CN102984428A

CN102984428A - Wet paper secret writing method based on wavelet transform

Info

Publication number: CN102984428A
Application number: CN2012104544405A
Authority: CN
Inventors: 陈志宏; 曹丽丽; 杨晓苹
Original assignee: Tianjin University of Technology
Current assignee: Tianjin University of Technology
Priority date: 2012-11-12
Filing date: 2012-11-12
Publication date: 2013-03-20

Abstract

The invention provides a wet paper secret writing method based on wavelet transform. The wavelet transform for a carrier image is conducted, and then selective embedding is conducted in a wavelet coefficient according to texture complexity degree in an image local neighborhood. When secret information is drawn, simple matrix multiply operation is only required, and invisibility of a secret writing method is achieved in the process of transport of the secret information.

Description

Wet paper steganographic method based on wavelet transform

技术领域 technical field

本发明属于数字图像处理技术领域，主要涉及一种基于小波变换的湿纸密写方法。The invention belongs to the technical field of digital image processing, and mainly relates to a wet paper steganography method based on wavelet transform.

背景技术 Background technique

密写是信息隐藏的一个分支，密写算法的工作域一般在空域或频域，空域内的密写方法往往具有很高的隐蔽性，但在鲁棒性方面的性能稍差，在面对主动攻击(如对图像的剪切、压缩等处理)时可能会造成秘密信息的丢失。频域内的密写方法在鲁棒性方面有很好的性能，缺点是对载体的破坏比较大，很多时候必须牺牲密写率以提高隐蔽性。近几年来，小波变换由于非常适宜模拟人眼视觉系统(human visual system，HVS)，越来越多地被科研人员应用到密写领域中。湿纸密写最早在2005年由Jessica Fridrich等提出并发表了相关论文，该作者将载体图像想象成一张部分潮湿的纸，只有干燥的部分可以用来嵌入秘密信息，密写完成后将整张纸烘干再传递给接收者。接收者不需要知道密写前纸张的潮湿区域，只需用一种特定的方法就可提取秘密信息．由于湿纸密写的这种特性，使秘密信息的发送者可以很自由地选择多种规则对载体图像的部分像素进行密写，而且无论对于接收者还是攻击者来说这些规则都是完全封闭的，极大地提高了密写的安全性，具有很高的实用价值。2007年张新鹏等人将湿纸密写用在联合编码中用来提高编码效率。目前湿纸密写的应用还不太成熟。Steganography is a branch of information hiding. The working domain of steganography algorithm is generally in airspace or frequency domain. The steganography method in airspace often has high concealment, but its performance in terms of robustness is slightly poor. Active attacks (such as image cutting, compression, etc.) may cause loss of secret information. The steganography method in the frequency domain has good performance in terms of robustness, but the disadvantage is that the damage to the carrier is relatively large, and the steganographic rate must be sacrificed in many cases to improve the concealment. In recent years, because wavelet transform is very suitable for simulating the human visual system (HVS), more and more researchers have been applied to the field of steganography. Wet paper steganography was first proposed and published by Jessica Fridrich et al. in 2005. The author imagined the carrier image as a partially wet paper, and only the dry part can be used to embed secret information. The paper is dried and passed to the recipient. The recipient does not need to know the wet area of the paper before steganography, but only needs to use a specific method to extract the secret information. Due to the characteristics of wet paper steganography, the sender of secret information can freely choose a variety of rules to steganographically write some pixels of the carrier image, and these rules are completely closed to both the receiver and the attacker. , which greatly improves the security of steganography and has high practical value. In 2007, Zhang Xinpeng and others used wet paper steganography in joint coding to improve coding efficiency. At present, the application of wet paper steganography is not yet mature.

发明内容 Contents of the invention

本发明的目的是解决密写鲁棒性差，安全性低的问题，提供一种基于小波变换的湿纸密写方法。The purpose of the present invention is to solve the problems of poor robustness and low security of steganography, and provide a wet paper steganography method based on wavelet transform.

本发明提供的基于小波变换的湿纸密写方法，包括以下步骤：The wet paper steganography method based on wavelet transform provided by the invention comprises the following steps:

步骤1、对原图像做小波变换；Step 1, do wavelet transform to original image;

步骤2、在小波密写的基础上设计适合人眼视觉系统的选择频道；Step 2, designing a selection channel suitable for the human visual system on the basis of wavelet cryptography;

步骤3、确定随机传输矩阵D，湿纸密写中的矩阵D由发送方和接收方共享的随机数字发生器种子生成；Step 3. Determine the random transmission matrix D, the matrix D in the wet paper steganography is generated by the random number generator seed shared by the sender and the receiver;

步骤4、参考人眼视觉特性确定阈值来保证所有的秘密信息位都通过取代载体图像的小波系数的LSB嵌人到有更大视觉冗余的图像纹理区域；Step 4, determine the threshold with reference to the visual characteristics of the human eye to ensure that all secret information bits are embedded in the image texture area with greater visual redundancy by replacing the LSB of the wavelet coefficient of the carrier image;

步骤5、在小波系数中嵌入秘密信息；Step 5, embedding secret information in wavelet coefficients;

步骤6、提取秘密图像时，只需对含密图像小波系数进行简单的乘法即可。Step 6. When extracting the secret image, it is only necessary to perform simple multiplication on the wavelet coefficients of the secret image.

其中，步骤1所述的小波变换的方法如下：Wherein, the method of the wavelet transform described in step 1 is as follows:

设一维信号{x1，x2}，平均值a=(x1+x2)/2,差值d=(x1-x2)/2;a看成信号的整体信息,d看成原信号用a表示时丢失的细节信息，对多元素信号{x₁，x₂，x₃，x₄},a_1，0=(x₁+x₂)/2,d_1，0=(x₁-x₂)/2,a_1，1=(x₃+x₄)/2,d_1，1=(x₃-x₄)/2,信号{x₁，x₂，x₃，x₄}可以表示为：{a_1，0,a_1，1,d_1，0,d_1，1}，其中a和d分别表示平均值和差值，其脚标逗号前的1表示信号维数，脚标逗号后0表示对{x1，x2}、1表示对{x3，x4}处理。Suppose a one-dimensional signal {x1, x2}, the average value a=(x1+x2)/2, the difference d=(x1-x2)/2; a is regarded as the overall information of the signal, and d is regarded as the original signal and represented by a The detail information lost when the multi-element signal {x ₁ ，x ₂ ，x ₃ ，x ₄ },a _1,0 =(x ₁ +x ₂ )/2,d _1,0 =(x ₁ -x ₂ )/2, a 1, ₁ =(x ₃ +x ₄ )/2, d _{1, 1} =(x ₃ -x ₄ )/2, the signal {x ₁ , x ₂ , x ₃ , x ₄ } can represent It is: {a _{1, 0} , a 1, ₁ , d _{1, 0} , d 1, ₁ }, where a and d represent the average value and difference respectively, and the 1 before the subscript comma represents the signal dimension, and the subscript After the comma, 0 means to process {x1, x2}, and 1 means to process {x3, x4}.

对于二维图像信号I(x,y)，首先对原图像信号I(x,y)沿行方向即水平方向进行滤波和2->1下采样，得到系数矩阵I_L(x,y)和I_H(x,y)，然后再对I_L(x,y)和I_H(x,y)分别沿列方向即垂直方向滤波和2->1下采样，最后得到一层小波分解的4个子图：For the two-dimensional image signal I(x,y), first filter the original image signal I(x,y) along the row direction, that is, the horizontal direction, and 2->1 down-sampling to obtain the coefficient matrix I _L (x,y) and I _H (x, y), and then filter I _L (x, y) and I _H (x, y) along the column direction (vertical direction) and 2->1 down-sampling, and finally get a layer of wavelet decomposition of 4 subgraph:

I_LL(x,y)—为I(x,y)的粗逼近子图I _LL (x,y)—is a coarse approximation subgraph of I(x,y)

I_HL(x,y)—为I(x,y)的水平方向细节子图I _HL (x,y)—is the horizontal detail subgraph of I(x,y)

I_LH(x,y)—为I(x,y)的垂直方向细节子图I _LH (x,y)—is the vertical detail subgraph of I(x,y)

I_HH(x,y)—为I(x,y)的对角线方向细节子图。I _HH (x, y)—is the diagonal direction detail subgraph of I(x, y).

所述步骤2选择频道由下式确定The channel selected in step 2 is determined by the following formula

上式反映了图像在2×2邻域内的纹理复杂程度，用K(l，i，j)表示，将其作为本发明的选择频道，l表示小波变换的层数，i和j分别表示第i行和第j列的位置，上式乘号前边的因子计算了载体图像小波域的所有细节子带的局部平均方值，而

是对应低频子带的平均方差；表示位置（i,j）处的各个子带和方向的像素值，其中k+l={0，1，2，3}表示各层子带，θ∈{0，1，2，3},分别表示各个方向的子带，分别为水平子带、对角子带、垂直子带和低频子带;由于人眼对纹理区域的边缘处有很高的敏感度，因此，将2个因子相乘作为小波域内湿纸密写的选择频道。The above formula reflects the texture complexity of the image in the 2 × 2 neighborhood, expressed by K (l, i, j), which is used as the selected channel of the present invention, l represents the number of layers of wavelet transform, and i and j represent the first The position of row i and column j, the factor in front of the multiplication sign in the above formula calculates the local mean square value of all detail subbands in the wavelet domain of the carrier image, and

is the average variance corresponding to the low frequency subband; Represents the pixel value of each sub-band and direction at position (i, j), where k+l={0, 1, 2, 3} represents each layer of sub-bands, θ∈{0, 1, 2, 3}, Indicate the subbands in each direction, respectively, the horizontal subband, the diagonal subband, the vertical subband and the low frequency subband; since the human eye has a high sensitivity to the edge of the texture area, the two factors are multiplied As a channel of choice for wet-paper steganography in the wavelet domain.

所述步骤3确定随机传输矩阵D的方法是，假设载体图像长度为a×b，秘密信息长度为m，要将秘密信息嵌入到3个最大的高频子带中，最多可以嵌入3ab／4长度的秘密信息，需要大小为m×(3ij／4)的矩阵D。The method for determining the random transmission matrix D in the step 3 is assuming that the length of the carrier image is a×b, and the length of the secret information is m. To embed the secret information into the three largest high-frequency subbands, at most 3ab/4 The length of the secret information requires a matrix D of size m×(3ij/4).

所述步骤4参考人眼视觉特性确定阈值，如下式The step 4 determines the threshold with reference to the visual characteristics of the human eye, as follows

其中in

$Ξ ξ ((11,, i i,, j j)) = = \frac{{[[{I I}_{11}^{00} ((i i,, j j))]]}^{22} + + {[[{I I}_{11}^{11} ((i i,, j j))]]}^{22} + + {[[{I I}_{11}^{22} ((i i,, j j))]]}^{22}}{33} \cdot &Center Dot; Var Var {{{I I}_{11} ((i i,, j j))}}$

l和θ分别是小波变换频率分解的子带和方向，i和j分别为图像像素所在位置的行数和列数，Θ(l,θ)表示噪声掩盖因子，∧(l,i,j)表示亮度敏感因子，Ξ(l,i,j)为纹理掩盖因子，

的3个因子分别反映了各个子带的小波系数对噪声的敏感度、局部明亮度和局部纹理的复杂程度，相乘后得到最终密写时需要的

l and θ are the sub-bands and directions of wavelet transform frequency decomposition, i and j are the number of rows and columns of image pixels respectively, Θ(l, θ) represents the noise masking factor, ∧(l, i, j) Indicates the brightness sensitivity factor, Ξ(l,i,j) is the texture masking factor,

The three factors of reflect the sensitivity of the wavelet coefficients of each sub-band to noise, the local brightness and the complexity of the local texture, and after multiplication, the final steganography needs

所述步骤5在小波系数中嵌入秘密信息的方法是The method for embedding secret information in the wavelet coefficients in the step 5 is

设S为编码后得到的秘密信息，

为原始小波系数，则根据如下规则嵌入秘密信息：Let S be the secret information obtained after encoding,

is the original wavelet coefficient, the secret information is embedded according to the following rules:

$\overset{^^}{{I I}_{11}^{θ θ}} ((i i,, j j)) = = {I I}_{11}^{θ θ} ((i i,, j j)) + + {αω αω}_{11}^{θ θ} ((i i,, j j)) K K ((l l,, i i,, j j)) {S S}_{11}^{θ θ} ((i i,, j j))$

式中：α为强度系数，用以调整秘密信息的强度；在位置(i,j)处，为权重系数，其中l和θ分别表示小波变换的层数和方向，K(l，i，j)为l层的选择频道，

为待嵌入的秘密信息，在小波系数

中非选择频道的位置替换为原始小波系数随后用含密的小波系数

替换其他元素，最终替换原始小波系数x₀得到新的小波系数x₀，进行小波反变换后得到含密图像。In the formula: α is the strength coefficient, which is used to adjust the strength of secret information; at position (i, j), is the weight coefficient, where l and θ represent the layer number and direction of wavelet transform respectively, K(l, i, j) is the selection channel of layer l,

For the secret information to be embedded, the wavelet coefficient

The position of the selected channel in the middle is replaced by the original wavelet coefficients Then with dense wavelet coefficients

Replace other elements, and finally replace the original wavelet coefficient x ₀ to obtain a new wavelet coefficient x ₀ , and obtain a dense image after inverse wavelet transformation.

所述步骤6提取秘密信息，如下式The step 6 extracts the secret information, as follows

D₀x₀’=sD ₀ x ₀ '=s

D₀是步骤2所述的大小为m×(3ab／4)的随机传输矩阵，x₀’是小波系数，s是长度为m的秘密信息此处矩阵D₀同步骤4的矩阵D。D ₀ is the random transmission matrix whose size is m×(3ab/4) mentioned in step 2, x ₀ ′ is the wavelet coefficient, s is the secret information with length m, here the matrix D ₀ is the same as the matrix D in step 4.

本发明的优点和有益效果：Advantages and beneficial effects of the present invention:

本发明的优点在于湿纸密写区别于其他密写方法的一个重要特点就是接收者不需要知道发送者所用的密写算法，而只对载体图像进行固定处理就可提取秘密信息，保证了发送者密写的灵活性，从而提高密写的隐蔽性。小波变换具有可以将信号的空间频率局部化的特性，非常适合密写。通常，结合人眼视觉系统的特性，在小波域内将秘密信息隐藏在小波变换系数中，在原图像中仅是与被改变的小波系数频率相应的区域发生变化。该方法既保持了小波域内密写方法鲁棒性好的特点，又通过湿纸密写的思想使密写的安全性有了很大提高。The advantage of the present invention is that wet paper steganography differs from other steganography methods in that an important feature is that the receiver does not need to know the steganography algorithm used by the sender, but can extract the secret information only by fixing the carrier image, ensuring the transmission The flexibility of steganographic writing, thereby improving the concealment of steganographic writing. Wavelet transform has the property of localizing the spatial frequency of the signal, which is very suitable for steganography. Usually, combined with the characteristics of the human visual system, the secret information is hidden in the wavelet transform coefficients in the wavelet domain, and only the area corresponding to the frequency of the changed wavelet coefficients changes in the original image. This method not only maintains the robustness of the steganography method in the wavelet domain, but also greatly improves the security of the steganography through the idea of wet paper steganography.

附图说明 Description of drawings

图1给出了4层小波分解示意图。Figure 1 shows a schematic diagram of four-layer wavelet decomposition.

图2给出了用作小波分解的例图girl。Figure 2 shows an example graph girl used for wavelet decomposition.

具体实施方式 Detailed ways

一种基于小波变换的湿纸密写方法，包括以下步骤：A method for wet paper steganography based on wavelet transform, comprising the following steps:

1由于例图所涉及的像素值庞大，从图2例图girl中的提取部分像素说明如下1 Due to the large number of pixel values involved in the example image, some pixels extracted from the example image girl in Figure 2 are explained as follows

$I I = = [\begin{matrix} 164164 & 117117 & 124124 & 117117 & 131131 & 117117 \\ 131131 & 117117 & 117117 & 117117 & 164164 & 117117 \\ 164164 & 117117 & 66 & 117117 & 164164 & 117117 \\ 66 & 117117 & 117117 & 66 & 117117 & 117117 \\ 4343 & 164164 & 66 & 4343 & 66 & 66 \\ 66 & 66 & 4343 & 66 & 4343 & 219219 \end{matrix}]$

对其做一层harr小波变换Do a layer of harr wavelet transform on it

$[\begin{matrix} \frac{[[I I ((1,1 1,1)) + + I I ((1,2 1,2))]]}{22} & \frac{[[I I ((1,3 1,3)) + + I I ((1,4 1,4))]]}{22} & \frac{[[I I 11 ((1,5 1,5)) + + I I ((1,6 1,6))]]}{22} & \frac{[[I I ((1,1 1,1)) - - I I ((1,2 1,2))]]}{22} & \frac{[[I I ((1,3 1,3)) - - I I ((1,4 1,4))]]}{22} & \frac{[[I I 11 ((1,5 1,5)) - - I I ((1,6 1,6))]]}{22} \\ \frac{[[I I ((2,1 2,1)) + + I I ((22,, 22))]]}{22} & \frac{[[I I ((2,3 2,3)) + + I I ((2,4 2,4))]]}{22} & \frac{[[I I 11 ((2,5 2,5)) + + I I ((2,6 2,6))]]}{22} & \frac{[[I I ((2,1 2,1)) - - I I ((22,, 22))]]}{22} & \frac{[[I I ((2,3 2,3)) - - I I ((2,4 2,4))]]}{22} & \frac{[[I I 11 ((2,5 2,5)) - - I I ((2,6 2,6))]]}{22} \\ \frac{[[I I ((3,1 3,1)) + + I I ((33,, 22))]]}{22} & \frac{[[I I ((3,3 3,3)) + + I I ((3,4 3,4))]]}{22} & \frac{[[I I 11 ((3,5 3,5)) + + I I ((3,6 3,6))]]}{22} & \frac{[[I I ((3,1 3,1)) - - I I ((33,, 22))]]}{22} & \frac{[[I I ((3,3 3,3)) - - I I ((3,4 3,4))]]}{22} & \frac{[[I I 11 ((3,5 3,5)) - - I I ((3,6 3,6))]]}{22} \\ \frac{[[I I ((44,, 11)) + + I I ((44,, 22))]]}{22} & \frac{[[I I ((4,3 4,3)) + + I I ((4,4 4,4))]]}{22} & \frac{[[I I 11 ((4,5 4,5)) + + I I ((4,6 4,6))]]}{22} & \frac{[[I I ((4,1 4,1)) - - I I ((44,, 22))]]}{22} & \frac{[[I I ((4,3 4,3)) - - I I ((4,4 4,4))]]}{22} & \frac{[[I I 11 ((4,5 4,5)) - - I I ((4,6 4,6))]]}{22} \\ \frac{[[I I ((5,1 5,1)) + + I I ((55,, 22))]]}{22} & \frac{[[I I ((5,3 5,3)) + + I I ((5,4 5,4))]]}{22} & \frac{[[I I 11 ((5,5 5,5)) + + I I ((5,6 5,6))]]}{22} & \frac{[[I I ((5,1 5,1)) - - I I ((55,, 22))]]}{22} & \frac{[[I I ((5,3 5,3)) - - I I ((5,4 5,4))]]}{22} & \frac{[[I I 11 ((5,5 5,5)) - - I I ((5,6 5,6))]]}{22} \\ \frac{[[I I ((6,1 6,1)) + + I I ((66,, 22))]]}{22} & \frac{[[I I ((6,3 6,3)) + + I I ((6,4 6,4))]]}{22} & \frac{[[I I 11 ((6,5 6,5)) + + I I ((6,6 6,6))]]}{22} & \frac{[[I I ((6,1 6,1)) - - I I ((66,, 22))]]}{22} & \frac{[[I I ((6,3 6,3)) - - I I ((6,4 6,4))]]}{22} & \frac{[[I I 11 ((6,5 6,5)) - - I I ((6,6 6,6))]]}{22} \end{matrix}]$

$[\begin{matrix} \frac{[[I I 11 ((1,1 1,1)) + + I I 11 ((2,1 2,1))]]}{22} & \frac{[[I I 11 ((3,1 3,1)) + + I I 11 ((4,1 4,1))]]}{22} & \frac{[[I I 11 ((5,1 5,1)) + + I I 11 ((6,1 6,1))]]}{22} & \frac{[[I I 11 ((1,1 1,1)) - - I I ((2,1 2,1))]]}{22} & \frac{[[I I 11 ((3,1 3,1)) - - I I ((4,1 4,1))]]}{22} & \frac{[[I I 11 ((5,1 5,1)) - - I I 11 ((6,1 6,1))]]}{22} \\ \frac{[[I I 11 ((1,2 1,2)) + + I I 11 ((2,2 2,2))]]}{22} & \frac{[[I I 11 ((3,2 3,2)) + + I I 11 ((4,2 4,2))]]}{22} & \frac{[[I I 11 ((55,, 22)) + + I I 11 ((6,2 6,2))]]}{22} & \frac{[[I I 11 ((1,2 1,2)) - - I I ((2,2 2,2))]]}{22} & \frac{[[I I 11 ((3,2 3,2)) - - I I ((4,2 4,2))]]}{22} & \frac{[[I I 11 ((5,2 5,2)) - - I I 11 ((6,2 6,2))]]}{22} \\ \frac{[[I I 11 ((1,3 1,3)) + + I I 11 ((2,3 2,3))]]}{22} & \frac{[[I I 11 ((3,3 3,3)) + + I I 11 ((4,3 4,3))]]}{22} & \frac{[[I I 11 ((5,3 5,3)) + + I I 11 ((6,3 6,3))]]}{22} & \frac{[[I I 11 ((11,, 33)) - - I I ((2,3 2,3))]]}{22} & \frac{[[I I 11 ((3,3 3,3)) - - I I ((4,3 4,3))]]}{22} & \frac{[[I I 11 ((5,3 5,3)) - - I I 11 ((6,3 6,3))]]}{22} \\ \frac{[[I I 11 ((1,4 1,4)) + + I I 11 ((2,4 2,4))]]}{22} & \frac{[[I I 11 ((3,4 3,4)) + + I I 11 ((4,4 4,4))]]}{22} & \frac{[[I I 11 ((5,4 5,4)) + + I I 11 ((6,4 6,4))]]}{22} & \frac{[[I I 11 ((1,4 1,4)) - - I I ((2,4 2,4))]]}{22} & \frac{[[I I 11 ((3,4 3,4)) - - I I ((4,4 4,4))]]}{22} & \frac{[[I I 11 ((5,4 5,4)) - - I I 11 ((6,4 6,4))]]}{22} \\ \frac{[[I I 11 ((1,5 1,5)) + + I I 11 ((2,5 2,5))]]}{22} & \frac{[[I I 11 ((33,, 55)) + + I I 11 ((4,5 4,5))]]}{22} & \frac{[[I I 11 ((5,5 5,5)) + + I I 11 ((6,5 6,5))]]}{22} & \frac{[[I I 11 ((1,5 1,5)) - - I I 11 ((2,5 2,5))]]}{22} & \frac{[[I I 11 ((3,5 3,5)) - - I I 11 ((4,5 4,5))]]}{22} & \frac{[[I I 11 ((5,5 5,5)) - - I I 11 ((6,5 6,5))]]}{22} \\ \frac{[[I I 11 ((1,6 1,6)) + + I I 11 ((2,6 2,6))]]}{22} & \frac{[[I I 11 ((33,, 66)) + + I I 11 ((4,6 4,6))]]}{22} & \frac{[[I I 11 ((5,6 5,6)) + + I I 11 ((6,6 6,6))]]}{22} & \frac{[[I I 11 ((1,6 1,6)) - - I I 11 ((2,6 2,6))]]}{22} & \frac{[[I I 11 ((3,6 3,6)) - - I I 11 ((4,6 4,6))]]}{22} & \frac{[[I I 11 ((5,6 5,6)) - - I I 11 ((6,6 6,6))]]}{22} \end{matrix}]$

$= = I I 11 = = [\begin{matrix} 132.25 132.25 & 101101 & 54.75 54.75 & 8.25 8.25 & 39.5 39.5 & 48.75 48.75 \\ 118.75 118.75 & 61.5 61.5 & 24.5 24.5 & 1.75 1.75 & 00 & 00 \\ 132.25 132.25 & 128.75 128.75 & 68.5 68.5 & - - 8.25 8.25 & 11.75 11.75 & - - 62.5 62.5 \\ 15.25 15.25 & - - 1616 & - - 30.25 30.25 & 8.25 8.25 & 39.5 39.5 & - - 30.25 30.25 \\ 1.75 1.75 & 00 & 00 & 1.75 1.75 & - - 55.5 55.5 & - - 18.5 18.5 \\ 15.25 15.25 & 11.75 11.75 & - - 4444 & - - 8.25 8.25 & 11.75 11.75 & 4444 \end{matrix}] = = [\begin{matrix} {I I}_{LL LL} & {I I}_{HL HL} \\ {I I}_{LH LH} & {I I}_{HH HH} \end{matrix}] = = [\begin{matrix} {I I}_{00}^{33} & {I I}_{00}^{00} \\ {I I}_{00}^{22} & {I I}_{00}^{11} \end{matrix}]$

得到四个3×3矩阵，I_HL(x,y)、I_HL(x,y)、I_LH(x,y)和I_HH(x,y)Get four 3×3 matrices, I _HL (x,y), I _HL (x,y), I _LH (x,y) and I _HH (x,y)

I_LL(x,y)—I(x,y)的（粗）逼近子图I _LL (x,y) — (coarse) approximation subgraph of I(x,y)

I_HL(x,y)—I(x,y)的水平方向细节子图I _HL (x,y)—Horizontal detail subgraph of I(x,y)

I_LH(x,y)—I(x,y)的垂直方向细节子图I _LH (x,y)—the vertical detail subgraph of I(x,y)

I_HH(x,y)—I(x,y)的对角线方向细节子图。I _HH (x,y)—diagonal direction detail subgraph of I(x,y).

2确定选择频道2 Confirm to select the channel

根据人眼视觉系统的特性可知，纹理复杂、细节较多的区域比纹理简单、细节较少的区域有更大的视觉冗余，因此为改善小波密写隐蔽性差的缺陷，对载体图像做小波变换后，在3个高频子带内选择部分小波系数嵌入秘密信息。在小波域中，判断图像纹理复杂与否需计算图像的局部方差，这样可以更准确地计算图像的纹理复杂程度，从而确定选择频道。计算图像的局部方差如下式According to the characteristics of the human visual system, the area with complex texture and more details has greater visual redundancy than the area with simple texture and less detail. Therefore, in order to improve the defect of poor concealment of wavelet steganography, wavelet After transformation, some wavelet coefficients are selected in the three high-frequency subbands to embed secret information. In the wavelet domain, it is necessary to calculate the local variance of the image to judge whether the texture of the image is complex, so that the complexity of the texture of the image can be calculated more accurately, so as to determine the channel to be selected. Calculate the local variance of the image as follows

对矩阵做一层小波变换，l＝0,Do a layer of wavelet transform on the matrix, l=0,

$K K ((0,1,1 0,1,1)) = = {Σ Σ}_{θ θ = = 00}^{22} {Σ Σ}_{x x = = 00}^{11} {Σ Σ}_{y the y = = 00}^{11} {[[{I I}_{00}^{θ θ} ((y the y + + 11,, x x + + 11))]]}^{22} \times \times = = {(({I I}_{00}^{00} {((1,1 1,1))}^{22} + + {I I}_{00}^{00} {((1,2 1,2))}^{22} + + {I I}_{00}^{00} {((2,1 2,1))}^{22} + + {I I}_{00}^{00} {((2,2 2,2))}^{22} + + {I I}_{00}^{11} {((1,1 1,1))}^{22} + + {I I}_{00}^{11} ((1,2 1,2))}^{22}$

$+ + 11_{00}^{11} {((2,1 2,1))}^{22} + + {I I}_{00}^{11} {((2,2 2,2))}^{22} + + {I I}_{00}^{22} {((1,1 1,1))}^{22} + + {I I}_{00}^{22} {((1,2 1,2))}^{22} + + {I I}_{00}^{22} {((2,1 2,1))}^{22} + + {I I}_{00}^{22} {((22,, 22))}^{22})) Var Var {{{I I}_{00}^{33} ((2,2 2,2)),, {I I}_{00}^{33} ((2,3 2,3)),, {I I}_{00}^{33} ((3,2 3,2)),, {I I}_{00}^{33} ((3,3 3,3))}}$

$= = (({8.25 8.25}^{22} + + {39.5 39.5}^{22} + + {1.75 1.75}^{22} + + 00 + + {8.25 8.25}^{22} + + {39.5 39.5}^{22} + + {1.75 1.75}^{22} + + {((- - 55.5 55.5))}^{22} + + {15.25 15.25}^{22} + + {((- - 1616))}^{22} + + {1.75 1.75}^{22} + + 00))$

$\times \times Var Var {{{I I}_{00}^{33} ((2,2 2,2)),, {I I}_{00}^{33} ((2,3 2,3)),, {I I}_{00}^{33} ((3,2 3,2)),, {I I}_{00}^{33} ((3,3 3,3))}}$

$= = 6834.6 6834.6 \times \times Var Var {{{I I}_{00}^{33} ((2,2 2,2)),, {I I}_{00}^{33} ((2,3 2,3)),, {I I}_{00}^{33} ((3,2 3,2)),, {I I}_{00}^{33} ((3,3 3,3))}}$

$ave ave = = \frac{{I I}_{00}^{33} ((2,2 2,2)) + + {I I}_{00}^{33} ((2,3 2,3)) + + {I I}_{00}^{33} ((3,2 3,2)) + + {I I}_{00}^{33} ((3,3 3,3))}{44} = = \frac{61.5 61.5 + + 24.5 24.5 + + 128.75 128.75 + + 68.5 68.5}{44} = = 70.8125 70.8125$

$Var Var {{{I I}_{00}^{33} ((2,2 2,2)),, {I I}_{00}^{33} ((2,3 2,3)),, {I I}_{00}^{33} ((3,2 3,2)),, {I I}_{00}^{33} ((3,3 3,3))}}$

$= = \sqrt{(({(({I I}_{00}^{33} ((2,2 2,2)) - - ave ave))}^{22} + + {(({I I}_{00}^{33} ((2,3 2,3)) - - ave ave))}^{22} + + {(({I I}_{00}^{33} ((3,2 3,2)) - - ave ave))}^{22} + + {(({I I}_{00}^{33} ((3,3 3,3)) - - ave ave))}^{22}))}$

$= = \sqrt{{((61.5 61.5 - - 70.8125 70.8125))}^{22} + + {((24.5 24.5 - - 70.8125 70.8125))}^{22} + + {((128.75 128.75 - - 70.8125 70.8125))}^{22} + + {((68.5 68.5 - - 70.8125 70.8125))}^{22}} = = 74.1909 74.1909$

$K K ((00_{: :} 11_{: :} 11)) = = 6834.6 6834.6 \times \times Var Var {{{I I}_{00}^{33} ((2,2 2,2)),, {I I}_{00}^{33} ((2,3 2,3)),, {I I}_{00}^{33} ((33,, 22)),, {I I}_{00}^{33} ((3,3 3,3))}} = = 507070507070$

3确定人眼可接受的阈值，如下式3 Determine the threshold acceptable to the human eye, as follows

其中in

的3个因子分别反映了各个子带的小波系数对噪声的敏感度、局部明亮度和局部纹理的复杂程度，相乘后得到最终密写时需要的权重系数

本发明做了一层小波变换，

其他Θ(0,0)=Θ(0,2)=Θ(0,3)=1；对于I_HL,∧(0,1,1)=8.25，对于I_HH,∧(0,1,1)=132.25，对于I_LH，∧(0,1,1)=15.25，对于I_HH,∧(0,1,1)=8.25；

The three factors of reflect the sensitivity of the wavelet coefficients of each sub-band to noise, the local brightness and the complexity of the local texture, and after multiplication, the weight coefficient required for the final steganography is obtained

The present invention has done a layer of wavelet transform,

Otherwise Θ(0,0)=Θ(0,2)=Θ(0,3)=1; for I _HL , ∧(0,1,1)=8.25, for I _HH , ∧(0,1,1 )=132.25, for I _LH , ∧(0,1,1)=15.25, for I _HH , ∧(0,1,1)=8.25;

$Ξ ξ ((00,, 11,, 11)) = = \frac{{[[{I I}_{00}^{00} ((11,, 11))]]}^{22} + + {[[{I I}_{00}^{11} ((11,, 11))]]}^{22} + + {[[{I I}_{00}^{22} ((11,, 11))]]}^{22}}{33} \cdot \cdot Var Var {{{I I}_{00} ((11,, 11))}}$

$= = \frac{{8.25 8.25}^{22} + + {8.25 8.25}^{22} + + {132.25 132.25}^{22}}{33} \cdot &Center Dot; Var Var {{{I I}_{00}^{00} ((1,1 1,1)),, {I I}_{00}^{11} ((1,1 1,1)),, {I I}_{00}^{22} ((1,1 1,1)),, {I I}_{00}^{33} ((1,1 1,1))}}$

$= = 5873.3 5873.3 \cdot \cdot Var Var {{{I I}_{00}^{00} ((1,1 1,1)),, {I I}_{00}^{11} ((1,1 1,1)),, {I I}_{00}^{22} ((1,1 1,1)),, {I I}_{00}^{33} ((1,1 1,1))}}$

$ave ave = = \frac{{I I}_{00}^{00} ((1,1 1,1)) + + {I I}_{00}^{11} ((1,1 1,1)) + + {I I}_{00}^{22} ((1,1 1,1)) + + {I I}_{00}^{33} ((1,1 1,1))}{44} = = \frac{8.25 8.25 + + 8.25 8.25 + + 132.25 132.25 + + 15.25 15.25}{44} = = 4141$

$Var Var {{{I I}_{00}^{00} ((1,1 1,1)),, {I I}_{00}^{11} ((1,1 1,1)),, {I I}_{00}^{22} ((1,1 1,1)),, {I I}_{00}^{33} ((1,1 1,1))}} = =$

$\sqrt{(({(({I I}_{00}^{00} ((1,0 1,0)) - - ave ave))}^{22} + + {(({I I}_{00}^{11} ((1,1 1,1)) - - ave ave))}^{22} + + {(({I I}_{00}^{22} ((1,1 1,1)) - - ave ave))}^{22} + + {(({I I}_{00}^{33} ((1,1 1,1)) - - ave ave))}^{22}))} = = 105.5225 105.5225 . .$

$Ξ ξ ((0,1,1 0,1,1)) = = 5875.3 5875.3 \cdot \cdot Var Var {{{I I}_{00}^{00} ((1,1 1,1)),, {I I}_{00}^{11} ((1,1 1,1)),, {I I}_{00}^{22} ((1,1 1,1)),, {I I}_{00}^{33} ((1,1 1,1))}} = = 5875.3 5875.3 \times \times 105.5225 105.5225 = = 619976.34425 619976.34425$

4嵌入秘密信息，对载体图像做小波变换，进行1层harr小波分解，在高频小波系数x₀中非选择频道的位置替换为原始小波系数

随后用含密的小波系数

替换其他元素，得到x₀，进行小波反变换后可以得到含密图像。S为编码后得到的秘密信息，为图像密写前的子带，则可根据如下规则嵌入秘密信息：4 Embed secret information, do wavelet transform on the carrier image, perform 1-layer harr wavelet decomposition, and replace the position of the non-selected channel in the high-frequency wavelet coefficient x ₀ with the original wavelet coefficient

Then with dense wavelet coefficients

Replace other elements to get x ₀ , and then get a dense image after inverse wavelet transform. S is the secret information obtained after encoding, is the subband before image steganography, then the secret information can be embedded according to the following rules:

${\overset{^^}{I I}}_{11}^{θ θ} ((i i,, j j)) = = {I I}_{11}^{θ θ} ((i i,, j j)) + + {αω αω}_{11}^{θ θ} ((i i,, j j)) {Z Z}_{11}^{θ θ} {S S}_{11}^{θ θ} ((i i,, j j))$

若选择大于0小于507071为选择频道，图像局部方差为K（0,1,1）=507070在选择频道内，此高频系数可以适合嵌入若选择大于507070为选择频道，则说明局部方差K（0,1,1）=507070不在选择频道内，不进行嵌入，

此处选择大于0小于507071为选择频道进行秘密信息的嵌入，

若秘密信息为二进制流010，则在高频小波系数

嵌入如下，其他系数不进行嵌入If the selected channel is greater than 0 and less than 507071, the local variance of the image is K(0,1,1)=507070. In the selected channel, this high-frequency coefficient can be suitable for embedding If the selected channel is greater than 507070, it means that the local variance K(0,1,1)=507070 is not in the selected channel, and no embedding is performed.

Here select a channel greater than 0 and less than 507071 to embed secret information,

If the secret information is a binary stream 010, the high-frequency wavelet coefficient

The embedding is as follows, other coefficients are not embedded

${\overset{^^}{I I}}_{00}^{00} ((1,1 1,1)) = = {I I}_{00}^{00} ((1,1 1,1)) + + {αω αω}_{00}^{00} ((1,1 1,1)) {Z Z}_{11}^{θ θ} {S S}_{00}^{00} ((1,1 1,1)) = = 8.25 8.25 + + 0.001 0.001 \times \times 118.8305 118.8305 \times \times 11 \times \times 00 = = 8.25 8.25$

${\overset{^^}{I I}}_{00}^{11} ((1,1 1,1)) = = {I I}_{00}^{11} ((1,1 1,1)) + + {αω αω}_{00}^{00} ((1,1 1,1)) {Z Z}_{11}^{θ θ} {S S}_{00}^{00} ((1,1 1,1)) = = 8.25 8.25 + + 0.001 0.001 \times \times 168.0517 168.0517 \times \times 11 \times \times 11 = = 8.4181 8.4181$

${\overset{^^}{I I}}_{00}^{22} ((1,1 1,1)) = = {I I}_{00}^{33} ((1,1 1,1)) + + {αω αω}_{00}^{00} ((1,1 1,1)) {Z Z}_{11}^{θ θ} {S S}_{00}^{00} ((1,1 1,1)) = = 15.25 15.25 + + 0.001 0.001 \times \times 219.6564 219.6564 \times \times 11 \times \times 00 = = 1515 . . 2525$

4、确定大小为3×27的矩阵D0，提取秘密信息，对于矩6×6维阵I,此处x0=[8.2539.5 48.75 1.75 00-8.75 11.75-6.258.25 39.5-30.25 1.75-55.5 -18.5 -8.25 11.75 44 15.25-16-30.25 1.75 0 0 15.25 11.75 -44]’为27×1维矩阵，矩阵4. Determine the matrix D0 with a size of 3×27 and extract the secret information. For the moment 6×6 dimensional matrix I, here x0=[8.2539.5 48.75 1.75 00-8.75 11.75-6.258.25 39.5-30.25 1.75-55.5 - 18.5 -8.25 11.75 44 15.25-16-30.25 1.75 0 0 15.25 11.75 -44]'is a 27×1-dimensional matrix, the matrix

${D D.}_{00} = = [\begin{matrix} 0000000000000000000000000000000000000000000000000000000 \\ - - 100000100000 - - 200200 - - 100000000000000000100000000000000000 \\ 0000000000000000000000000000000000000000000000000000000 \end{matrix}],,$

根据公式D₀x₀=s，经计算s=[0 0 1]’。According to the formula D ₀ x ₀ =s, s=[0 0 1]' is calculated.

Claims

1. l Water Paper steganographic method based on wavelet transformation is characterized in that the method may further comprise the steps:

Step 1, original image is done wavelet transformation;

Step 2, be fit to human visual system's selection channel in the design of the basis of small echo secret writing;

Step 3, definite at random transmission matrix D, the transmission matrix D in the l Water Paper secret writing is generated by the random number generator seed that transmit leg and recipient share;

Step 4, with reference to the human-eye visual characteristic definite threshold guarantee all secret information positions all the LSB embedding people of the wavelet coefficient by the replacement vector image to the image texture zone that larger visual redundancy is arranged;

Step 5, in wavelet coefficient, embed secret information;

When step 6, extraction Secret Image, only need to carry out simple multiplication to the stego-image wavelet coefficient and get final product.

2. method according to claim 1 is characterized in that the method for the described wavelet transformation of step 1 is as follows:

If one-dimensional signal { x1, x2}, mean value a=(x1+x2)/2, difference d=(x1-x2)/2; A regards the Global Information of signal as, and d regards the detailed information of losing when original signal represents with a as, to multielement signal { x ₁, x ₂, x ₃, x ₄, a _1,0=(x ₁+ x ₂)/2, d _1,0=(x ₁-x ₂)/2, a _1,1=(x ₃+ x ₄)/2, d _1,1=(x ₃-x ₄)/2, signal { x ₁, x ₂, x ₃, x ₄Can be expressed as: { a _1,0, a _1,1, d _1,0, d _1,1, wherein a and d represent respectively mean value and difference, 1 expression signal dimension in the footnote before the comma, and 0 expression is to { x1, x2}, 1 represent { x3, x4} processing behind the footnote comma;

For two dimensional image signal I (x, y), at first original image signal I (x, y) being followed direction is that horizontal direction is carried out filtering and 2-〉1 down-sampling, obtain coefficient matrix I _L(x, y) and I _H(x, y), and then to I _L(x, y) and I _H(x, y) is vertical direction filtering and 2-along column direction respectively〉1 down-sampling, obtain at last 4 subgraphs of one deck wavelet decomposition:

I _LL(x, y)-be the thick ll channel of I (x, y)

I _HL(x, y)-be the horizontal direction details subgraph of I (x, y)

I _LH(x, y)-be the vertical direction details subgraph of I (x, y)

I _HH(x, y)-be the diagonal details subgraph of I (x, y).

3. method according to claim 1 is characterized in that the described selection channel of step 2 determined by following formula:

Following formula has reflected the texture complexity of image in 2 * 2 neighborhoods, with K (l, i, j) expression, as selection channel of the present invention, l represents the number of plies of wavelet transformation with it, and i and j represent respectively the position that i is capable and j is listed as, the following formula multiplication sign factor in front has been calculated local average side's value of all detail subbands of carrier image wavelet field, and

It is the average variance of corresponding low frequency sub-band;

Each subband of locating of expression position (i, j) and the pixel value of direction, k+l={0 wherein, 1,2,3} represents each straton band, { 0,1,2,3} represents respectively the subband of all directions to be respectively horizontal subband, diagonal angle subband, vertical subband and low frequency sub-band θ ∈; Because human eye has very high susceptibility to the edge of texture region, therefore, 2 factors is multiplied each other as the selection channel of l Water Paper secret writing in the wavelet field.

4. method according to claim 1, it is characterized in that the described definite at random method of transmission matrix D of step 3 is, suppose that carrier image length is a * b, Secret Message Length is m, secret information to be embedded in the high-frequency sub-band of 3 maximums, can embed at most the secret information of 3ab/4 length, needing size is the matrix D of m * (3ij/4).

5. method according to claim 1, it is characterized in that step 4 is described is undertaken by following formula with reference to the human-eye visual characteristic definite threshold:

Wherein

Ξ (1, i, j) = \frac{{[I_{1}^{0} (i, j)]}^{2} + {[I_{1}^{1} (i, j)]}^{2} + {[I_{1}^{2} (i, j)]}^{2}}{3} \cdot Var {I_{1} (i, j)}

L and θ are respectively subband and the directions of wavelet transformation frequency decomposition, and i and j are respectively line number and the columns of image pixel position, Θ (l) the expression noise takeover factor, ∧ (l, i, j) expression brightness sensitive factor, Ξ (l, i, j) cover the factor for texture

3 factors reflected respectively the wavelet coefficient of each subband to the complexity of the susceptibility of noise, local lightness and local grain, need when obtaining final secret writing after multiplying each other

6. method according to claim 5 is characterized in that the described method that embeds secret information in wavelet coefficient of step 5 is

If the secret information of S for obtaining after encoding,

Be original wavelet coefficients, then embed secret information according to following rule:

\hat{I_{1}^{θ}} (i, j) = I_{1}^{θ} (i, j) + {αω}_{1}^{θ} (i, j) K (l, i, j) S_{1}^{θ} (i, j)

In the formula: a is strength factor, in order to adjust the intensity of secret information; (i, j) locates in the position,

Be weight coefficient, wherein l and θ represent respectively the number of plies and the direction of wavelet transformation, and K (l, i, i) is the selection channel of l layer, For secret information to be embedded, at wavelet coefficient

In the position of non-selection channel replace with original wavelet coefficients

Subsequently with containing close wavelet coefficient

Replace other elements, finally replace original wavelet coefficients x ₀Obtain new wavelet coefficient x ₀, carry out obtaining stego-image behind the inverse wavelet transform.

7. method according to claim 4 is characterized in that the described extraction secret information of step 6, as shown in the formula

D ₀x ₀’=s

D ₀That the described size of step 2 is the at random transmission matrix of m * (3ab/4), x ₀' be wavelet coefficient, s is that length is the secret information of m, herein matrix D ₀Matrix D with right 4.