CN111047497A - JPEG image steganography information positioning method based on same-frequency sub-image filtering - Google Patents

JPEG image steganography information positioning method based on same-frequency sub-image filtering Download PDF

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CN111047497A
CN111047497A CN201911344997.1A CN201911344997A CN111047497A CN 111047497 A CN111047497 A CN 111047497A CN 201911344997 A CN201911344997 A CN 201911344997A CN 111047497 A CN111047497 A CN 111047497A
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CN111047497B (en
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杨春芳
王杰
王平
宋晓锋
卢记仓
朱玛
刘粉林
罗向阳
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Information Engineering University of PLA Strategic Support Force
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Abstract

The invention discloses a JPEG image steganography information positioning method based on same-frequency subgraph filtering, which combines coefficients at the same position of 8 multiplied by 8 blocks in a JPEG image to obtain 64 steganography images with the same frequency, then carries out low-pass filtering on the same-frequency subgraphs of the steganography images to estimate the carrier image with the same frequency subgraph, thereby estimating a carrier JPEG image and obtaining the estimation of DCT coefficients of the carrier JPEG image; and then calculating a residual error mean value of each position in the multiple concealed images to be detected with the same embedding path and embedding rate, realizing concealed position estimation according to the residual error mean value, and considering the characteristic that information is not embedded in a specific coefficient when the JPEG image is concealed when calculating the residual error, thereby obviously improving the positioning accuracy of the concealed position of JSTEG concealed writing.

Description

JPEG image steganography information positioning method based on same-frequency sub-image filtering
Technical Field
The invention relates to the technical field of information security, in particular to a JPEG image steganography information positioning method based on same-frequency subgraph filtering.
Background
At present, digital steganography is a technology for embedding information in redundancy of multimedia data such as digital images, video, audio, and text to realize secret communication. Researchers have proposed many distinctive steganographic algorithms for different application scenarios. The steganographic algorithms can be used for normal secure communication, and can be easily used by lawless persons to steal privacy, business secrets and the like of the Internet of things so as to avoid security protection. Therefore, in order to protect the security and privacy of the internet of things, it is necessary to develop a reverse steganalysis technology research.
At present, a series of steganography detection algorithms with excellent performance have been proposed for steganography algorithms taking images as carriers. The steganography detection algorithms can accurately judge the steganographic images of the traditional steganography, can effectively distinguish novel self-adaptive steganographic images, and can even estimate the information ratio of steganography embedding or the change ratio of the steganographic embedded information to a carrier. Theoretically, for a steganographic system, the steganographic analyst can consider the steganographic system to have been breached as long as the steganographic analyst can correctly distinguish the carrier from the hidden object with a probability that exceeds random guessing. However, actually, the forensics are not always satisfied with being able to detect the confidential object, and it is more desirable to be able to accurately extract the embedded secret information. Compared with the hidden object detection, the extraction of the steganographic information is much more difficult, and the embedded information length and the steganographic position selection mechanism and the embedded position information are often required to be known.
Since the sequential steganography sequentially embeds the steganographic information in local areas of the carrier, the statistical properties of the local areas containing the steganographic information and other areas are obviously different. Therefore, early work on steganographic information localization focused primarily on sequential steganography. Researchers have proposed a variety of steganographic information positioning methods such as chi-square test method, local hue consistency method, continuous probability ratio test and optimization accumulation sum method, weighted steganographic image optimization method, JPEG blocking discontinuity sequence mutation point estimation method, and the like, successively for sequential space domain Least Significant Bit (LSB) replacement steganography, spread spectrum steganography, JSteg steganography, and the like.
Compared with sequential steganography, random steganography randomly distributes steganography information in the whole carrier, and local areas with obvious abnormal statistical characteristics cannot appear in the carrier, so that difficulty is brought to positioning of random steganography information. Therefore, early studies on the positioning of random steganographic information were rare and poor in performance. Such as: in 2004, Davidson and Paul use the idea of anomaly point detection in data mining for reference, regard the hidden pixel positioning problem as image anomaly point detection based on energy, and provide an airspace hidden write information positioning algorithm based on anomaly point detection, wherein the algorithm has a large error for judging hidden positions and almost has no effect on the hidden pixel positioning result of a texture complex area; the Ambalavanan and Chandramouli model images by using a Markov random field, and provide a space domain steganography information positioning algorithm based on Bayesian estimation by using the similarity between the images and a statistical mechanics system, wherein the algorithm fails to apply to steganography with small changes to a carrier, such as LSB replacement, LSB matching steganography and the like.
In 2008, Ker and the like provide an information positioning algorithm for replacing steganography by a spatial domain LSB based on a weighted steganography residual error under the condition of having a plurality of steganography images with the same embedding positions for the first time. Under the condition, researchers propose various steganographic information positioning algorithms with higher positioning accuracy. Such as: the method proposed by Ker is improved by Chiew and Pieprzyk in combination with the local entropy of the block where the pixel is located, and a binary image replacement steganography information positioning algorithm based on the weighted steganography residual error and the local entropy is proposed; ker and Lubenko provide an information positioning algorithm of spatial domain LSB matching steganography based on wavelet filtering by performing wavelet filtering on the steganographic image and inversely transforming the obtained wavelet residual error into a spatial domain residual error; the Quach utilizes a hidden Markov model to model a carrier image, then utilizes a Viterbi decoding algorithm to search the optimal estimation of the carrier image, and provides an information positioning algorithm of LSB replacement and LSB matching steganography based on maximum posterior probability estimation; then, the Quach models the carrier image by using a Markov random field model, then searches the optimal estimation of the carrier image by using a quadratic pseudo-binary optimization algorithm (QPBO), and provides an information positioning algorithm of LSB replacement and LSB matching steganography based on maximum a posteriori probability (MAP); gui and the like obtain 9 estimated carrier images through 4 neighborhood means and MAP estimation along 8 different directions, and improve the information positioning precision of LSB matching steganography by a steganography information positioning algorithm based on MAP by fusing corresponding residual errors; liu and the like can more accurately estimate the spatial domain carrier image subjected to JPEG compression by JPEG compression and decompression of the hidden image, and provide an LSB replacement and LSB matching steganography information positioning algorithm based on JPEG recompression to position steganography information with high precision. (ii) a Yang et al have proved that the most optimal steganography subset property is replaced by the lowest multiple bits, and the wavelet filtering is utilized to estimate the carrier image, and an information positioning algorithm of replacing steganography by the lowest multiple bits (MLSB) based on the most optimal steganography subset is provided. Compared with the early steganographic information positioning algorithm, the positioning accuracy of random steganographic information is greatly improved by the algorithm, and under certain specific conditions, partial algorithms are already used for estimating grouping of group parity steganographic and determining the steganographic pixel embedding sequence of random steganographic, even used for recovering steganographic keys, and extraction of steganographic information is realized. However, the above algorithms are only directed to LSB replacement, LSB matching, and MLSB replacement steganography with spatial domain images as carriers.
JPEG is the first digital image compression standard in the world, and is the most widely used image compression standard that has been used to date. JPEG images generated by compression according to this standard are the most widely used image formats at present.
Actually, JPEG images on the internet are more widely applied, and the steganography and steganography analysis of JPEG images have become a hotspot of research in the field of information hiding.
The main process of JPEG compression is as follows. The image is first converted to YCbCr color space, e.g., the current image is R, G, B three-color spatial domain image, which is converted to three-color representation with Y, Cb, Cr. And secondly, downsampling the chroma and the saturation according to the set sampling mode. For example, when the set sampling mode is YUV411 or YUV422, the sampling ratio of the three components of Y, Cb and Cr is 4:1:1 or 4:2: 2. Each component after sampling is then divided into 8 x 8 non-overlapping partitions. Next, 128 is subtracted from the data in each 8 × 8 block and a Discrete Cosine Transform (DCT) is performed thereon. And quantizing each 8 x 8 DCT coefficient block obtained by transformation by using a set quantization table. And finally, performing Huffman coding on the quantized DCT coefficient to obtain a JPEG image. JPEG decompression is the inverse of JPEG compression.
Random steganography taking a JPEG image as a carrier randomly selects quantized DCT coefficients from the JPEG image and then embeds information into the DCT coefficients. The method can be described as pseudo-randomly scrambling the quantized DCT coefficients in the JPEG image according to a given steganographic key, and then sequentially selecting a certain number of coefficient embedding information from the scrambled coefficient sequence. Because some JPEG image steganography algorithms consider that some specific position or value coefficients are not available for embedding information, only the coefficients that can embed information may be scrambled during scrambling. Therefore, according to whether the non-embeddable coefficient is eliminated or not during the pseudo-random scrambling, the method for selecting the embedding position in the JPEG image random steganography can be divided into two types: a pseudo-random scrambling method for eliminating non-embeddable coefficients and a pseudo-random scrambling method for not eliminating non-embeddable coefficients.
When the JPEG image steganography adopts a pseudo-random scrambling method without eliminating non-embeddable coefficients, taking typical JSTEG steganography as an example, the embedding process is shown as follows.
(1) Performing Huffman decoding on the JPEG image or performing JPEG compression on the spatial domain image until the DCT coefficient is quantized to obtain the quantized DCT coefficient;
(2) scrambling all quantized DCT coefficients in the whole JPEG image according to the steganographic key to obtain a scrambled DCT coefficient matrix;
(3) sequentially selecting coefficients from the scrambled DCT coefficient matrix, and executing the following operations on the selected coefficients:
1) if the currently selected coefficient is a DCT coefficient or a JSTEG steganographic non-embeddable coefficient such as an AC coefficient with the value of 0 and 1, the coefficient is considered to be non-embeddable information, and the next coefficient is selected by skipping the coefficient;
2) and if the currently selected coefficient is the JSTEG steganographically embeddable coefficient, replacing the least significant bit of the selected coefficient by the currently to-be-embedded bit in the secret information, selecting the next coefficient, and reading the next to-be-embedded bit information.
3) And when the embedding of the secret information is finished, or the ratio of the selected coefficients to all the coefficients exceeds a certain threshold value, the embedding is finished.
(4) Inversely scrambling the coefficient matrix after embedding the information;
(5) and carrying out Huffman coding on the hidden coefficient matrix to generate a hidden JPEG image.
Researchers have proposed many steganography algorithms using JPEG images as carriers and designed many effective steganography detection algorithms. However, due to the weak correlation between the DCT coefficients in the JPEG image, accurate estimation of the carrier image is difficult. And it is difficult to align the hidden positions in multiple hidden images to obtain the positions where information is hidden in different hidden images or the positions where information is not hidden. These reasons make the information localization algorithm hidden in the JPEG image not seen at present.
Disclosure of Invention
The invention aims to provide a JPEG image steganography information positioning method based on same-frequency sub-image filtering, which can estimate the steganography position of a JPEG image so as to realize the JPEG image steganography information positioning.
The technical scheme adopted by the invention is as follows:
a JPEG image steganography information positioning method based on same-frequency subgraph filtering comprises the following steps:
a: for given T pieces of hidden images to be detected with the same embedding position, estimating a quantized DCT coefficient in each position of the carrier JPEG image corresponding to each hidden image to be detected by adopting a carrier JPEG image estimation method based on same-frequency sub-image filtering to obtain an estimated DCT coefficient of each position of the carrier JPEG image;
b: calculating the residual error between the actual DCT coefficient of each position in each to-be-detected hidden image and the estimated DCT coefficient; if the actual DCT coefficient of a certain position in a certain to-be-detected hidden image is an embeddable coefficient, setting the residual error of the position in the hidden image to be 0;
c: averaging the residual errors of the same positions of all the hidden images to obtain the residual error average value of each position of the hidden image to be detected;
d: judging whether the residual error mean value of each position is a hidden position or not according to the residual error mean value of each position, so as to judge the positions of all hidden actual DCT coefficients; for a hidden image, if the position of an actual DCT coefficient is the estimated hidden position and the actual DCT coefficient is an embeddable coefficient, the actual DCT coefficient is judged to contain embedded secret information, and the position of the actual DCT coefficient is judged to be the hidden position.
Specifically, the step a specifically includes the following steps:
a1: carrying out Huffman decoding on the hidden image to be detected to obtain a matrix S formed by quantized actual DCT coefficients;
Figure BDA0002333090550000051
wherein M represents the height of the to-be-detected hidden image, N represents the width of the to-be-detected hidden image, and both M and N are integral multiples of 8; sp,qThe actual DCT coefficients of the p +1 th row and the q +1 th column in the matrix S are the quantized actual DCT coefficients of the (p, q) position of the to-be-detected hidden image, p is more than or equal to 0 and less than or equal to M-1, and q is more than or equal to 0 and less than or equal to N-1;
a2: carrying out hidden image same-frequency subgraph division on the matrix S; combining actual DCT coefficients of the same position in the 8 x 8 blocks of the to-be-detected hidden image, namely the 8 x 8 blocks of the to-be-detected hidden image, and obtaining 64 same-frequency subgraphs of the hidden image for 64 different positions in the 8 x 8 blocks, S(i,j)Representing the same-frequency subgraph of the hidden image at the position of (i, j) in the 8 multiplied by 8 block, wherein i is more than or equal to 0 and less than or equal to 7, and j is more than or equal to 0 and less than or equal to 7;
Figure BDA0002333090550000052
wherein
Figure BDA0002333090550000053
M is the height of the to-be-detected hidden image, and N is the width of the to-be-detected hidden image;
a3: low-pass filtering F is carried out on 64 hidden image same-frequency subgraphs by utilizing a low-pass filterlow(S(i,j)) Obtaining the estimated quantized carrier image same-frequency subgraph
Figure BDA0002333090550000054
Figure BDA0002333090550000055
Wherein
Figure BDA0002333090550000056
Same-frequency subgraph S for representing hidden image(i,j)Corresponding carrier image same-frequency subgraph C(i,j)I is more than or equal to 0 and less than or equal to 7, and j is more than or equal to 0 and less than or equal to 7;
a4: combining the same-frequency subgraphs of the carrier image to obtain an estimated carrier JPEG image; placing the estimated DCT coefficient in the same-frequency subgraph of the carrier image at the position of the corresponding actual DCT coefficient to obtain the estimated DCT coefficient of each position in the JPEG image of the carrier:
Figure BDA0002333090550000061
wherein
Figure BDA0002333090550000062
A matrix representing the composition of the estimated DCT coefficients in the carrier image,
Figure BDA0002333090550000063
representation matrix
Figure BDA0002333090550000064
And the estimated DCT coefficients of the p +1 th row and the q +1 th column are quantized DCT coefficients of the (p, q) position of the carrier image, wherein p is more than or equal to 0 and less than or equal to M-1, and q is more than or equal to 0 and less than or equal to N-1.
Specifically, the step a3 specifically includes the following steps:
a3.1: respectively carrying out wavelet decomposition on all same-frequency subgraphs in the hidden image to be detected: co-frequency subgraph S of a hidden image using an 8-tapDaubechies filter(i,j)Decomposing to obtain hidden image same-frequency subgraph S(i,j)The four sub-bands comprise a low-frequency sub-band L, a horizontal sub-band H, a vertical sub-band V and a diagonal sub-band D;
l (x, y) represents a hidden image same-frequency subgraph S(i,j)H (x, y) represents the same-frequency subgraph S of the hidden image(i,j)The wavelet coefficient value of (x, y) position in the horizontal sub-band H of (A), V (x, y) represents the same-frequency sub-image S of the hidden image(i,j)The wavelet coefficient value of (x, y) position in the vertical sub-band V of (D, x, y) represents the same-frequency sub-image S of the hidden image(i,j)The wavelet coefficient value at the (x, y) position in the diagonal sub-band D of (1) x ≦ He,1 ≦ y ≦ Wi, He represents the height of any one of the four sub-bands, and Wi represents the width of any one of the four sub-bands;
a3.2: respectively in the hidden image same frequency subgraph S(i,j)The minimum local variance solution is performed in the horizontal sub-band H, the vertical sub-band V and the diagonal sub-band D: obtaining the local variance of each wavelet coefficient of the same-frequency subgraph of the carrier image by utilizing the maximum posterior estimation of 4 square dxd neighborhoods on a horizontal sub-band H, a vertical sub-band V and a diagonal sub-band D by utilizing a formula (5);
Figure BDA0002333090550000065
wherein
Figure BDA0002333090550000066
Representing the local variance of (x, y) position in the horizontal sub-band H of the same-frequency subgraph of the carrier image;
Figure BDA0002333090550000067
representing the local variance of the (x, y) position in the vertical sub-band V of the same-frequency subgraph of the carrier image,
Figure BDA0002333090550000071
representing the local variance of (x, y) positions in the diagonal sub-band D of the same-frequency subgraph of the carrier image;
Figure BDA0002333090550000072
representing the variance of the steganographic noise,
Figure BDA0002333090550000073
represents the mean of the squares of the wavelet coefficients in a square d x d neighborhood centered at the (x, y) position in the horizontal subband H,
Figure BDA0002333090550000074
represents the mean of the squares of the wavelet coefficients in a square d x d neighborhood centered at the (x, y) position in the vertical subband V,
Figure BDA0002333090550000075
represents the mean of the squares of the wavelet coefficients in a square D x D neighborhood centered at the (x, y) position in the diagonal subband D; d belongs to {3,5,7,9 };
a3.3: wavelet coefficients of a horizontal sub-band H, a vertical sub-band V and a diagonal sub-band D are subjected to low-pass filtering by using a wiener filter:
Figure BDA0002333090550000076
Hlow(x, y) denotes the low-pass filtered horizontal sub-band HlowEstimated coefficient values for the (x, y) position;
Vlow(x, y) denotes the low-pass filtered vertical sub-band VlowEstimated coefficient values for the (x, y) position;
Dlow(x, y) denotes the low-pass filtered diagonal sub-band DlowEstimated coefficient values for the (x, y) position;
a3.4: low frequency sub-band L and low pass filtered horizontal sub-band HlowLow pass filtered sagStraight strap VlowLow pass filtered diagonal sub-band DlowAnd performing inverse wavelet transform to obtain an estimated DCT coefficient in the carrier image.
Combining coefficients at the same position of each 8 multiplied by 8 block in a JPEG image to obtain 64 hidden image same-frequency subgraphs, then carrying out low-pass filtering on the hidden image same-frequency subgraphs, estimating a carrier image same-frequency subgraph, estimating a carrier JPEG image and obtaining estimation of DCT coefficients of the carrier JPEG image; and then calculating a residual error mean value of each position in the multiple concealed images to be detected with the same embedding path and embedding rate, realizing concealed position estimation according to the residual error mean value, and considering the characteristic that information is not embedded in a specific coefficient when the JPEG image is concealed when calculating the residual error, thereby obviously improving the positioning accuracy of the concealed position of JSTEG concealed writing.
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FIG. 1 is a flow chart of a method of the present invention;
FIG. 2 is a schematic diagram of the process of the present invention;
FIG. 3 is a schematic diagram of a carrier JPEG image estimation method of the invention;
FIG. 4 is a schematic diagram of a hidden image same-frequency subgraph dividing method according to the invention;
FIG. 5 is a schematic diagram of T hidden images with the same embedding path and embedding rate according to the present invention;
Detailed Description
As shown in fig. 1 and fig. 2, the JPEG image steganography information positioning method based on co-frequency subgraph filtering according to the present invention includes the following steps:
a: for given T hidden images to be detected with the same embedding position, a carrier based on same-frequency sub-image filtering is adopted
The JPEG image estimation method estimates the quantized DCT coefficient in each position of the JPEG image of the carrier corresponding to each to-be-detected hidden image to obtain the estimated DCT coefficient of each position of the JPEG image of the carrier, namely the estimated carrier
A JPEG image.
Specifically, as shown in fig. 3, the step a specifically includes the following steps,
a1: carrying out Huffman decoding on the hidden image to be detected to obtain a matrix S formed by quantized actual DCT coefficients;
Figure BDA0002333090550000081
wherein M represents the height of the to-be-detected hidden image, N represents the width of the to-be-detected hidden image, and both M and N are integral multiples of 8; sp,qThe actual DCT coefficients of the p +1 th row and the q +1 th column in the matrix S are the quantized actual DCT coefficients of the (p, q) position of the to-be-detected hidden image, p is more than or equal to 0 and less than or equal to M-1, and q is more than or equal to 0 and less than or equal to N-1;
a2: carrying out hidden image same-frequency subgraph division on the matrix S; combining actual DCT coefficients of the same frequency spectrum of all 8 multiplied by 8 blocks in the matrix S, namely the same position of all 8 multiplied by 8 blocks of the hidden image to be detected, and obtaining 64 same-frequency subgraphs of the hidden image for 64 different positions in the 8 multiplied by 8 blocks, S(i,j)Representing the same-frequency subgraph of the hidden image at the position of (i, j) in the 8 multiplied by 8 block, wherein i is more than or equal to 0 and less than or equal to 7, and j is more than or equal to 0 and less than or equal to 7;
Figure BDA0002333090550000082
wherein
Figure BDA0002333090550000091
M is the height of the to-be-detected hidden image, and N is the width of the to-be-detected hidden image;
a3: low-pass filtering F is carried out on 64 hidden image same-frequency subgraphs by utilizing a low-pass filterlow(S(i,j)) Obtaining the estimated quantized carrier image same-frequency subgraph
Figure BDA0002333090550000092
Figure BDA0002333090550000093
Figure BDA0002333090550000094
Same-frequency subgraph S for representing hidden image(i,j)Corresponding carrier image same-frequency subgraph C(i,j)I is greater than or equal to 0 and less than or equal to 7, and j is greater than or equal to 0 and less than or equal to 7.
S in setting step A2(i,j)K +1 row and l +1 column of (d) has an actual DCT coefficient of si+8k,j+8lIn step A3
Figure BDA0002333090550000095
The estimated DCT coefficient of the k +1 th row and l +1 st column is si+8k,j+8lObtained by low-pass filtering and is represented as
Figure BDA0002333090550000096
Namely, it is
Figure BDA0002333090550000097
Representing co-frequency subgraphs of carrier images located in estimation
Figure BDA0002333090550000098
Row k +1, column l + 1. K is more than or equal to 0 and less than or equal to m, and l is more than or equal to 0 and less than or equal to n.
A4: combining the same-frequency subgraphs of the carrier image to obtain an estimated carrier JPEG image; placing the estimated DCT coefficient in the same-frequency subgraph of the carrier image at the position of the corresponding actual DCT coefficient to obtain the estimated DCT coefficient of each position in the JPEG image of the carrier:
Figure BDA0002333090550000099
Figure BDA00023330905500000910
a matrix representing the composition of the estimated DCT coefficients in the carrier image,
Figure BDA00023330905500000911
representation matrix
Figure BDA00023330905500000912
The estimated DCT coefficient of the middle p +1 row and q +1 column is the quantized (p, q) position of the carrier imageIn the actual DCT coefficient, p is more than or equal to 0 and less than or equal to M-1, and q is more than or equal to 0 and less than or equal to N-1.
The different locations of each 8 x 8 block of actual DCT coefficients in a JPEG image represent different frequency spectra, and the coefficients at each location represent energy over different frequency spectra. The coefficient at the (0,0) position is a direct current coefficient DC, the coefficients at other positions are alternating current coefficients AC, the coefficient at the upper left corner is a low frequency coefficient, and the coefficient at the lower right corner is a high frequency coefficient. Since the image contents of adjacent 8 × 8 blocks in a JPEG image usually have strong correlation, the quantized DCT coefficient matrix has strong correlation between the same spectral energy, i.e. the same position coefficient, in the adjacent 8 × 8 blocks. Therefore, 64 hidden image co-frequency subgraphs can be obtained by combining all 8 × 8 blocks in the JPEG image with the same frequency spectrum, namely, coefficients at the same position, and then the estimation of the carrier JPEG image is realized by low-pass filtering the hidden image co-frequency subgraphs, so that the problem that the carrier JPEG image is difficult to obtain is solved.
B: calculating the residual error between the actual DCT coefficient of each position in each to-be-detected hidden image and the estimated DCT coefficient; if the actual DCT coefficient of a certain position in a certain to-be-detected hidden image is an embeddable coefficient, setting the residual error of the position in the hidden image to be 0;
c: averaging the residual errors of the same positions of all the hidden images to obtain the residual error average value of each position of the hidden image to be detected;
d: judging whether the residual error mean value of each position is a hidden position or not according to the residual error mean value of each position, so as to judge the positions of all hidden actual DCT coefficients; for a hidden image, if the position of an actual DCT coefficient is judged to be an estimated hidden position and the actual DCT coefficient is an embeddable coefficient, the actual DCT coefficient is judged to contain embedded secret information, and the position of the actual DCT coefficient is judged to be the hidden position.
When the embedding position is selected by adopting a pseudo-random scrambling method without eliminating the non-embeddable coefficient, the T pieces of the to-be-detected hidden image S with the same embedding path and embedding rate are subjected to1,S2,…,STActual DCT coefficients of the same position (i, j)S1(i,j),S2(i,j),…,ST(i, j) should belong to one of the following two cases as shown in FIG. 5. In fig. 5, black squares represent non-embeddable coefficients, white squares represent embeddable coefficients without embedded information, grid squares represent embeddable coefficients with embedded information, and numbers in circles represent the positions of the coefficients in the pre-scrambling graph.
1) When position (i, j) is a steganographic position, the steganographer will determine whether to embed information based on whether the coefficient is embeddable, at which time S1(i,j),S2(i,j),…,ST(i, j) belongs to the first case: s1(i,j),S2(i,j),…,ST(i, j) any coefficient St(i, j) either non-embeddable coefficients or steganographic coefficients of embedded information;
2) when the position (i, j) is a non-cryptic position, regardless of whether the coefficient can be embedded, the steganographer will not embed information therein, at which time S1(i,j),S2(i,j),…,ST(i, j) belongs to the second case: s1(i,j),S2(i,j),…,ST(i, j) any coefficient St(i, j) are all non-secret coefficients with no information embedded.
Therefore, for each to-be-detected hidden image, if the position of an actual DCT coefficient is determined to be an estimated hidden position and the actual DCT coefficient is an embeddable coefficient, the actual DCT coefficient is determined to contain embedded secret information, and the position of the actual DCT coefficient is determined to be a hidden position.
In this embodiment, the low-pass filtering F of step a3low(S(i,j)) Specifically, a wavelet filtering mode is adopted to obtain an estimated quantized DCT coefficient subgraph
Figure BDA0002333090550000111
The wavelet filtering has good multi-direction and multi-resolution analysis capability, can capture fine detail difference in an image, and the steganographic noise has the characteristic of small noise, so that the high-pass wavelet filtering can capture the steganographic noise well and shows excellent performance in JPEG image steganographic detection. Correspondingly, low-pass wavelet filtering can be very goodAnd the steganography noise in the steganography image is removed, and the carrier image is estimated more accurately. Therefore, the low-pass wavelet filtering is used for estimating the carrier image co-frequency subgraph in the hidden image co-frequency subgraph.
The step a3 specifically includes the following steps:
a3.1: carrying out wavelet decomposition on the actual DCT coefficient in each same-frequency subgraph of the hidden image to be detected: same-frequency subgraph S of hidden image by using 8-tap Daubechies filter(i,j)Decomposing to obtain hidden image same-frequency subgraph S(i,j)The four sub-bands comprise a low-frequency sub-band L, a horizontal sub-band H, a vertical sub-band V and a diagonal sub-band D;
l (x, y) represents a hidden image same-frequency subgraph S(i,j)H (x, y) represents the same-frequency subgraph S of the hidden image(i,j)The coefficient value of (x, y) position in the horizontal sub-band H, V (x, y) represents the same-frequency sub-image S of the hidden image(i,j)The wavelet coefficient value of (x, y) position in the vertical sub-band V of (D, x, y) represents the same-frequency sub-image S of the hidden image(i,j)The wavelet coefficient value at the (x, y) position in the diagonal sub-band D of (1) x ≦ He,1 ≦ y ≦ Wi, He represents the height of any one of the four sub-bands, and Wi represents the width of any one of the four sub-bands;
a3.2: respectively in the hidden image same frequency subgraph S(i,j)The minimum local variance solution is performed in the horizontal sub-band H, the vertical sub-band V and the diagonal sub-band D: obtaining the local variance of each wavelet coefficient of the same-frequency subgraph of the carrier image by utilizing the maximum posterior estimation of 4 square dxd neighborhoods on a horizontal sub-band H, a vertical sub-band V and a diagonal sub-band D by utilizing a formula (5);
Figure BDA0002333090550000112
Figure BDA0002333090550000113
representing the local variance of (x, y) position in the horizontal sub-band H of the same-frequency subgraph of the carrier image;
Figure BDA0002333090550000114
representing the local variance of the (x, y) position in the vertical sub-band V of the same-frequency subgraph of the carrier image,
Figure BDA0002333090550000115
representing the local variance of (x, y) positions in the diagonal sub-band D of the same-frequency subgraph of the carrier image;
Figure BDA0002333090550000116
representing the variance of the steganographic noise,
Figure BDA0002333090550000117
represents the mean of the squares of the wavelet coefficients in a square d x d neighborhood centered at the (x, y) position in the horizontal subband H,
Figure BDA0002333090550000121
represents the mean of the squares of the wavelet coefficients in a square d x d neighborhood centered at the (x, y) position in the vertical subband V,
Figure BDA0002333090550000122
represents the mean of the squares of the wavelet coefficients in a square D x D neighborhood centered at the (x, y) position in the diagonal subband D; d belongs to {3,5,7,9 };
a3.3: wavelet coefficients of a horizontal sub-band H, a vertical sub-band V and a diagonal sub-band D are subjected to low-pass filtering by using a wiener filter:
Figure BDA0002333090550000123
Hlow(x, y) denotes the low-pass filtered horizontal sub-band HlowEstimated coefficient values for the (x, y) position;
Vlow(x, y) denotes the low-pass filtered vertical sub-band VlowEstimated coefficient values for the (x, y) position;
Dlow(x, y) denotes the low-pass filtered diagonal sub-band DlowEstimated coefficient values for the (x, y) position;
a3.4: low frequency sub-band L and low pass filtered horizontal sub-bandHlowLow pass filtered vertical sub-band VlowLow pass filtered diagonal sub-band DlowAnd performing inverse wavelet transform to obtain an estimated DCT coefficient in the carrier image.
And D, according to the residual mean value of each position in the step D, judging whether the position is a hidden position or not, and demonstrating:
let C1,C2,…,CTRepresenting T number of to-be-detected hidden images S1,S2,…,STCorresponding carrier image, StRepresenting the t-th latent image to be detected, CtRepresenting the carrier image, p, corresponding to the t-th steganographic image to be detected0Denotes S1(i,j),S2(i,j),…,STRatio of non-embeddable coefficients in (i, j), p1Denotes S1(i,j),S2(i,j),…,ST(i, j) ratio of embeddable coefficients, St(i, j) represents the actual DCT coefficient of the position of the t-th to-be-detected hidden image (i, j), Ct(i, j) represents the DCT coefficient of the carrier image (i, j) position corresponding to the t-th to-be-detected hidden image, R (i, j) represents the mean value of the absolute difference values of the DCT coefficients of all to-be-detected hidden images and the carrier image at the (i, j) position, namely the residual error between the actual DCT coefficient of the to-be-detected hidden image at the (i, j) position and the DCT coefficient of the corresponding carrier image
Figure BDA0002333090550000124
1≤t≤T；
When the steganographically embedded information is pseudo-random information and the average modification amplitude for each embeddable coefficient is α, if position (i, j) is a hidden position, then the mean value R of the absolute difference of the position coefficients (i, j)1(i,j)≈p1α。
If the position (i, j) is a non-hidden position, the mean value R of the absolute difference of the position coefficients0(i,j)＝0。
From R1(i, j) and R0(i, j) it can be seen that the mean value of the absolute difference values of the same position coefficients of the carrier image at the hidden position and the non-hidden position and the hidden image to be detected has obvious existenceTherefore, whether the position is a hidden position or not can be judged according to the residual mean value of each position.
Specifically, in the step B, after the carrier image corresponding to each to-be-detected hidden image is estimated, for the residual error between the actual DCT coefficient at each position in each to-be-detected hidden image and the estimated DCT coefficient, the calculation may be performed by using a method of calculating an absolute value in formula (7), or may be performed by using another suitable method according to a manner of changing the actual DCT coefficient by a steganography algorithm.
Taking a typical JSteg steganography as an example, the steganography embeds information by replacing the LSBs of embeddable coefficients. Research results in the aspect of positioning of spatial domain LSB replacement steganographic information show that WS (Weighted Stego-image) residual errors adjust difference signs according to asymmetry of sample change during LSB replacement (namely, even numbers can only be added with 1, and odd numbers can be subtracted with 1), and excellent performance is shown in LSB replacement steganographic information positioning. Therefore, the method can be applied to the calculation of the residual error in the step B of the invention when the JSTEG is steganographically, and can be adjusted according to whether the coefficient can be embedded or not. Since the JSteg steganography regards the coefficients with values of 0 and 1 and the DC coefficient as non-embeddable coefficients, the WS residual calculation formula of the JSteg steganography of each to-be-detected steganographic image is as follows:
Figure BDA0002333090550000131
wherein r ist(i, j) representing a concealed image subjected to JSTEG concealed writing, wherein all concealed images to be detected and estimated carrier images are aligned, and (i, j) the average value of absolute difference values of the actual DCT coefficient and the estimated DCT coefficient at the position, namely WS residual error between the actual DCT coefficient and the estimated DCT coefficient at the position (i, j);
Strepresenting the t-th hidden image;
Figure BDA0002333090550000132
representing an image obtained after LSB (least significant bit) of the embeddable coefficient of the T-th hidden image is turned, wherein T is more than or equal to 1 and less than or equal to T;
St(i, j) represents the t-th steganographic image to be detected (i,j) the actual DCT coefficients of the location are,
Figure BDA0002333090550000133
and (3) representing DCT coefficients of the position of the image (i, j) obtained after LSB inversion of the embeddable coefficients of the t-th hidden image.
mod (i,8) represents the calculation of the remainder of i divided by 8.
Experiments are performed below on the JPEG image steganography information positioning method of the present invention.
In this embodiment, 10000 images with 512 × 512 PGM format from bossbase1.0 image library are JPEG-compressed by a quality factor of 75 in Matlab to obtain 10000 JPEG images. And then, randomly selecting 1000 carrier images with nonzero coefficients of 30000-50000 from 10000 carrier JPEG images. And scrambling the integers of 1-512 x512 by using a randderm function to obtain a pseudo-random path. And finally, selecting embeddable coefficients with the ratio q being equal to {0.1,0.2,0.3,0.4,0.5,0.6,0.7,0.8 and 0.9} in the front part of the pseudo-random path from 1000 carrier JPEG images, embedding pseudo-random information in the selected coefficients by JSTEG steganography, and respectively generating 10 test hidden image sets with different embedding ratios.
The algorithm presented herein will be tested for effectiveness and compared to other algorithms for performance, using the generated 10 sets of hidden images as samples.
In order to test the advantages of adopting same-frequency subgraph filtering and JSTEG steganography WS residual error given by the formula (8), the coefficient of the whole graph is subjected to low-pass wavelet filtering, and wavelet filtering is carried out on the same-frequency subgraph of the hidden image in the invention; then, the WS residual error of JSTEG steganography given by the formula (8) and the original WS residual error without setting the residual error of the non-embeddable position to 0 are respectively calculated, and the JSTEG steganography information positioning algorithm under two different residual error calculation modes is realized. Finally, comparing the performance difference of two JSteg steganography information positioning algorithms (SFSW-JSteg and SFS4-JSteg) based on same-frequency sub-image filtering and the steganography information positioning algorithms (WIW-JSteg and WIW) based on full-image coefficient wavelet filtering.
SFSW-JSTEG (same-frequency subgraph wavelet filtering + JSTEG steganography residual setting of non-embeddable coefficients to 0): estimating a carrier DCT coefficient by adopting wavelet filtering of a same-frequency subgraph, setting a residual error of a non-embeddable coefficient to be 0 when calculating a JSTEG steganography residual error between an actual DCT coefficient of a to-be-detected steganographic image and the estimated carrier image DCT coefficient, and finally realizing steganography information positioning according to an average value of residual errors at the same position of all to-be-detected images.
SFS4-JSTEG (intra-frequency subgraph 4 neighborhood filtering + JSTEG steganography non-embeddable coefficient residual put 0): estimating a carrier DCT coefficient by adopting same-frequency subgraph 4 neighborhood filtering, setting a residual error of a non-embeddable coefficient to be 0 when calculating a JSTEG steganography residual error between an actual DCT coefficient of a to-be-detected steganography image and the estimated carrier image DCT coefficient, and finally realizing steganography information positioning according to an average value of residual errors at the same position of all to-be-detected images.
WIW-JSTEG (full-map spatial wavelet filtering + JSTEG steganographic residual of non-embeddable coefficients set to 0): and performing wavelet filtering on the actual DCT coefficient of the full image to estimate the DCT coefficient of the carrier, setting the residual error of the non-embeddable coefficient to 0 when calculating the JSTEG steganography residual error between the actual DCT coefficient of the steganography image to be detected and the estimated DCT coefficient of the carrier image, and finally realizing steganography information positioning according to the average value of the residual errors at the same position of all the images to be detected.
WIW (whole-image coefficient wavelet filtering + left to set 0 the residual of JSteg stego un-embeddable coefficients): and performing wavelet filtering on the actual DCT coefficient of the full image to estimate the DCT coefficient of the carrier, then not setting the residual error of the non-embeddable coefficient to 0 when calculating the JSTEG steganography residual error between the actual DCT coefficient of the steganography image to be detected and the estimated DCT coefficient of the carrier image, and finally realizing steganography information positioning according to the average value of the residual errors at the same position of all the images to be detected.
Table 1 gives the positioning accuracy of four different steganographic information positioning algorithms SFSW-JSteg, SFS4-JSteg, WIW-JSteg, and WIW for different numbers of stego positions (i.e. the first 50% positions of the embedding path) in the stego image with an embedding rate q of 0.5.
Table 2 shows the positioning accuracy of the steganographic position in 1000 steganographic images with the same embedding path and embedding rate by four different steganographic information positioning algorithms SFSW-JSteg, SFS4-JSteg, WIW-JSteg and WIW under different embedding rates. As can be seen from tables 1 and 2, the four algorithms can position the hidden positions with a correct rate exceeding random guessing, and the correct rate of positioning the hidden positions is obviously improved as the number of the hidden images increases and the embedding rate increases. The positioning accuracy of the two JSTEG steganographic information positioning algorithms based on the same-frequency sub-image filtering to the hidden position is obviously higher than that of the steganographic information positioning algorithm based on the full-image coefficient wavelet filtering. Particularly, the JSteg steganography information positioning algorithm SFSW-JSteg based on the same-frequency subgraph wavelet filtering is the most excellent in performance. The performance of the steganographic information positioning algorithm WIW based on the wavelet filtering of the full image coefficient is the worst, on one hand, because the correlation between adjacent position coefficients in the JPEG image is weak, the estimation precision of the carrier image coefficient through the wavelet filtering of the full image coefficient is poor; on the other hand, the WIW algorithm fails to consider the characteristics of JSTEG steganography, and the residual error of the JSTEG steganography non-embeddable coefficient is not set to 0.
TABLE 1 accuracy of four steganographic information positioning algorithms at different steganographic image quantities
Figure BDA0002333090550000161
Table 2 accuracy rate of positioning hidden positions in 1000 images by four steganographic information positioning algorithms under different embedding rates
Figure BDA0002333090550000162

Claims (3)

1. A JPEG image steganography information positioning method based on same-frequency subgraph filtering is characterized in that: the method comprises the following steps:
a: for given T pieces of hidden images to be detected with the same embedding position, estimating a quantized DCT coefficient in each position of the carrier JPEG image corresponding to each hidden image to be detected by adopting a carrier JPEG image estimation method based on same-frequency sub-image filtering to obtain an estimated DCT coefficient of each position of the carrier JPEG image;
b: calculating the residual error between the actual DCT coefficient of each position in each to-be-detected hidden image and the estimated DCT coefficient; if the actual DCT coefficient of a certain position in a certain to-be-detected hidden image is an embeddable coefficient, setting the residual error of the position in the hidden image to be 0;
c: averaging the residual errors of the same positions of all the hidden images to obtain the residual error average value of each position of the hidden image to be detected;
d: judging whether the residual error mean value of each position is a hidden position or not according to the residual error mean value of each position, so as to judge the positions of all hidden actual DCT coefficients; for a hidden image, if the position of an actual DCT coefficient is the estimated hidden position and the actual DCT coefficient is an embeddable coefficient, the actual DCT coefficient is judged to contain embedded secret information, and the position of the actual DCT coefficient is judged to be the hidden position.
2. The JPEG image steganography information positioning method based on same-frequency subgraph filtering according to claim 1, characterized in that: the step A specifically comprises the following steps:
a1: carrying out Huffman decoding on the hidden image to be detected to obtain a matrix S formed by quantized actual DCT coefficients;
Figure FDA0002333090540000011
wherein M represents the height of the to-be-detected hidden image, N represents the width of the to-be-detected hidden image, and both M and N are integral multiples of 8; sp，qThe actual DCT coefficients of the p +1 th row and the q +1 th column in the matrix S are the quantized actual DCT coefficients of the (p, q) position of the to-be-detected hidden image, p is more than or equal to 0 and less than or equal to M-1, and q is more than or equal to 0 and less than or equal to N-1;
a2: carrying out hidden image same-frequency subgraph division on the matrix S; combining actual DCT coefficients of the same position in the 8 x 8 blocks of the to-be-detected hidden image, namely the 8 x 8 blocks of the to-be-detected hidden image, and obtaining 64 same-frequency subgraphs of the hidden image for 64 different positions in the 8 x 8 blocks, S(i，j)Representing the same-frequency subgraph of the hidden image at the position of (i, j) in the 8 multiplied by 8 block, i is more than or equal to 0 and less than or equal to 7, j is more than or equal to 0 and less than or equal to 7；
Figure FDA0002333090540000021
Wherein
Figure FDA0002333090540000022
M is the height of the to-be-detected hidden image, and N is the width of the to-be-detected hidden image;
a3: low-pass filtering F is carried out on 64 hidden image same-frequency subgraphs by utilizing a low-pass filterlow(S(i，j)) Obtaining the estimated quantized carrier image same-frequency subgraph
Figure FDA0002333090540000023
Figure FDA0002333090540000024
Wherein
Figure FDA0002333090540000025
Same-frequency subgraph S for representing hidden image(i，j)Corresponding carrier image same-frequency subgraph C(i，j)I is more than or equal to 0 and less than or equal to 7, and j is more than or equal to 0 and less than or equal to 7;
a4: combining the same-frequency subgraphs of the carrier image to obtain an estimated carrier JPEG image; placing the estimated DCT coefficient in the same-frequency subgraph of the carrier image at the position of the corresponding actual DCT coefficient to obtain the estimated DCT coefficient of each position in the JPEG image of the carrier:
Figure FDA0002333090540000026
wherein
Figure FDA0002333090540000029
A matrix representing the composition of the estimated DCT coefficients in the carrier image,
Figure FDA0002333090540000027
representation matrix
Figure FDA0002333090540000028
And the estimated DCT coefficients of the p +1 th row and the q +1 th column are quantized DCT coefficients of the (p, q) position of the carrier image, wherein p is more than or equal to 0 and less than or equal to M-1, and q is more than or equal to 0 and less than or equal to N-1.
3. The JPEG image steganography information positioning method based on same-frequency subgraph filtering according to claim 2, characterized in that: the step a3 specifically includes the following steps:
a3.1: respectively carrying out wavelet decomposition on all same-frequency subgraphs in the hidden image to be detected: co-frequency subgraph S of a hidden image using an 8-tapDaubechies filter(i，j)Decomposing to obtain hidden image same-frequency subgraph S(i，j)The four sub-bands comprise a low-frequency sub-band L, a horizontal sub-band H, a vertical sub-band V and a diagonal sub-band D;
l (x, y) represents a hidden image same-frequency subgraph S(i，j)H (x, y) represents the same-frequency subgraph S of the hidden image(i，j)The wavelet coefficient value of (x, y) position in the horizontal sub-band H of (A), V (x, y) represents the same-frequency sub-image S of the hidden image(i，j)The wavelet coefficient value of (x, y) position in the vertical sub-band V of (D, x, y) represents the same-frequency sub-image S of the hidden image(i ，j)The wavelet coefficient value at the (x, y) position in the diagonal sub-band D of (1) x ≦ He,1 ≦ y ≦ Wi, He represents the height of any one of the four sub-bands, and Wi represents the width of any one of the four sub-bands;
a3.2: respectively in the hidden image same frequency subgraph S(i，j)The minimum local variance solution is performed in the horizontal sub-band H, the vertical sub-band V and the diagonal sub-band D: obtaining the local variance of each wavelet coefficient of the same-frequency subgraph of the carrier image by utilizing the maximum posterior estimation of 4 square dxd neighborhoods on a horizontal sub-band H, a vertical sub-band V and a diagonal sub-band D by utilizing a formula (5);
Figure FDA0002333090540000031
wherein
Figure FDA0002333090540000033
Representing the local variance of (x, y) position in the horizontal sub-band H of the same-frequency subgraph of the carrier image;
Figure FDA0002333090540000038
representing the local variance of the (x, y) position in the vertical sub-band V of the same-frequency subgraph of the carrier image,
Figure FDA0002333090540000034
representing the local variance of (x, y) positions in the diagonal sub-band D of the same-frequency subgraph of the carrier image;
Figure FDA0002333090540000039
representing the variance of the steganographic noise,
Figure FDA0002333090540000035
represents the mean of the squares of the wavelet coefficients in a square d x d neighborhood centered at the (x, y) position in the horizontal subband H,
Figure FDA0002333090540000036
represents the mean of the squares of the wavelet coefficients in a square d x d neighborhood centered at the (x, y) position in the vertical subband V,
Figure FDA0002333090540000037
represents the mean of the squares of the wavelet coefficients in a square D x D neighborhood centered at the (x, y) position in the diagonal subband D; d belongs to {3,5,7,9 };
a3.3: wavelet coefficients of a horizontal sub-band H, a vertical sub-band V and a diagonal sub-band D are subjected to low-pass filtering by using a wiener filter:
Figure FDA0002333090540000032
Hlow(x, y) denotes the low-pass filtered horizontal sub-band HlowEstimated coefficient values for the (x, y) position;
Vlow(x, y) denotes the low-pass filtered vertical sub-band VlowEstimated coefficient values for the (x, y) position;
Dlow(x, y) denotes the low-pass filtered diagonal sub-band DlowEstimated coefficient values for the (x, y) position;
a3.4: low frequency sub-band L and low pass filtered horizontal sub-band HlowLow pass filtered vertical sub-band VlowLow pass filtered diagonal sub-band DlowAnd performing inverse wavelet transform to obtain an estimated DCT coefficient in the carrier image.
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