level images and can be simply expanded to the application of more carriers such as index images, RGB images and the like.
In order to achieve the above object, the present invention adopts the following technical solutions:
a reversible information hiding framework with contrast pull-up using histogram shifting, comprising:
(1) the optimal coding of the histogram constructs a transfer matrix: preprocessing a carrier image, reserving a certain amount of frequency vacancy in a carrier image histogram, and calculating a transfer matrix by using an OPTM algorithm to obtain a transfer matrix T finally used for information embedding;
in the present invention, the process of the OPTM algorithm can be referred to as: zhang W, Chen B, Yu N.Capacity-adaptive codes for reversible data linking [ C ]// International Workshop on information linking.
(2) Recursive information embedding extraction using arithmetic coding: adopting a block embedding method, converting the secret information into a gray value sequence according to the transfer matrix by using arithmetic decoding for each small block, thereby realizing the embedding of the secret information;
(3) dual information embedding of the framework: the first embedding is based on optimal coding of a prediction error histogram, the second embedding is a contrast pull-up RDH algorithm combined with histogram translation, and secret information to be hidden is embedded into a carrier image in a binary code stream mode;
(4) frame information extraction and image restoration: the process is the reverse process of information embedding, wherein the first stage is to embed the intermediate image I after the first round1And the second stage is to restore the original carrier image I.
Preferably, in (1), the specific algorithm process is as follows: given an input histogram of X ═ X0,x1,…,x255And let the final output histogram be Y ═ Y0,y1,…,y255};
Constructing a transfer matrix T, and expressing the mapping relation between the carrier image and the image pixels after the first embedding:
wherein, ti,jRepresenting the number of pixels in the carrier image with a gray value i shifted to j, and in the initial state, T is the diagonal matrix, i.e.:
the distortion D caused to the image pixel values when information is embedded is defined as mean square Error distortion (MSE), i.e.:
wherein d isi,jRepresenting the distortion degree generated by converting the gray value i into j;
according to the transition matrix T, D, the following formula is calculated:
constructing a function L of the Lagrangian multiplier term based on the histogram information entropy according to the information theory knowledge:
L=H(Y)-H(X)-λD
wherein,
and: λ is the lagrange multiplier factor. Because H (Y), H (X), D are all ti,jI is more than or equal to 0 and less than or equal to 255, j is more than or equal to 0 and less than or equal to 255, and t is obtained from Li,jAnd making the partial derivative zero, we can obtain:
for all ternary combinations (i, j, k) in T, i is greater than or equal to 0 and less than or equal to 255, j is greater than or equal to 0 and less than or equal to 255, and k is greater than or equal to 0 and less than or equal to 255, different Lagrangian multiplier factors can be obtained:
using OPTM algorithm, and making each iteration process use the above-mentioned lambdai,j,kFor the minimum to be obtained, the transition matrix is calculated and Δ is used as the iteration termination condition, i.e. when max (λ)i,j,k) The OPTM calculation is terminated when the value is less than delta, and a transfer matrix T finally used for information embedding is obtained.
Preferably, in (2), the specific algorithmic processes are an embedding process and an extraction process, wherein the embedding process is as follows:
dividing the carrier information into X ═ X (X)1,x2,...,xL) The secret information is correspondingly classified as M ═ M (M)1,m2,...,mL) And divides the image into L small blocks correspondingly, the information hider recursively embeds the information into the image starting with the first small block, for small block k, assuming a small block BkOf which there are s different gray values, denoted as { b }k,1,bk,2,…,bk,sTheir pixel numbers are respectively marked as n (b)k,1),n(bk,2),…,n(bk,s)};
Firstly, the pixels belonging to the same gray value in the small blocks are classified into a sequence,
bk,u=[bk,u,bk,u,...,bk,u]T,|bk,u|=n(bk,u),1≤u≤s
according to the obtained transition matrix, the probability of transitioning an original pixel from value i to value j is:
thus, each bk,u(1. ltoreq. u. ltoreq.s) can be determined according to the correspondingShifting to other values, obtaining b from the shift matrixk,uAll transition probabilities corresponding to gray valuesAnd uses arithmetic decoding to decode a section of binary secret information mk,uConverting into a sequence of gray values;
then, corresponding n (b)k,u) Individual gray value of bk,uThe pixels of (a) are replaced according to the result of the arithmetic decoding, thereby completing the information embedding of the small block; then, it is necessary to further generate side information of the small block, so that the receiver can successfully recover the small block, and the side information will beIs restored to bk,uThe small block B after the information is embedded is briefk' there are t different gray values, abbreviated asThe numbers of pixels are respectively abbreviated as n (c)k,1),n(ck,2),…,n(ck,t) Are generated by a similar methodSequences for classifying pixels having the same gray value, from the transition matrix, the probability of a dense pixel being transformed from the value i to j can also be obtained
And because the embedder knowsThe original gray value of each pixel in the sequence, abbreviated as ck,uUsing arithmetic coding, c is determined by transition probabilityk,uEncoding into binary sequences
Wherein Ari _ Enc corresponds to arithmetic coding;
b is obtained after the hidden information is arithmetically decoded by utilizing the gray values in all Bkk' will be the small block of information received by the receiver, hence, further to Bk' all gray values are arithmetically encoded, generating side information of a binary stream,
for the last small block of the intermediate image, it is necessary to compareDirectly hidden in the image to ensure that the information extractor can directly obtain the information, and simultaneously, the extractor also needs to obtain AMTo start information extraction, so the extractor needs to directly obtainThis part of the information is done by replacing the least significant bits (L SB) of the first tile and correspondingly, the L SB information of the first tile is also needed as part of the side information, included in the information to be embedded, to be embedded in the image in advance.
More preferably, in (2), the extraction process is as follows:
the receiver divides the image into L small blocks in the same blocking mode, and obtains L SB of the first small blockThen, using AMConstructing a transfer matrix of an initial state, obtaining the transfer matrix for information embedding by using the same iteration rule as an embedder, andto start block extraction and image restoration for gray values thereinThe transition probabilities between the various gray values are first obtained from the transition matrix:
P′L,u=[pL,u(0),...,pL,u(255)]
AL,uis dependent on n (c)k,u) And all possible codewords at decoding;
then, the extract willWith CL,uThe replacement is performed such that the grey value of the pixel before the information is embedded is obtained, whereby, using arithmetic decoding, BLCan be recovered without loss;
after the current tile is restored, the information extractor classifies the pixels in the tile as b by gray valueL,1,bL,2,...,bL,tFor each b }L,iThe extractor observes the pixels in the dense imageGradation value { bL,1,bL,2,...,bL,tThus all n (b) are coded arithmeticallyL,u) The code words corresponding to the pixels are encoded into embedded binary information:
through a pair of BLAfter extraction, the secret information m can be accurately recoveredL=[mL,1,mL,2,...,mL,2]In the header of the extracted secret information, a hidden one can be obtainedBy usingThe same method can be used to iteratively extract the concealment at BL-1The secret information in (1) and so on;
finally, before the recovery of the first small block is executed, the extractor recovers the L SB information of the extracted first small block to the original position, and finally utilizes the informationRealize to B1Namely, the secret information M can be accurately recovered to be M1,m2…,mL}。
Further preferably, in (3), the first embedding process is as follows: dividing pixels of the carrier image into two groups which are not overlapped with each other according to a chessboard-shaped format, and setting the groups as Set A and setB; for each pixel p in SetAu,vUsing 4 pixels p adjacent thereto in SetBu+1,v、pu-1,v、pu,v+1、pu,v-1Predicting the data, and setting a prediction parameter used for prediction as w+1,0、w-1,0、w0,+1、w0,-1And initialized to 0.25;
The prediction error is expressed as:
using traditional machine learning algorithm to obtain the optimal prediction coefficient w+1,0、w-1,0、w0,+1、w0,-1So that the mean square sum of the prediction errors is minimal:
next, SetA is obtained for each pixel pu,vPrediction error e ofu,vAnd e is combinedu,vThe statistics is in the form of histogram to obtain prediction error histogram G of SetASetA={...,g-1,g0,g1,...}
Using the same method, a prediction error histogram G of SetB is further obtainedSet B,
Generating a transfer matrix: for GSet A、GSet BRespectively carrying out simple quantization processing, setting a quantization interval to be r c/2048, carrying out truncation at two ends, discarding predicted values smaller than r c/4096 in the histogram, and obtaining a processed histogram G'Set A、G′Set BRespectively applying the optimal histogram coding transfer matrix generation method to G'Set A、G′Set BTo obtain a transfer matrix TSetA、TSet B;
The first round of embedding process: firstly, T isSetASecret information m1Is embedded in the prediction error of SetA using an iterative algorithm, and then m is added1Is left overPart, and side information from SetA, are combined, again embedded into the prediction error of SetA using an iterative embedding algorithm, and finally SetB generates side information ASetBWith the second part of secret information m2Combining, hiding the image in the second round of embedding, and making the generated dense image I after the embedding process1。
Specifically, the conventional machine learning method is a random gradient descent method.
Still further preferably, in (3), the second embedding process is as follows:
merging histogram frequency: obtaining a dense image I through first embedding1Histogram, let h ═ h0,h1,...,h255H isiThe histogram gray value which is equal to 0 is named as histogram vacancy, M original histogram vacancies in the carrier image are assumed, N histogram vacancies are assumed to be expected after the histogram vacancy reservation algorithm, so the residual N-M vacancies need to be additionally generated, N-M frequency numbers with the minimum pixel number in h are selected, the nearby and non-empty frequency numbers are combined according to the minimum modification degree principle, the corresponding frequency number mapping is carried out on the image, and the combined image is obtained
Reserving a histogram vacancy: all h areiThe gray value of 0 (histogram bin) is first removed from the h-sequence, resulting in a new sequenceWhere K is 256-N, the slot is placed at hseqOn both sides of the element in (1), with ω ═ ω0,ω1,...,ωKThe abbreviation is placed at each hseqThe number of the vacant sites on the two sides of the element is used for carrying out iterative insertion on the reserved histogram vacant sites, the gray value with the largest number of pixels in the histogram is selected in the first round of vacant site insertion, and vacant sites are arranged on the sides of the gray value;
after the iteration is finished, inserting the vacant position into h according to omegaseqIn (1),thereby obtaining a new histogram he. Mapping pixels in the image after histogram merging processing according to the mapping relation corresponding to the gray value to obtain a preprocessed intermediate image, and finally, if the number of the original histogram vacancies is excessive and the number of the required vacancies is excessive, the excessive vacancies are added to two ends of the histogram, and the inserted rule is that the gravity center of the histogram is as close to one half of the maximum gray value as possible, thereby obtaining the image after vacancy reservation
Then, side information is generated for image restoration: first, interpolation E before and after histogram mergingmI-I' needs to be saved to distinguish which pixels are merged for the same merged gray value, the interpolation is saved as a binary position pattern and compressed into a binary sequence a using a compression algorithm (e.g., JBIG2 compression technique)E(ii) a In addition, h' and heThe difference also needs to be recorded, since the receiver getsIt can be observed how many gray values in the histogram are non-null, so only a binary sequence a of length 256 is neededOTo store heThat is, the way is to identify a gray value by "1" when it is not empty, otherwise, to identify it by "0"; finally, the two parts of information are connected to obtain the additional information A which needs to be embedded togetherC=[AO,AE];
Generating a transfer matrix: applying the optimal histogram coding transfer matrix generation method to heTo obtain a transfer matrix T2And using an iterative algorithm to convert m2Is embedded intoAnd the generated side information is hidden to L SB of the first small block of the image, which is directly obtained by the abstractor,the final generated dense image is I2。
Still further preferably, the aforementioned step of iteratively inserting reserved histogram bins is as follows:
first, the gray value with the largest number of pixels in the histogram is selected in the first round of null insertion, and the null is placed on its side. Order toRepresenting the selected gray value in each round, let ω be in the first roundp,1 Update corresponding e 1p,rIn each subsequent round of fitting room, the potential entropy gain of the selected gray value is
And in the 2 nd to N th embedding, e is selected respectivelyp,rMaximum gray value and in ωp,rModified to omegap,r=ωp,r+1 denotes the null placement and the latest entropy gain e for the current gray value is recalculatedp,r。
Still further preferably, the process of the aforementioned first stage is as follows: information extractors obtain I2Partitioning the image, obtaining side information for image restoration from L SB of the first small block, and extracting information1And the extraction of M hidden therein, which contains secret information M2And side information A for further restoring the original carrier imageSetB。
Still further preferably, in (4), the process of the second stage is as follows: information extractor is realized by1Recovery to I. Information extractors obtain I1Partitioning the image, obtaining side information for image restoration from L SB of the first small block, and extracting information1And the extraction of M hidden therein, which contains secret information M2And side information [ A ] for further restoring the original carrier imageO,AE](by A)SetBObtained), and A isO,AERespectively resolving into position pattern and merged histogram position information, and converting I into1Mapping the non-empty gray value to the position of the merged image, performing corresponding mapping on the pixels in the image to obtain an image I 'after histogram merging, and finally adding the I' and the position pattern to obtain a carrier image without loss recovery, namely I-Em+I′。
The invention develops a reversible information hiding algorithm (namely a main algorithm) with contrast pull-up by utilizing histogram translation, designs an improved RDH based on optimal coding of a prediction error histogram, and expands the main algorithm into an efficient hiding framework with double embedding capability. In the specific implementation process, the gray image is used as an RDH action object, so that the secret information can be reversibly hidden in the carrier image, the contrast of the carrier image is effectively improved, and the visual effect of the carrier image is improved. The secret information to be hidden is embedded into the carrier image in the form of a binary code stream, thus supporting any format document as a hidden object. A reversible information hiding method with contrast pull-up effect (RDHCE-HS) combined with histogram transfer is proposed, which allows for a double embedding of secret information, i.e. the information hiding can be divided into two stages. Firstly, the carrier image is preprocessed by the algorithm, a certain amount of frequency vacancy is reserved in a carrier image histogram, and the histogram vacancy can well help an information embedder to promote the entropy of the image in the subsequent process and ensure that the introduced mean square error is as small as possible. And a transfer matrix generation algorithm is designed, the entropy of the image histogram is expanded as much as possible, and the transfer probability among the frequency numbers is calculated. And adopting a block embedding method, and converting the secret information into a gray value sequence according to the transfer matrix by using arithmetic decoding for each small block so as to realize secret information embedding. In order to realize lossless recovery and information extraction, arithmetic coding is further adopted, and the original gray value corresponding to each frequency number containing the dense small blocks is transferred into binary side information from the arithmetic coding. The method is further combined with a conventional RDH method based on prediction error histogram transfer. Experiments prove that compared with many previous RDH technologies based on contrast ratio lifting, the framework provided by the invention not only has higher information embedding rate, but also can generate a confidential image with higher quality, and in addition, security tests also prove that the framework provided by the invention can effectively resist many famous steganalysis technologies (such as an Ensemble classifier and the like).
In particular, in a main algorithm, a "vacancy reservation method" is designed to preprocess a carrier image, the algorithm reserves some vacancies in a histogram by a histogram combination method, thereby generating an intermediate image (intermediate image), and then, a transition matrix generation algorithm is proposed, wherein the histogram entropy of the image is increased by using a Mean Squared Error (MSE) as a constraint term, so as to obtain transition probabilities between histograms, then, the intermediate image is divided into blocks according to the obtained transition probabilities, and secret information is iteratively embedded into the blocks.
Has the advantages that: the algorithm main part of the invention has reversibility, and the information extraction and image recovery process is the inverse process of the above process. As an extension, an improved prediction error histogram-based RDH-PEH method is proposed, so that the method is more suitable for the application scenario. Therefore, the information Embedding of the carrier image has Dual (Dual Embedding), one round of Embedding is carried out through RDHOVT, and the second round of Embedding is carried out through the RDHCE-HS main body part, so that the Embedding rate of most images is higher than that of some RDHCE methods which show the highest level. The contrast of the carrier image can be improved while information is embedded effectively. Compared with the traditional reversible information hiding method, the framework of the invention has double embedding functions, and copyright information such as image identification, serial numbers, characters and the like is embedded into the carrier on the premise of ensuring the original appearance of the digital carrier, so as to realize the purposes of copyright protection, integrity check and the like of the carrier.
Drawings
FIG. 1 is a body algorithm and overall framework schematic diagram of the reversible information hiding framework with contrast pull-up using histogram shifting of the present invention; wherein, fig. 1(a) is a schematic diagram of a main algorithm, fig. 1(b) is a schematic diagram of an overall framework, HS represents histogram translation, SI represents auxiliary information, and AD represents additional data;
FIG. 2 is a flow chart of a recursive information embedding process using arithmetic coding;
FIGS. 3(a) and 3(b) are schematic diagrams of a prediction error grid classification structure diagram and a prediction error histogram, respectively;
FIG. 4 is an information extraction and image restoration flow diagram; fig. 4(a) is a flowchart of the first stage recovery and information extraction, and fig. 4(b) is a flowchart of the second stage recovery and information extraction.
Detailed Description
The invention is described in detail below with reference to the figures and the embodiments.
In this embodiment, a grayscale image with 8-bit precision is taken as a carrier, and the length and width of the carrier image are r and c, respectively. Secret information m is embedded in an image in the form of a binary code stream and is divided into two parts for dual embedding, m ═ m { (m })1,m2}。
Referring to fig. 1, the technique of the present invention includes several aspects as follows: the histogram optimal coding transfer matrix calculation technology, the recursive information embedding and extraction by using arithmetic coding and decoding, the dual information embedding process of the frame, the frame information extraction and the image restoration process are described one by combining the following drawings:
first, histogram optimum coding transfer matrix calculation technology
Given an input histogram of X ═ X0,x1,…,x255And let the final output histogram be Y ═ Y0,y1,…,y255}. Constructing a transfer matrix T, and expressing the mapping relation between the carrier image and the image pixels after the first embedding:
wherein, ti,jRepresenting the number of pixels in the carrier image with a gray value i shifted to j, and in the initial state, T is the diagonal matrix, i.e.:
the distortion D caused to the image pixel values when information is embedded is defined as mean square Error distortion (MSE), i.e.:
then, according to the above transition matrix T, D, it is calculated by the following formula:
constructing a function L of the Lagrangian multiplier term based on the histogram information entropy according to the information theory knowledge:
L=H(Y)-H(X)-λD
wherein,
and: λ is the lagrange multiplier factor. Because H (Y), H (X), D are all ti,jI is more than or equal to 0 and less than or equal to 255, j is more than or equal to 0 and less than or equal to 255, and t is obtained from Li,jAnd making the partial derivative zero, we can obtain:
for all ternary combinations (i, j, k) in T, i is greater than or equal to 0 and less than or equal to 255, j is greater than or equal to 0 and less than or equal to 255, and k is greater than or equal to 0 and less than or equal to 255, different Lagrangian multiplier factors can be obtained:
using OPTM algorithm, and making each iteration process use the above-mentioned lambdai,j,kFor minimum values to be obtained, countingCalculating a transition matrix and using delta as an iteration termination condition, namely when max (lambda)i,j,k) The OPTM calculation is terminated when the value is less than delta, and a transfer matrix T finally used for information embedding is obtained.
Recursive information embedding extraction using arithmetic coding and decoding
A flowchart of a recursive information embedding process using arithmetic coding is shown in fig. 2. Given an input transfer matrix T, the carrier information is first divided into X ═ X (X)1,x2,...,xL) The secret information is correspondingly classified as M ═ M (M)1,m2,...,mL) The information concealer recursively embeds the information into the image starting with the first small block, for small block k, assuming a small block BkOf which there are s different gray values, denoted as { b }k,1,bk,2,…,bk,sTheir pixel numbers are respectively marked as n (b)k,1),n(bk,2),…,n(bk,s)}。
Firstly, the pixels belonging to the same gray value in the small blocks are classified into a sequence,
bk,u=[bk,u,bk,u,...,bk,u]T,|bk,u|=n(bk,u),1≤u≤s。
according to the obtained transition matrix, the probability of transitioning an original pixel from value i to value j is:
thus, each bk,u(1. ltoreq. u. ltoreq.s) can be determined according to the correspondingBranch to other values, thus, b is derived from the branch matrixk,uAll transition probabilities corresponding to gray valuesAnd using arithmetic decoding to decode a segment of binary secret informationmk,uConverted into a sequence of gray values. The gray-scale value with low transition probability has low occurrence probability, so that the gray-scale value corresponds to a long secret information.
Thereby obtaining a secret-containing sequence Wherein Ari _ Dec is abbreviated arithmetic decoding.
Then, corresponding n (b)k,u) Individual gray value of bk,uThe pixels of (a) are replaced according to the result of the arithmetic decoding, thereby completing the information embedding of the small block. Then, it is necessary to further generate side information of the small block so that the receiver can successfully recover the small block. The side information willIs restored to bk,u. Small block B after information embeddingk' there are t different gray values, abbreviated asThe numbers of pixels are respectively abbreviated as n (c)k,1),n(ck,2),…,n(ck,t) Are generated by a similar methodAnd the sequence is used for classifying the pixels with the same gray value. From the transition matrix, the probability of transitioning a dense pixel from value i to j can also be obtained as
And because the embedder knowsThe original gray value of each pixel in the sequence, abbreviated as ck,uThus, arithmetic coding can be usedCode, by transition probability ck,uEncoded into a binary sequence.
Where Ari _ Enc corresponds to arithmetic coding. B obtained by arithmetically decoding the gray values in all Bk to hide informationk' will be the small block of information received by the receiver, hence, further to Bk' all gray values are arithmetically encoded, generating side information of a binary stream,
for the last small block of the intermediate image, it is necessary to compareDirectly hidden in the image to ensure that the information extractor can directly obtain the information, and simultaneously, the extractor also needs to obtain AMTo start information extraction, so the extractor needs to directly obtainThis part of the information is done by replacing the least significant bits (L SB) of the first tile and correspondingly, the L SB information of the first tile is also needed as part of the side information, included in the information to be embedded, to be embedded in the image in advance.
The recipient divides the image into L patches in the same blocking manner and obtains L SB from the first patchThen he utilizes AMAnd constructing a transition matrix of an initial state, and obtaining the transition matrix for information embedding by using the same iteration rule as that of an embedder. He then takes againTo turn on block fetchingWith image restoration, for gray values thereinHe first obtains the transition probabilities between the various gray values from the transition matrix:
P′L,u=[pL,u(0),...,pL,u(255)]
AL,uis dependent on n (c)k,u) And all possible codewords at decoding time. Then, the extract willWith CL,uThe replacement is performed such that the grey value of the pixel before the information is embedded is obtained, whereby, using arithmetic decoding, BLCan be recovered without loss.
After the current tile is restored, the information extractor classifies the pixels in the tile as b by gray valueL,1,bL,2,...,bL,tFor each b }L,iThe extractor observes the gray values of these pixels in the dense image { b }L,1,bL,2,...,bL,tThus all n (b) are coded arithmeticallyL,u) The code words corresponding to the pixels are encoded as embedded binary information.
Through a pair of BLAfter extraction, can be recovered accuratelyReissue secret information, mL=[mL,1,mL,2,...,mL,2]. In the header of the extracted secret information, the hidden one can be obtainedBy usingThe same method can be used to iteratively extract the concealment at BL-1And so on.
Finally, before the recovery of the first small block is executed, the extractor recovers the L SB information of the extracted first small block to the original position, and finally utilizes the informationRealize to B1The recovery of (1). By the method, secret information M can be accurately recovered by extracting1,m2…,mL}。
Triple, frame dual information embedding process
The framework provided by the invention has double information embedding functions, and an information extractor can restore an original image without damage and extract secret information.
1. Embedding for the first time: optimal coding technique based on prediction error histogram
1) Calculating a prediction error histogram for the carrier image according to the following rule:
the pixels of the carrier image are divided into two groups that do not overlap each other in a checkerboard-like format shown in fig. 2, and Set a and SetB are Set. For each pixel p in SetAu,vUsing 4 pixels p adjacent thereto in SetBu+1,v、pu-1,v、pu,v+1、pu,v-1Predicting the data, and setting a prediction parameter used for prediction as w+1,0、w-1,0、w0,+1、w0,-1And is initialized to 0.25.
The prediction error is expressed as
The optimal prediction coefficient w is found using a conventional machine learning algorithm, here using a stochastic gradient descent (sgd)+1,0、w-1,0、w0,+1、w0,-1So that the mean square sum of the prediction errors is minimal:
next, SetA is obtained for each pixel pu,vPrediction error e ofu,vAnd e is combinedu,vThe statistics is in the form of histogram to obtain prediction error histogram G of SetASetA={...,g-1,g0,g1,...}。
Using the same method, a prediction error histogram G of SetB can be further obtainedSet BSee fig. 3.
2) Generating a transfer matrix: for GSetA、GSetBRespectively carrying out simple quantization processing, setting a quantization interval to be r c/2048, carrying out truncation at two ends, discarding predicted values smaller than r c/4096 in the histogram, and obtaining a processed histogram G'Set A、G′Set B. Respectively applying the optimal histogram coding transfer matrix generation method to G'Set A、G′Set BTo obtain a transfer matrix TSetA、TSet B。
3) The first round of embedding process: firstly, T isSetASecret information m1Is embedded in the prediction of SetA using an iterative algorithmIn error, then m is1The remainder of (d), and the side information combination from SetA, are again embedded into the prediction error of SetA using an iterative embedding algorithm. Final SetB generated side information aSetBWith the second part of secret information m2The combination is made to hide the image in the second round of embedding. After the embedding process, the generated dense image is made to be I1。
2. And (3) embedding for the second time: contrast pull-up RDH algorithm (i.e., subject algorithm in FIG. 1) combined with histogram translation
1) Merging histogram frequency: obtaining a dense image I through first embedding1Histogram, let h ═ h0,h1,...,h255H isiThe histogram gray value which is equal to 0 is named as histogram vacancy, M original histogram vacancies in the carrier image are assumed, N histogram vacancies are assumed to be expected after the histogram vacancy reservation algorithm, so the residual N-M vacancies need to be additionally generated, N-M frequency numbers with the minimum pixel number in h are selected, the nearby and non-empty frequency numbers are combined according to the minimum modification degree principle, the corresponding frequency number mapping is carried out on the image, and the combined image is obtained
2) Reserving a histogram vacancy: all h areiThe gray value of 0 (histogram bin) is first removed from the h-sequence, resulting in a new sequenceWherein K is 256-N. Placing a vacancy at hseqOn both sides of the element in (1), and therefore with ω ═ ω0,ω1,...,ωKThe abbreviation is placed at each hseqNumber of vacancies on both sides of the element. And performing iterative insertion on the reserved histogram blank, selecting the gray value with the maximum number of pixels in the histogram in the first round of blank insertion, and arranging the blank on the side of the gray value.
As known from the information theory knowledge, if a gray value (containing g)iIndividual pixels) are mapped to (1+ ω) by information hidingi) Different gray values, the gray values together can then represent g0log2(1+ωi) Bit information, therefore, the histogram entropy gain can be expressed as g0log2(1+ωi)-giThis is also the bit capacity that this grey value can theoretically be hidden from this. With e ═ e0,e1,...,eKRepresents the initial state of the quantity that could theoretically contribute to the histogram entropy gain after each insertion of a null,
the step of iteratively inserting the reserved histogram slots is as follows:
first, the gray value with the largest number of pixels in the histogram is selected in the first round of null insertion, and the null is placed on its side. Order toRepresenting the selected gray value in each round, let ω be in the first roundp,1 Update corresponding e 1p,rIn each subsequent round of fitting room, the potential entropy gain of the selected gray value is
And in the 2 nd to N th embedding, e is selected respectivelyp,rMaximum gray value and in ωp,rModified to omegap,r=ωp,r+1 denotes the null placement and the latest entropy gain e for the current gray value is recalculatedp,r。
In this embodiment, the upper limit ω of the number of vacancies is setb5. After the iteration is finished, inserting the vacant position into h according to omegaseqThus obtaining a new histogram he. And mapping the pixels in the image after the histogram merging processing according to the mapping relation corresponding to the gray value, so as to obtain a preprocessed intermediate image. Finally, if it isThe number of starting histogram bins is more than the number of bins needed, then more than one bin will be added at both ends of the histogram, with the rule of interpolation being such that the center of gravity of the histogram is as close as possible to one-half of the maximum value of the gray scale. Thus obtaining an image with reserved vacant positions
3) Generating side information for image restoration: first, interpolation E before and after histogram mergingmI-I' needs to be saved to distinguish which pixels are merged for the same merged gray value, the interpolation is saved as a binary position pattern and compressed into a binary sequence a using a compression algorithm (e.g., JBIG2 compression technique)E. In addition, h' and heThe difference also needs to be recorded, since the receiver getsIt can be observed how many gray values in the histogram are non-null, so only a binary sequence a of length 256 is neededOTo store heThat is, by identifying a gray value as non-empty by "1" or otherwise by "0". Finally, the two parts of information are connected to obtain the additional information A which needs to be embedded togetherC=[AO,AE]。
4) Generating a transfer matrix: applying the optimal histogram coding transfer matrix generation method to heTo obtain a transfer matrix T2And using an iterative algorithm to convert m2Is embedded intoHiding the generated side information to L SB of the first small block of the image, and obtaining the side information directly by the extracter2。
Fourthly, frame information extraction and image recovery process
The information extraction process of the framework is information embeddingAn inverse process, see fig. 4, can be specifically divided into two stages: the first stage is to embed the intermediate image I after the first round1And the second stage is to restore the original carrier image I.
1) And (3) information extraction and image restoration corresponding to the second round of information embedding: information extractors obtain I2Partitioning the image, obtaining side information for image restoration from L SB of the first small block, and extracting information1And the extraction of M hidden therein, which contains secret information M2And side information A for further restoring the original carrier imageSetB。
2) Information extraction and image restoration corresponding to the first round of information embedding: information extractor is realized by1Recovery to I. Information extractors obtain I1Partitioning the image, obtaining side information for image restoration from L SB of the first small block, and extracting information1And the extraction of M hidden therein, which contains secret information M2And side information [ A ] for further restoring the original carrier imageO,AE](by A)SetBObtained), and A isO,AEAnd respectively resolving into a position pattern and merged histogram position information. Will I1Mapping the non-empty gray value to the position of the merged image, performing corresponding mapping on the pixels in the image to obtain an image I 'after histogram merging, and finally adding the I' and the position pattern to obtain a carrier image without loss recovery, namely I-Em+I′。
In summary, the frame with contrast pull-up invertible information hiding and histogram translation of the invention firstly preprocesses the carrier image, reserves a certain amount of frequency vacancy in the carrier image histogram, and the histogram vacancy can well help the information embedder to ensure that the introduced mean square error is as small as possible while improving the image entropy in the subsequent process. And a transfer matrix generation algorithm is designed, the entropy of the image histogram is expanded as much as possible, and the transfer probability among the frequency numbers is calculated. And then, adopting a block embedding method, and converting the secret information into a gray value sequence according to the transfer matrix by using arithmetic decoding for each small block so as to realize secret information embedding. And finally, in order to realize lossless recovery and information extraction, further adopting arithmetic coding to transfer the original gray value corresponding to each frequency number containing the dense small blocks into binary side information from the arithmetic coding. The method is further combined with a traditional RDH method based on prediction error histogram transfer, compared with a plurality of previous RDH technologies based on contrast ratio pull-up, the method not only has higher information embedding rate, but also can generate a confidential image with higher quality, and in addition, the security test also proves that the method can effectively resist a plurality of famous steganalysis technologies (such as an Ensemble classifier and the like).
The foregoing illustrates and describes the principles, general features, and advantages of the present invention. It should be understood by those skilled in the art that the above embodiments do not limit the present invention in any way, and all technical solutions obtained by using equivalent alternatives or equivalent variations fall within the scope of the present invention.
Claims (10)
1. A reversible information hiding framework with contrast pull-up using histogram shifting, comprising:
(1) the optimal coding of the histogram constructs a transfer matrix: preprocessing a carrier image, reserving a certain amount of frequency vacancy in a carrier image histogram, and calculating a transfer matrix by using an OPTM algorithm to obtain a transfer matrix T finally used for information embedding;
(2) recursive information embedding extraction using arithmetic coding: adopting a block embedding method, converting the secret information into a gray value sequence according to the transfer matrix by using arithmetic decoding for each small block, thereby realizing the embedding of the secret information;
(3) dual information embedding of the framework: the first embedding is based on optimal coding of a prediction error histogram, the second embedding is a contrast pull-up RDH algorithm combined with histogram translation, and secret information to be hidden is embedded into a carrier image in a binary code stream mode;
(4) frame information elevatorTaking and restoring images: the process is the reverse process of information embedding, wherein the first stage is to embed the intermediate image I after the first round1And the second stage is to restore the original carrier image I.
2. The reversible information hiding framework with contrast pulling using histogram shifting as claimed in claim 1, wherein in (1), the specific algorithm procedure is: given an input histogram of X ═ X0,x1,...,x255And let the final output histogram be Y ═ Y0,y1,...,y255};
Constructing a transfer matrix T, and expressing the mapping relation between the carrier image and the image pixels after the first embedding:
wherein, ti,jRepresenting the number of pixels in the carrier image with a gray value i shifted to j, and in the initial state, T is the diagonal matrix, i.e.:
the distortion D caused to the image pixel values when information is embedded is defined as Mean square error distortion (MSE), i.e.:
wherein d isi,jIndicating the degree of distortion resulting from the gray value i converted to j,
according to the transition matrix T, D, the following formula is calculated:
constructing a function L of the Lagrangian multiplier term based on the histogram information entropy according to the information theory knowledge:
L=H(Y)-H(X)-λD
wherein,
and: λ is the lagrange multiplier factor. Because H (Y), H (X), D are all ti,jI is more than or equal to 0 and less than or equal to 255, j is more than or equal to 0 and less than or equal to 255, and t is obtained from Li,jAnd making the partial derivative zero, we can obtain:
for all ternary combinations (i, j, k) in T, i is greater than or equal to 0 and less than or equal to 255, j is greater than or equal to 0 and less than or equal to 255, and k is greater than or equal to 0 and less than or equal to 255, different Lagrangian multiplier factors can be obtained:
using OPTM algorithm, and making each iteration process use the above-mentioned lambdai,j,kFor the minimum to be obtained, the transition matrix is calculated and Δ is used as the iteration termination condition, i.e. when max (λ)i,j,k) The OPTM calculation is terminated when the value is less than delta, and a transfer matrix T finally used for information embedding is obtained.
3. The reversible information hiding framework with contrast pulling using histogram shifting as claimed in claim 1, wherein in (2), the specific algorithm process is embedding process and extracting process, wherein the embedding process is as follows:
dividing the carrier information into X ═ X (X)1,x2,...,xL) The secret information is correspondingly classified as M ═ M (M)1,m2,...,mL) And divides the image into L small blocks correspondingly, the information hider recursively embeds the information into the image starting with the first small block, for small block k, assuming a small block BkOf which there are s different gray values, denoted as { b }k,1,bk,2,...,bk,sTheir pixel numbers are respectively marked as n (b)k,1),n(bk,2),...,n(bk,s)};
Firstly, the pixels belonging to the same gray value in the small blocks are classified into a sequence,
bk,u=[bk,u,bk,u,...,bk,u]T,|bk,u|=n(bk,u),1≤u≤s
according to the obtained transition matrix, the probability of transitioning an original pixel from value i to value j is:
thus, each bk,u(1. ltoreq. u. ltoreq.s) can be determined according to the correspondingj is 0, 255, and the other values are transferred, and b is obtained according to the transfer matrixk,uAll transition probabilities corresponding to gray valuesAnd uses arithmetic decoding to decode a section of binary secret information mk,uConverting into a sequence of gray values;
then, corresponding n (b)k,u) Individual gray value of bk,uThe pixels of (a) are replaced according to the result of the arithmetic decoding, thereby completing the information embedding of the small block; then, it is necessary to further generate side information of the small block, so that the receiver can successfully recover the small block, and the side information will beIs restored to bk,uThe small block B after the information is embedded is briefk' there are t different gray values, abbreviated asThe numbers of pixels are respectively abbreviated as n (c)k,1),n(ck,2),...,n(ck,t) Are generated by a similar methodSequences for classifying pixels having the same gray value, from the transition matrix, the probability of a dense pixel being transformed from the value i to j can also be obtained
And because the embedder knowsThe original gray value of each pixel in the sequence, abbreviated as Ck,uUsing arithmetic coding, c is determined by transition probabilityk,uEncoding into binary sequences
Wherein Ari _ Enc corresponds to arithmetic coding;
b obtained by arithmetically decoding the gray values in all Bk to hide informationkWill be received by the recipientSmall pieces of information, therefore, further for Bk' all gray values are arithmetically encoded, generating side information of a binary stream,
for the last small block of the intermediate image, it is necessary to compareDirectly hidden in the image to ensure that the information extractor can directly obtain the information, and simultaneously, the extractor also needs to obtain AMTo start information extraction, so the extractor needs to directly obtainThis part of the information is done by replacing the least significant bits (L SB) of the first tile and correspondingly, the L SB information of the first tile is also needed as part of the side information, included in the information to be embedded, to be embedded in the image in advance.
4. The reversible information hiding framework with contrast pulling using histogram shifting as claimed in claim 3, wherein in (2), the extraction process is as follows:
the receiver divides the image into L small blocks in the same blocking mode, and obtains L SB of the first small blockThen, using AMConstructing a transfer matrix of an initial state, obtaining the transfer matrix for information embedding by using the same iteration rule as an embedder, andto start block extraction and image restoration for gray values thereinThe transition probabilities between the various gray values are first obtained from the transition matrix:
P′L,u=[pL,u(0),...,pL,u(255)]
AL,uis dependent on n (c)k,u) And all possible codewords at decoding;
then, the extract willWith CL,uThe replacement is performed such that the grey value of the pixel before the information is embedded is obtained, whereby, using arithmetic decoding, BLCan be recovered without loss;
after the current tile is restored, the information extractor classifies the pixels in the tile as b by gray valueL,1,bL,2,...,bL,tFor each b }L,iThe extractor observes the gray values of these pixels in the dense image { b }L,1,bL,2,...,bL,tThus all n (b) are coded arithmeticallyL,u) The code words corresponding to the pixels are encoded into embedded binary information:
through a pair of BLAfter extraction, the secret information m can be accurately recoveredL=[mL,1,mL,2,...,mL,2]In the header of the extracted secret information, a hidden one can be obtainedBy usingThe same method can be used to iteratively extract the concealment at BL-1The secret information in (1) and so on;
finally, before the recovery of the first small block is executed, the extractor recovers the L SB information of the extracted first small block to the original position, and finally utilizes the informationRealize to B1Namely, the secret information M can be accurately recovered to be M1,m2...,mL}。
5. The reversible information hiding framework with contrast pull-up using histogram shifting as claimed in claim 1, wherein in (3), the first embedding process is as follows: dividing pixels of the carrier image into two groups which are not overlapped with each other according to a chessboard-shaped format, and setting the groups as SetA and SetB; for each pixel p in SetAu,vUsing 4 pixels p adjacent thereto in SetBu+1,v、pu-1,v、pu,v+1、pu,v-1Predicting the data, and setting a prediction parameter used for prediction as w+1,0、w-1,0、w0,+1、w0,-1And initialized to 0.25;
The prediction error is expressed as:
using traditional machine learning algorithm to obtain the optimal prediction coefficient w+1,0、w-1,0、w0,+1、w0,-1So that the mean square sum of the prediction errors is minimal:
next, SetA is obtained for each pixel pu,vPrediction error e ofu,vAnd e is combinedu,vThe statistics is in the form of histogram to obtain prediction error histogram G of SetASeta={...,g-1,g0,g1,...}
Using the same method, a prediction error histogram G of SetB is further obtainedSet B,
Generating a transfer matrix: for GSetA、GSet BRespectively carrying out simple quantization processing, setting a quantization interval to be r c/2048, carrying out truncation at two ends, discarding predicted values smaller than r c/4096 in the histogram, and obtaining a processed histogram G'Set A、G′Set BRespectively applying the optimal histogram coding transfer matrix generation method to G'Set A、G′Set BTo obtain a transfer matrix TSetA、Tset B;
The first round of embedding process: firstly, T isSetASecret information m1Is embedded in the prediction error of SetA using an iterative algorithm, and then m is added1And the side information from SetA, again using an iterative embedding algorithm to embed into the prediction error of SetA, the resulting force information a from SetBSetBWith the second part of secret information m2Combining, hiding the image in the second round of embedding, and making the generated dense image I after the embedding process1。
6. The reversible information hiding framework with contrast pulling-up using histogram shifting according to claim 5, characterized in that said traditional machine learning method is a stochastic gradient descent method.
7. The reversible information hiding framework with contrast pull-up using histogram shifting as claimed in claim 1, wherein in (3), the second embedding process is as follows:
merging histogram frequency: obtaining a dense image I through first embedding1Histogram, let h ═ h0,h1,...,h255H isiThe histogram gray value which is equal to 0 is named as histogram vacancy, M original histogram vacancies in the carrier image are assumed, N histogram vacancies are assumed to be expected after the histogram vacancy reservation algorithm, so the residual N-M vacancies need to be additionally generated, N-M frequency numbers with the minimum pixel number in h are selected, the nearby and non-empty frequency numbers are combined according to the minimum modification degree principle, the corresponding frequency number mapping is carried out on the image, and the combined image is obtained
Reserving a histogram vacancy: all h areiThe gray value of 0 (histogram bin) is first removed from the h-sequence, resulting in a new sequenceWhere K is 256-N, the slot is placed at hseqOn both sides of the element in (1), with ω ═ ω0,ω1,...,ωKThe abbreviation is placed at each hseqThe number of the vacant sites on the two sides of the element is used for carrying out iterative insertion on the reserved histogram vacant sites, the gray value with the largest number of pixels in the histogram is selected in the first round of vacant site insertion, and vacant sites are arranged on the sides of the gray value;
after the iteration is finished, inserting the vacant position into h according to omegaseqThus obtaining a new histogram he. Combining the histogramsAnd mapping the pixels in the processed image according to the mapping relation corresponding to the gray value to obtain a preprocessed intermediate image, and finally, if the number of the original histogram vacancies is excessive and the number of the required vacancies is excessive, the excessive vacancies are added to the two ends of the histogram, and the rule of insertion is to make the gravity center of the histogram as close to one half of the maximum value of the gray value as possible, thereby obtaining the image with reserved vacancies
Then, side information is generated for image restoration: first, interpolation E before and after histogram mergingmI-I' needs to be saved to distinguish which pixels are merged for the same merged gray value, the interpolation is saved as a binary position pattern and compressed into a binary sequence a using a compression algorithm (e.g., JBIG2 compression technique)E(ii) a In addition, h' and heThe difference also needs to be recorded, since the receiver getsIt can be observed how many gray values in the histogram are non-null, so only a binary sequence a of length 256 is neededOTo store heThat is, the way is to identify a gray value by "1" when it is not empty, otherwise, to identify it by "0"; finally, the two parts of information are connected to obtain the additional information A which needs to be embedded togetherC=[AO,AE];
Generating a transfer matrix: applying the optimal histogram coding transfer matrix generation method to heTo obtain a transfer matrix T2And using an iterative algorithm to convert m2Is embedded intoHiding the generated side information to L SB of the first small block of the image, directly obtaining the extracted side information, and finally generating the dense side informationThe image is I2。
8. The reversible information hiding frame with contrast pull-up using histogram shifting as claimed in claim 7 wherein said step of iteratively inserting reserved histogram bins is as follows:
first, the gray value with the largest number of pixels in the histogram is selected in the first round of null insertion, and the null is placed on its side. Order toRepresenting the selected gray value in each round, let ω be in the first roundp,1Update corresponding e 1p,rIn each subsequent round of fitting room, the potential entropy gain of the selected gray value is
And in the 2 nd to N th embedding, e is selected respectivelyp,rMaximum gray value and in ωp,rModified to omegap,r=ωp,r+1 denotes the null placement and the latest entropy gain e for the current gray value is recalculatedp,r。
9. The reversible information hiding framework with contrast pull-up using histogram shifting according to claim 1, wherein in (4), the procedure of the first stage is as follows: information extractors obtain I2Partitioning the image, obtaining side information for image restoration from L SB of the first small block, and extracting information1And the extraction of M hidden therein, which contains secret information M2And side information A for further restoring the original carrier imageSetB。
10. The reversible information hiding framework with contrast pull-up with histogram shifting as claimed in claim 1,characterized in that, in (4), the process of the second stage is as follows: information extractor is realized by1Recovery to I. Information extractors obtain I1Partitioning the image, obtaining side information for image restoration from L SB of the first small block, and extracting information1And the extraction of M hidden therein, which contains secret information M2And side information [ A ] for further restoring the original carrier imageO,AE](by A)SetBObtained), and A isO,AERespectively resolving into position pattern and merged histogram position information, and converting I into1Mapping the non-empty gray value to the position of the merged image, performing corresponding mapping on the pixels in the image to obtain an image I 'after histogram merging, and finally adding the I' and the position pattern to obtain a carrier image without loss recovery, namely I-Em+I′。
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CN115134142A (en) * | 2022-06-28 | 2022-09-30 | 南京信息工程大学 | Information hiding method and system based on file segmentation |
CN115134142B (en) * | 2022-06-28 | 2023-09-22 | 南京信息工程大学 | Information hiding method and system based on file segmentation |
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