CN109543425B - Image data hiding method based on tensor decomposition - Google Patents
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Abstract
The invention discloses an image data hiding method based on tensor decomposition, which is characterized in that high-order singular value decomposition is applied to an image of required embedded information, the required embedded information replaces a left singular matrix element corresponding to a minimum singular value obtained by tensor decomposition, and an original image is reconstructed by the replaced singular matrix. The method comprises the following steps: putting an image of the required embedded data into a third-order cube tensor; decomposing the cube tensor by using a high-order singular value decomposition method to obtain a core tensor, singular values on each mode and a singular matrix; replacing a left singular matrix element corresponding to a minimum singular value under a certain mode obtained by tensor decomposition by the needed embedded information; reconstructing a third-order tensor by the three left singular matrixes and the core tensor which are embedded with the information; and extracting the image with the embedded information from the third-order tensor. The method applies tensor decomposition to image data hiding, improves the safety of information transmission, and simultaneously does not cause the reduction of image quality after extracting embedded information.
Description
Technical Field
The invention relates to a data hiding technology, in particular to an image data hiding method based on tensor decomposition.
Background
The data hiding technology is a comprehensive technology, which relates to the knowledge of multiple disciplines such as human physiology, computer graphics, cryptography, information processing, and the like, and mainly studies on how to hide confidential information in public information and then transmit the confidential information through the public information. The general data hiding technology changes original data in the process of information embedding, and damages the original data after extracting embedded information, so that the lossless data hiding technology becomes an important research direction of the data hiding technology.
The image data hiding technology is a branch of data hiding technology, and confidential information is embedded into a certain public image and is transmitted through the image in a mode of not attracting attention of attackers and being safer compared with a password technology. The existing image data hiding method comprises the following steps:
fridrich.j proposes a reversible information hiding method based on lossless data compression. The lossless data compression method mainly extracts and compresses LSB information of an original image, and a space generated after compression is used for embedding hidden information.
Tian proposes a reversible information hiding method based on difference value expansion. The basic idea of difference expansion is to hide information by expanding the difference between adjacent pixel points. The method proposed by Tian extends the difference value k 'by calculating' l ＝2k l +w l The method is easy to cause pixel value overflow, and the problem of pixel overflow can be solved by utilizing the positioning graph to realize image recovery, but the influence on the capacity of embedded information is large.
Ni proposes a reversible information hiding method based on histogram adjustment. The basic idea of histogram adjustment is to embed information using zero redundancy by adjusting the histogram of the original image. Ni proposes a method of embedding information using three maximum points and minimum points in an image histogram, which has a large capacity of embedded information but is highly complex, and the maximum points are not the best positions to embed information.
The invention provides an image data hiding method based on tensor decomposition, which is characterized in that an original RGB image is placed in a three-order cube tensor, the position of the three-order cube tensor is used as a key, the tensor is decomposed by using high-order singular value decomposition to obtain singular matrixes under three modes, a left singular vector corresponding to the minimum singular value in the mode determined by the size of the original image is used for replacing a column of elements with required embedded information, the three-order tensor is reconstructed by the core tensor obtained by decomposition and the left singular matrix under the three modes (including the left singular matrix of the embedded information in the mode), the RGB image after the information is embedded is obtained by using the position key, and the embedded information (the left singular matrix element corresponding to the minimum singular value in the mode) can be obtained by performing high-order singular value decomposition on the RGB image.
Disclosure of Invention
The invention aims to fully utilize the spatial structure in the RGB image, resist attack to a certain extent, increase the safety of embedded information and keep the image quality basically unchanged after the embedded information is extracted.
In order to achieve the above object, the present invention provides an image data hiding method based on tensor decomposition, which includes:
putting an original RGB image into a three-order cube tensor with random values, and taking the put position as a secret key;
decomposing the third-order tensor by using high-order singular value decomposition to obtain a core tensor and singular matrixes (comprising three left singular matrixes, three singular value matrixes and three right singular matrixes) under three modes respectively;
selecting a singular value matrix obtained by decomposition under a mode determined by the size of an original image to find a left singular matrix element corresponding to the minimum singular value in the singular value matrix, and replacing the row of elements with the required embedded information to obtain a new left singular matrix under the mode;
reconstructing a third-order tensor by using a left singular matrix and a core tensor under three modes, and extracting an image with embedded information through a key;
obtaining a singular matrix by decomposing the image of the embedded information through a high-order singular value, finding a left singular matrix element corresponding to a minimum singular value in the mode, wherein the column vector is the embedded information;
and after information is extracted, reconstructing the tensor by using the core tensor obtained by decomposition and the left singular matrix under the three modes, and finding the image after the information is extracted through the position key.
Wherein, according to the third order cube tensor, comprising:
the magnitude of the third order cube tensor is determined from the selected image: a = max (size (I)), I being the selected image;
the tensor element takes a value of 0-255;
the position of a third-order cube tensor is put into the image to serve as a key;
according to the method, the decomposition of the third-order cube tensor by the high-order singular value is carried out, and the method comprises the following steps:
decomposing the third-order cube tensor by a Tucker to obtain a core tensor and expansion matrixes under three modes;
SVD decomposition is carried out on the expansion matrixes under the three modes to obtain singular matrixes (a left singular matrix, a singular value matrix and a right singular matrix), and the matrixes corresponding to the three modes are the same in size.
Wherein reconstructing the third order tensor extracted image according to the embedded information comprises:
finding a left singular matrix column vector corresponding to the minimum singular value in the mode, and replacing the column vector with information to be embedded;
reconstructing a third-order tensor by the left singular matrix, the left singular matrix in other modes and the core tensor;
and extracting the original image embedded with the information through the position key.
Wherein, according to the extracting the embedded information, the method comprises the following steps:
putting the embedded information image into the original three-order cube tensor through a position key;
performing high-order singular value decomposition on the third-order tensor;
finding a left singular matrix element corresponding to the minimum singular value in the mode, wherein the column vector element is embedded information;
reconstructing a third-order tensor by the left singular matrix after the information is extracted, the left singular matrix in other modes and the core tensor;
and finding the image with the embedded information extracted in the third-order cube tensor through the position key.
Based on the invented method, compared with the existing method, the method has the outstanding differences and contributions that:
1. the invention relates to an image expression in a tensor form, which fully utilizes the spatial structure of an RGB image, the formed tensor obtains three modes through Tucker decomposition, more image details can be reserved in the next step of SVD decomposition by expanding the mode determined by the size of an original image, and the influence on the image quality after the embedded information is extracted is very small.
2. According to the three-order cube tensor related by the invention, the matrix size of the three modes obtained by Tucker decomposition after expansion is the same, when the three modes are attacked, an attacker cannot intuitively find out which mode is determined by the original image size, information embedded in a singular matrix under the mode is protected, and the safety of the information in the transmission process is improved.
Description of the drawings:
the technical scheme of the invention is further explained by combining the attached drawings.
Fig. 1 is a flowchart of an image data hiding method based on tensor decomposition according to an embodiment of the present application.
FIG. 2 is a flowchart illustrating the three-order cube tensor placement of an image according to an embodiment of the present application.
Fig. 3 is a flowchart of information embedding according to an embodiment of the present application.
Fig. 4 is a flowchart of information extraction according to an embodiment of the present application.
The specific implementation mode is as follows:
the objects, aspects and advantages of the present invention will be described in detail with reference to the following detailed description and accompanying drawings.
Fig. 1 is a schematic view of the entire process of the embodiment of the present application, which is specifically implemented as follows:
in step S110, the original RGB image is put into a randomly created third-order cube tensor.
And step S120, performing high-order singular value decomposition on the third-order tensor to obtain singular values and singular vectors.
Step S130, the left singular matrix element corresponding to the minimum singular value in a certain mode is replaced with the required embedded information.
And step S140, reconstructing a tensor by the replaced left singular matrix and the core tensor, and finding an image in the tensor.
And S150, obtaining the original three-order cube tensor and the image after embedding the information, and performing high-order singular value decomposition to obtain the embedded information.
The following describes some key steps of the embodiments of the present application in detail.
1. FIG. 2 shows the creation of a third order cube tensor
The embodiment of the application uses an original RGB image I O Putting the cubic tensor into a three-order cubic tensor T with random values, wherein:
original RGB image I O The size is n multiplied by m multiplied by 3;
three-order cube tensor T with random values O ；
Cubic tensor T of third order O If n > m, the tensor size is nxnxnxnxn, the corresponding mode is the first mode, if n < m, the tensor size is mxmxmxmxm, and the corresponding mode is the second mode (in this embodiment, it is assumed that n > m, the first mode is selected);
the elements of the filling are between 0 and 255; (ii) a
In third order tensor T O Randomly selecting a certain position to put in an original RGB image I O Obtaining a third order tensor T put into the image E ；
This location is a key, determined by the encryptor.
2. FIG. 3 shows a process for embedding hidden information
The embodiment of the application utilizes the minimum singular value to embed information, wherein:
step S310, using high-order singular value decomposition to the third-order tensor T E Carrying out decomposition;
performing Tucker decomposition on the tensor to obtain a core tensor and a matrix under each mode;
the Tucker decomposition process may be expressed as: t is E ＝[S，A，B，C]Where S is the core tensor, A, B, C are the matrices under the three modes, respectively, which is approximately equal to T E ≈S× 1 A U × 2 B U × 3 C U . Respectively carrying out SVD decomposition on A, B and C to obtain singular matrixes under each mode:
[A U ，A S ，A V ]＝SVD(A)；
[B U ，B S ，B V ]＝SVD(B)；
[C U ，C S ，C V ]＝SVD(C)；
the subscripts U, S and V respectively represent a left singular matrix, a singular value matrix and a right singular matrix under the mode;
step S320, selecting a singular value matrix A obtained by SVD decomposition under a mode S Selecting the minimum singular value sigma min At the left singular matrix A U To find the sigma min The corresponding column vector;
step S330, replacing the column vector with the information to be embedded to obtain a left singular matrix A 'with the embedded information' U ；
Step S340, embedding information into the core tensor S and the mode I to form a left singular matrix A' U And left singular matrix B in mode two and mode three U ，C U Obtaining a third-order tensor after information embedding;
extracting information-embedded image I from reconstructed third-order tensor by using position key R 。
3. FIG. 4 shows a process for embedded information extraction
Step S410, using the position key to embed the image I of the information R Put the initial third order cube tensor T O Obtain a new third order tensor T N ；
Step S420, for T N Performing high-order singular value decomposition (and for T) E The same decomposition is done) to obtain a core tensor S 2 And the singular matrixes under each mode comprise three modes and nine singular matrixes;
step S430, finding a left singular matrix under the mode one, wherein the singular vectors of the row corresponding to the minimum singular value are embedded information;
step S440, after extracting the embedded information, the core tensor S 2 Reconstructing a third order tensor T by using the left singular matrix extracted with information in the first mode and the corresponding left singular matrices in the other two modes K ；
Step S450, using the position key, the third order tensor T after reconstruction K Extracting the image to obtain the image with the embedded information, the image quality and the originalThe starting image quality is similar.
Claims (5)
1. An image data hiding method based on tensor decomposition, which is used for transmitting information through an image, and is characterized by comprising the following steps:
establishing a third-order cube tensor with an element value between 0 and 255, and putting an original RGB image into the third-order cube tensor;
performing Tucker decomposition on the third-order cube tensor by using high-order singular value decomposition to obtain a core tensor and singular matrixes under three modes, namely:
T E ＝[S，A，B，C]
wherein, T E Representing a third-order cube tensor to be decomposed, wherein S is a decomposed core tensor, and A, B and C are singular matrixes under three modes;
SVD decomposition is carried out on the singular matrixes under each mode respectively to obtain a left singular matrix, a singular value matrix and a right singular matrix under the mode:
[A U ，A S ，A V ]＝SVD(A)
[B U ，B S ，B V ]＝SVD(B)
[C U ，C S ，C V ]＝SVD(C)
subscripts U, S and V respectively represent a left singular matrix, a singular value matrix and a right singular matrix in the mode;
selecting a singular value matrix obtained by decomposition in a first mode to find a left singular matrix element corresponding to the minimum singular value, and replacing the column of elements with the information to be embedded to obtain a new left singular matrix in the mode;
reconstructing a third-order cube tensor by using a left singular matrix and a core tensor under three modes, and extracting an image after information embedding from the third-order cube tensor;
and (4) placing the image after embedding the information into the original three-order cube tensor to obtain the embedded information through high-order singular value decomposition.
2. The method for hiding image data based on tensor decomposition as recited in claim 1, wherein the original RGB image is put into a third-order cube tensor, and comprises:
putting an RGB image of the required embedded information into a third-order cube tensor;
the position of the placement is used as a key;
the value of the third-order cube tensor element is between 0 and 255;
the size is the maximum of the image size.
3. The tensor decomposition-based image data hiding method according to claim 1, wherein performing a Tucker decomposition on the third-order cube tensor by using a higher-order singular value decomposition comprises:
decomposing the three-order cube tensor put into the image by using high-order singular value decomposition;
obtaining a core tensor and singular matrixes of the core tensor on three modes, wherein the singular matrixes comprise a singular value matrix, a left singular matrix and a right singular matrix;
selecting a left singular matrix element corresponding to a minimum singular value obtained by modal decomposition corresponding to the original image size;
and replacing the column of elements with the required embedded information to obtain a left singular matrix after the information is embedded in the mode.
4. The tensor decomposition-based image data hiding method according to claim 1, wherein reconstructing an image by using the replaced left singular matrix and the core tensor comprises:
reconstructing a third-order cube tensor by using the left singular matrix in the modality and the left singular matrices in other modalities after embedding information and the core tensor;
finding out an RGB image embedded with information from the reconstructed third-order cube tensor by using the position key;
the size of the RGB image after embedding the information is consistent with that of the original RGB image.
5. The tensor decomposition-based image data hiding method as recited in claim 1, wherein the extracting of the embedded information is obtained by performing high-order singular value decomposition on a third-order cubic tensor of the image in which the embedded information is placed, and comprises the following steps:
the image embedded with the information is placed into the initial third-order cube tensor by using the position key;
performing high-order singular value decomposition on the three-order cube tensor in which the image is placed;
the embedded information is a singular vector corresponding to the smallest singular value in the modality corresponding to the original image size.
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