CN103700061B - A kind of digital figure watermark based on compressed sensing embeds and extracting method - Google Patents

Abstract

Translated fromChinese

一种基于压缩感知的数字图像水印嵌入和提取方法，属于信息隐藏和图像处理技术领域。对二值数字图像水印信息进行稀疏化处理，得到稀疏化的一维水印信息，构造测量矩阵，将测量矩阵作为密钥；用密钥稀疏化的一维水印信息进行测量，实现维水印信息的压缩和加密；对原始载体图像信息进行离散余弦变换并对变换后得到的离散余弦变换域信息进行分块，将处理后的水印信息嵌入到载体图像中得到含水印图像。本发明采用压缩感知方法对水印进行处理，实现水印压缩和加密的双重作用，嵌入量增加，使不可见性和安全性增强，水印总体性能显著提高；应用SB字E矩阵，存储空间小，计算速度快，硬件简单；压缩感知重建过程引入稀疏度，极大提高重建准确性及效果。

A digital image watermark embedding and extraction method based on compressed sensing belongs to the technical fields of information hiding and image processing. Sparse the binary digital image watermark information to obtain the sparse one-dimensional watermark information, construct the measurement matrix, and use the measurement matrix as the key; measure the one-dimensional watermark information with the key sparse to realize the one-dimensional watermark information Compression and encryption; discrete cosine transform is performed on the original carrier image information, and the transformed discrete cosine transform domain information is divided into blocks, and the processed watermark information is embedded into the carrier image to obtain a watermarked image. The present invention uses the compressed sensing method to process the watermark, realizes the dual functions of watermark compression and encryption, increases the embedding amount, enhances the invisibility and security, and significantly improves the overall performance of the watermark; the SB word E matrix is applied, the storage space is small, and the calculation The speed is fast and the hardware is simple; the compression sensing reconstruction process introduces sparsity, which greatly improves the accuracy and effect of reconstruction.

Description

Translated fromChinese

一种基于压缩感知的数字图像水印嵌入和提取方法A Digital Image Watermark Embedding and Extraction Method Based on Compressive Sensing

技术领域technical field

本发明属于信息隐藏和图像处理技术领域，特别涉及一种基于压缩感知的数字图像水印嵌入和提取方法。The invention belongs to the technical field of information hiding and image processing, in particular to a digital image watermark embedding and extraction method based on compressed sensing.

背景技术Background technique

信息隐藏是信息安全领域的一个新的研究热点，信息隐藏为在开放的网络环境下进行涉密的数据通信、数字产品的知识产权保护、重要文件和数字签名的真实性鉴别以及机密文件泄密后的消息源头追踪提供了可靠的信息安全保障。数字水印技术是信息隐藏技术的重要分支。Information hiding is a new research hotspot in the field of information security. Information hiding includes secret-related data communication in an open network environment, intellectual property protection of digital products, authenticity identification of important documents and digital signatures, and post-disclosure of confidential documents. The source tracking of news provides reliable information security guarantee. Digital watermarking technology is an important branch of information hiding technology.

数字水印技术是一种有效的版权保护、内容认证以及数据完整性保护的方法，一直以来受到版权保护相关领域研究者的关注与重视。数字图像水印算法主要分为：空间域水印技术和变换域水印技术，空间域水印技术存在鲁棒性差，水印信息嵌入不均衡，抗攻击能力和安全性差等缺点，而变换域水印技术针对噪声的鲁棒性比较强，却存在嵌入容量小的缺点。Digital watermarking technology is an effective method for copyright protection, content authentication and data integrity protection, and has always been concerned and valued by researchers in the field of copyright protection. Digital image watermarking algorithms are mainly divided into: spatial domain watermarking technology and transform domain watermarking technology. Spatial domain watermarking technology has disadvantages such as poor robustness, unbalanced watermark information embedding, poor anti-attack ability and security, and transform domain watermarking technology for noise. The robustness is relatively strong, but it has the disadvantage of small embedding capacity.

发明内容Contents of the invention

针对现有技术存在的不足，本发明的目的是提供一种基于压缩感知的数字图像水印方法，融合了压缩感知理论，引入测量矩阵作为数字图像水印密钥，增强了数字图像水印的安全性，通过对水印信息的压缩，增加大了嵌入容量，隐藏能力更强，具有较强的鲁棒性，实现简单快速，成本低廉。In view of the deficiencies in the prior art, the purpose of the present invention is to provide a digital image watermarking method based on compressed sensing, which integrates the compressed sensing theory, introduces a measurement matrix as a digital image watermark key, and enhances the security of digital image watermarking. By compressing the watermark information, the embedding capacity is increased, the hiding ability is stronger, the robustness is stronger, the realization is simple, fast, and the cost is low.

本发明的技术方案是这样实现的：一种基于压缩感知的数字图像水印嵌入方法，包括以下步骤：The technical scheme of the present invention is achieved in that a kind of digital image watermark embedding method based on compressed sensing comprises the following steps:

步骤1：对二值数字图像水印信息进行稀疏化处理，得到稀疏化的一维水印信息；Step 1: Perform sparse processing on the binary digital image watermark information to obtain sparse one-dimensional watermark information;

读取二值数字图像水印信息W=(w_s,q)_S×Q，二值数字图像水印信息W是大小为S×Q的矩阵，其中，S表示矩阵的行，Q表示矩阵的列，w_s,q为二值数字图像水印信息W的第s行、第q列位置上的元素，w_s,q∈{0,1}；Read the binary digital image watermark information W=(w_s,q )_S×Q , the binary digital image watermark information W is a matrix with a size of S×Q, where S represents the row of the matrix, Q represents the column of the matrix, w_s,q are the elements at the sth row and qth column of the binary digital image watermark information W, w_s,q ∈{0,1};

对二值数字图像水印信息W进行逐列扫描，将其转换成一维水印信息一维水印信息C^w是一维列向量，共有L行，且有L=S×Q；w表示二值数字图像水印信息，是watermark的缩写；Scan the binary digital image watermark information W column by column and convert it into one-dimensional watermark information One-dimensional watermark information C^w is a one-dimensional column vector, which has L rows in total, and has L=S×Q; w represents binary digital image watermark information, which is the abbreviation of watermark;

一维水印信息C^w经过离散余弦变换，得到离散余弦变换域信息即稀疏化的一维水印信息稀疏化的一维水印信息D^w是一维列向量，共有L行；The one-dimensional watermark information C^w undergoes the discrete cosine transform to obtain the discrete cosine transform domain information, that is, the sparse one-dimensional watermark information The sparse one-dimensional watermark information D^w is a one-dimensional column vector with a total of L rows;

设定稀疏化一维水印信息的稀疏度K，0<K＜＜1，采样数据量为K*L，保留K值；Set the sparseness K of the sparse one-dimensional watermark information, 0<K<<1, the amount of sampled data is K*L, and keep the K value;

步骤2：构造测量矩阵，将测量矩阵作为密钥，用密钥对步骤1确定的稀疏化的一维水印信息进行测量，实现对一维水印信息的压缩和加密；Step 2: Construct a measurement matrix, use the measurement matrix as a key, and use the key to measure the sparse one-dimensional watermark information determined in step 1, so as to realize the compression and encryption of the one-dimensional watermark information;

将P个大小为b×b的哈德马矩阵块H_Block按照如下公式组成H：Compile P Hadamard matrix blocks H_Block with size b×b to form H according to the following formula:

式中，P和b均为整数，取值满足：P*b=L；对矩阵H的列向量进行随机排序，然后对行向量进行随机排序，抽取排序后矩阵H中的任意L_cs行组成测量矩阵测量矩阵Φ是大小为L_cs×L的矩阵，为测量矩阵Φ的第l_cs行、第l列位置上的元素，L_cs满足条件：L_cs＜＜L，L_cs∈[K*L,L)；cs表示压缩感知，是Compressivesensing的缩写；In the formula, both P and b are integers, and the value satisfies: P*b=L; the column vectors of the matrix H are randomly sorted, and then the row vectors are randomly sorted, and any L_cs row composition in the sorted matrix H is extracted measurement matrix The measurement matrix Φ is a matrix of size L_cs ×L, It is the element on the l_cs row and the l column of the measurement matrix Φ, L_cs satisfies the condition: L_cs << L, L_cs ∈ [K*L, L); cs means compressed sensing, which is the abbreviation of Compressivesensing;

将上述测量矩阵Φ作为密钥保存；Save the above measurement matrix Φ as a key;

用密钥Φ的每个行向量分别与稀疏化的一维水印信息做内积，得到一维水印信息在密钥上的投影，即测量值测量值Y^w是一维列向量，共L_cs行；因为一维水印信息的总数据量为L，测量值的总数据量为L_cs，L_cs＜＜L，所以测量过程实现了数据压缩，又因为在未知密钥Φ的情况下，压缩过程不可逆，所以压缩过程也是对数据的加密过程；Use the inner product of each row vector of the key Φ with the sparse one-dimensional watermark information to obtain the projection of the one-dimensional watermark information on the key, that is, the measured value The measurement value Y^w is a one-dimensional column vector, with a total of L_cs rows; because the total data volume of the one-dimensional watermark information is L, the total data volume of the measurement value is L_cs , and L_cs << L, so the measurement process realizes data compression , and because the compression process is irreversible when the key Φ is unknown, the compression process is also an encryption process for data;

步骤3：读取待进行版权保护的数字图像，将其作为原始载体图像信息，保留一份原始载体图像信息的备份，对原始载体图像信息进行离散余弦变换并对变换后得到的离散余弦变换域信息进行分块，将步骤2处理后的水印信息嵌入到载体图像中得到含水印图像；Step 3: Read the digital image to be protected by copyright, use it as the original carrier image information, keep a backup of the original carrier image information, perform discrete cosine transform on the original carrier image information and transform the discrete cosine transform domain The information is divided into blocks, and the watermark information processed in step 2 is embedded into the carrier image to obtain a watermarked image;

读取待进行版权保护的数字图像信息，即原始载体图像信息A=(a_m,n)_M×N，原始载体图像信息A是大小为M×N的矩阵，其中，M表示行，N表示列，a_m,n为原始载体图像A的第m行、第n列位置上的元素；Read the digital image information to be protected by copyright, that is, the original carrier image information A=(am_,n )_M×N , the original carrier image information A is a matrix with a size of M×N, where M represents rows and N represents Column, a_{m, n} is the element on the mth row and nth column position of the original carrier image A;

对原始载体图像信息A逐列进行扫描，将其转换成一维的原始载体图像C^A是一维列向量，共有L_A行，L_A=M×N；Scan the original carrier image information A column by column and convert it into a one-dimensional original carrier image C^A is a one-dimensional column vector with a total of L_A rows, L_A =M×N;

对一维的原始载体图像C^A做离散余弦变换，得到原始载体图像的离散余弦变换域信息原始载体图像的离散余弦变换域信息D^A是一维列向量，共有L_A行；Perform discrete cosine transform on the one-dimensional original carrier image C^A to obtain the discrete cosine transform domain information of the original carrier image The discrete cosine transform domain information D^A of the original carrier image is a one-dimensional column vector with a total of L_A rows;

将原始载体图像的离散余弦变换域信息DA的低频部分分割成大小为B×1的矩阵块，式中为向下取整符号，B是矩阵块的行数，β为伸缩系数，且有β∈(代,代.5]，用来调节分块的大小，原始载体图像的离散余弦变换域信息D^A总共被分割成块，为向上取整符号；Divide the low-frequency part of the discrete cosine transform domain information DA of the original carrier image into matrix blocks with a size of B×1, In the formula is the symbol of rounding down, B is the number of rows of the matrix block, β is the expansion coefficient, and there is β∈(generation, generation.5], which is used to adjust the size of the block, and the discrete cosine transform domain information D of the original carrier image^A is divided into piece, is the symbol for rounding up;

然后将水印信息测量值嵌入到原始载体图像的离散余弦变换域信息D^A前L_cs个分块的每个分块第一行数据中，此过程可描述为：Then the watermark information measurement value Embedded into the first line of data of each block of the first L_cs blocks of the discrete cosine transform domain information D^A of the original carrier image, this process can be described as:

式中，α∈(0,1)是调节嵌入强度的权值，α越大嵌入强度越大，水印鲁棒性越强，嵌入水印后载体图像质量下降也越大，反之，α越小，水印鲁棒性越弱，嵌入水印后载体图像质量越好；嵌入水印后得到含水印的载体图像离散余弦变换域信息为一维列向量，行数为L_A；In the formula, α∈(0,1) is the weight to adjust the embedding strength. The larger the α, the greater the embedding strength, the stronger the robustness of the watermark, and the greater the quality degradation of the carrier image after embedding the watermark. Conversely, the smaller the α, The weaker the robustness of the watermark, the better the quality of the carrier image after embedding the watermark; after embedding the watermark, the discrete cosine transform domain information of the carrier image containing the watermark is obtained is a one-dimensional column vector, and the number of rows is L_A ;

含水印的载体图像离散余弦变换域信息做离散余弦逆变换，得到一维含水印的图像信息一维含水印的图像信息是一维列向量，共有L_A行；Watermarked carrier image discrete cosine transform domain information Do inverse discrete cosine transform to get one-dimensional watermarked image information One-dimensional watermarked image information Is a one-dimensional column vector with a total of L_A rows;

将一维含水印的图像信息按照逐列扫描的逆过程复原成大小为M×N的含水印图像为含水印图像的第m行、第n列位置上的元素；One-dimensional watermarked image information According to the reverse process of column-by-column scanning, it is restored to a watermarked image of size M×N for watermarked images The element at the mth row and nth column position of ;

水印的嵌入过程结束，步骤1、步骤2和步骤3需要分别保留稀疏化一维水印信息的稀疏度K、密钥Φ、伸缩系数β、权值α以及原始载体图像的备份。The embedding process of the watermark is over, step 1, step 2 and step 3 need to retain the sparsity K of the sparse one-dimensional watermark information, the key Φ, the expansion coefficient β, the weight α and the backup of the original carrier image.

一种基于压缩感知的数字图像水印提取方法，包括以下步骤：A digital image watermark extraction method based on compressed sensing, comprising the following steps:

步骤1：分别读入含水印图像和原始载体图像备份，对两者分别做离散余弦变换，得到含水印图像离散余弦变换域信息和原始载体图像离散余弦变换域信息，计算一维水印信息测量值；Step 1: Read in the backup of the watermarked image and the original carrier image respectively, and perform discrete cosine transform on them respectively to obtain the discrete cosine transform domain information of the watermarked image and the discrete cosine transform domain information of the original carrier image, and calculate the one-dimensional watermark information measurement value ;

读取含水印图像含水印图像是大小为M×N的矩阵，为含水印图像的第m行、第n列位置上的元素；Read watermarked image watermarked image is a matrix of size M×N, for watermarked images The element at the mth row and nth column position of ;

读取原始载体图像信息的备份，原始载体图像信息A=(a_m,n)_M×N是大小为M×N的矩阵，a_m,n为原始载体图像信息A的第m行、第n列位置上的元素；Read the backup of the original carrier image information, the original carrier image information A=(am_,n )_M×N is a matrix with a size of M×N, a_m,n is the mth row and the nth row of the original carrier image information A element at column position;

对原始载体图像信息A逐列进行扫描，将其转换成一维的原始载体图像C^A是一维列向量，共有L_A行，L_A=M×N；Scan the original carrier image information A column by column and convert it into a one-dimensional original carrier image C^A is a one-dimensional column vector with a total of L_A rows, L_A =M×N;

对含水印图像信息逐列进行扫描，将其转换成一维含水印图像信息是一维列向量，共有L_A行；For watermarked image information Scan column by column and convert it into one-dimensional watermarked image information Is a one-dimensional column vector with a total of L_A rows;

一维原始图像信息C^A做离散余弦变换得到原始载体图像的离散余弦变换域信息原始载体图像的离散余弦变换域信息D^A是一维列向量，共有L_A行；The one-dimensional original image information C^A performs discrete cosine transform to obtain the discrete cosine transform domain information of the original carrier image The discrete cosine transform domain information D^A of the original carrier image is a one-dimensional column vector with a total of L_A rows;

一维含水印图像信息做离散余弦变换得到含水印的载体图像离散余弦变换域信息为一维列向量，行数为L_A；One-dimensional watermarked image information Do the discrete cosine transform to obtain the discrete cosine transform domain information of the watermarked carrier image is a one-dimensional column vector, and the number of rows is L_A ;

将原始载体图像的离散余弦变换域信息D^A和含水印的载体图像离散余弦变换域信息分别进行分块，分块大小为B×1矩阵，此处B与水印嵌入过程中B的值相同，即B为矩阵块的行数，L_cs是密钥Φ的行数，可由密钥Φ求得，β为伸缩系数，β用来调节分块的大小，β的取值同嵌入过程中的β值相同；原始载体图像的离散余弦变换域信息D^A和含水印的载体图像离散余弦变换域信息分别被分割成块；The discrete cosine transform domain information D^A of the original carrier image and the discrete cosine transform domain information of the watermarked carrier image Carry out block respectively, the block size is B×1 matrix, where B is the same as the value of B in the watermark embedding process, that is B is the number of rows of the matrix block, L_cs is the number of rows of the key Φ, which can be obtained from the key Φ, β is the expansion coefficient, β is used to adjust the size of the block, and the value of β is the same as the value of β in the embedding process The same; the discrete cosine transform domain information D^A of the original carrier image and the discrete cosine transform domain information of the watermarked carrier image are divided into piece;

将二者前L_cs个分块的每个分块第一行数据对应求差值，公式为：Calculate the difference value corresponding to the first row of data of each block in the first L_cs blocks of the two, the formula is:

${\stackrel{<span><span>^</span>^</span>}{\mathrm{<span><span>y</span>the\; y</span>}}}_{\mathrm{<span><span>j</span>j</span>}<span><span>+</span>+</span>\mathrm{<span><span>1</span>1</span>}}^{\mathrm{<span><span>w</span>w</span>}}<span><span>=</span>=</span>\frac{{\stackrel{<span><span>^</span>^</span>}{\mathrm{<span><span>d</span>d</span>}}}_{\mathrm{<span><span>B</span>B</span>}<span><span>*</span>*</span>\mathrm{<span><span>j</span>j</span>}<span><span>+</span>+</span>\mathrm{<span><span>1</span>1</span>}}^{\mathrm{<span><span>A</span>A</span>}}<span><span>-</span>-</span>{\mathrm{<span><span>d</span>d</span>}}_{\mathrm{<span><span>B</span>B</span>}<span><span>*</span>*</span>\mathrm{<span><span>j</span>j</span>}<span><span>+</span>+</span>\mathrm{<span><span>1</span>1</span>}}^{\mathrm{<span><span>A</span>A</span>}}}{\mathrm{<span><span>\&alpha;</span>\&alpha;</span>}}<span><span>,</span>,</span><span><span>(</span>(</span>\mathrm{<span><span>j</span>j</span>}<span><span>=</span>=</span>\mathrm{<span><span>0,1</span>0,1</span>}<span><span>,</span>,</span><span><span>.</span>.</span><span><span>.</span>.</span><span><span>.</span>.</span><span><span>,</span>,</span>{\mathrm{<span><span>L</span>L</span>}}_{\mathrm{<span><span>cs</span>cs</span>}}<span><span>-</span>-</span>\mathrm{<span><span>1</span>1</span>}<span><span>)</span>)</span><span><span>;</span>;</span>$

式中，α为水印嵌入过程中保存的权值α，通过计算得到一维水印信息测量值一维水印信息测量值是一维列向量，共L_cs行；In the formula, α is the weight α saved in the watermark embedding process, and the one-dimensional watermark information measurement value is obtained by calculation Measured value of one-dimensional watermark information is a one-dimensional column vector with a total of L_cs rows;

步骤2：调入密钥，对一维水印信息进行解压缩；Step 2: Call in the key to decompress the one-dimensional watermark information;

应用子空间追踪算法对一维水印信息解压缩，重构水印信息：Apply the subspace tracking algorithm to decompress the one-dimensional watermark information and reconstruct the watermark information:

子空间追踪算法需要输入的信号分别为：一维水印信息测量值密钥Φ、稀疏度K，应用子空间追踪算法解压重构出稀疏化的一维水印信息；The input signals required by the subspace tracking algorithm are: one-dimensional watermark information measurement value The key Φ and the sparsity K are used to decompress and reconstruct the sparse one-dimensional watermark information by using the subspace tracking algorithm;

步骤3：稀疏化后的一维水印信息恢复成二值数字图像水印信息；Step 3: The sparse one-dimensional watermark information is restored to binary digital image watermark information;

对稀疏化的一维水印信息进行离散余弦逆变换，转换成一维水印信息，再将一维水印信息按照逐列扫描的逆过程复原成大小为M行N列的数字图像水印信息。Perform discrete cosine inverse transform on the sparse one-dimensional watermark information, convert it into one-dimensional watermark information, and then restore the one-dimensional watermark information into digital image watermark information with a size of M rows and N columns according to the reverse process of column-by-column scanning.

本发明的有益效果：Beneficial effects of the present invention:

首先，传统的数字图像水印技术停留在变换域基础上，嵌入的信息量小，变换域嵌入水印不存在加密过程，容易遭受非法提取，安全性不佳。而本发明采用压缩感知算法对水印进行处理，实现了水印压缩和加密的双重作用，嵌入量增加，不可见性和安全性增强，水印总体性能显著提高。First of all, the traditional digital image watermarking technology stays on the basis of the transform domain, and the amount of embedded information is small. There is no encryption process for embedding the watermark in the transform domain, and it is easy to be illegally extracted, and the security is not good. However, the present invention uses a compressed sensing algorithm to process the watermark, realizes the dual functions of watermark compression and encryption, increases the amount of embedding, enhances invisibility and security, and significantly improves the overall performance of the watermark.

其次，目前应用压缩感知技术处理图像时，多数采用高斯随机矩阵或贝努力随机矩阵，对图像信号进行测量需要很大的内存空间和计算量，实现困难，成本大，而本发明应用SBHE矩阵需要很小的存储空间，计算速度快，硬件简单，利于实现。Secondly, when applying compressive sensing technology to process images at present, most of them use Gaussian random matrix or Bernoulli random matrix, which requires a lot of memory space and calculation amount to measure the image signal, which is difficult to implement and costly. However, the application of SBHE matrix in the present invention requires Small storage space, fast calculation speed, simple hardware, and easy to implement.

最后，压缩感知重建过程引入稀疏度，可以极大提高重建的准确性，提高重建效果。Finally, the sparsity introduced in the compressed sensing reconstruction process can greatly improve the accuracy of reconstruction and improve the reconstruction effect.

附图说明Description of drawings

图1为本发明实施方式水印图像嵌入过程流程图；FIG. 1 is a flow chart of a watermark image embedding process according to an embodiment of the present invention;

图2为本发明实施方式水印图像提取过程流程图；Fig. 2 is a flow chart of the watermark image extraction process in the embodiment of the present invention;

图3为本发明实施方式水印视觉影响比较图示意图，其中，(a)为原始图像，(b)为水印图像，(c)为含水印图像，(d)为提取的水印图像；3 is a schematic diagram of a comparison diagram of watermark visual impact according to an embodiment of the present invention, wherein (a) is an original image, (b) is a watermark image, (c) is an image containing a watermark, and (d) is an extracted watermark image;

图4为本发明实施方式不同的采样率下含水印图像与原始图像的PSNR以及NC情况示意图，其中，(a)为不同的采样率下含水印图像与原始图像的PSNR情况，(b)为不同的采样率下含水印图像与原始图像的NC情况；Fig. 4 is a schematic diagram of the PSNR and NC of the watermarked image and the original image under different sampling rates according to the embodiment of the present invention, wherein (a) is the PSNR of the watermarked image and the original image at different sampling rates, and (b) is The NC situation of the watermarked image and the original image at different sampling rates;

图5为本发明实施方式椒盐噪声攻击实验结果示意图，其中，(a)为椒盐噪声攻击后的含水印图像，(b)为提取的水印图像；5 is a schematic diagram of the salt and pepper noise attack experiment results according to the embodiment of the present invention, wherein (a) is the watermarked image after the salt and pepper noise attack, and (b) is the extracted watermark image;

图6为本发明实施方式JPEG压缩攻击实验结果示意图，其中，(a)为JPEG压缩攻击后的含水印图像，(b)为提取的水印图像；6 is a schematic diagram of the experimental results of JPEG compression attack according to the embodiment of the present invention, wherein (a) is the watermarked image after JPEG compression attack, and (b) is the extracted watermark image;

图7为本发明实施方式高斯白噪声攻击实验结果示意图，其中，(a)为高斯白噪声攻击后的含水印图像，(b)为提取的水印图像；7 is a schematic diagram of the Gaussian white noise attack experiment results of the embodiment of the present invention, wherein (a) is the watermarked image after the Gaussian white noise attack, and (b) is the extracted watermark image;

图8为本发明实施方式剪切攻击实验结果示意图，(a)为剪切攻击后的含水印图像，(b)为提取的水印图像。Fig. 8 is a schematic diagram of the experimental results of the clipping attack according to the embodiment of the present invention, (a) is the watermarked image after the clipping attack, and (b) is the extracted watermarked image.

具体实施方式detailed description

下面结合附图对本发明的实施方式作进一步详细的说明。Embodiments of the present invention will be further described in detail below in conjunction with the accompanying drawings.

本发明实施方式采用基于压缩感知的数字图像水印嵌入和提取方法对图像进行处理。其中，一种基于压缩感知的数字图像水印嵌入方法，其流程如图1所示，包括如下步骤：Embodiments of the present invention process images by using a method for embedding and extracting digital image watermarks based on compressed sensing. Among them, a digital image watermark embedding method based on compressed sensing, its process is shown in Figure 1, including the following steps:

步骤1：对二值数字图像水印信息进行稀疏化处理，得到稀疏化的一维水印信息；Step 1: Perform sparse processing on the binary digital image watermark information to obtain sparse one-dimensional watermark information;

本实施方式主要融合了压缩感知理论，压缩感知理论是一种充分的利用信号稀疏性或可压缩性的全新信号采集和编解码理论；This embodiment mainly integrates the compressed sensing theory, which is a new signal acquisition and encoding and decoding theory that fully utilizes the signal sparsity or compressibility;

传统方式下的信号处理，依照Shannon/Nyquist采样理论，在采样过程中产生大量的采样数据，而压缩感知理论打破了Shannon/Nyquist采样理论对信号采样的要求，其具体指：信号只要在某个正交空间具有稀疏性，就能以较低的频率对信号采样，并可以通过非线性的优化算法从采样信号中高概率重构出原信号；然而，一般的自然信号并不是绝对稀疏的，需要在某种稀疏基上进行稀疏表示，即稀疏化；In traditional signal processing, according to the Shannon/Nyquist sampling theory, a large amount of sampling data is generated during the sampling process, while the compressed sensing theory breaks the requirements of the Shannon/Nyquist sampling theory for signal sampling, which specifically refers to: as long as the signal is in a certain Orthogonal space is sparse, so the signal can be sampled at a lower frequency, and the original signal can be reconstructed from the sampled signal with a high probability through a nonlinear optimization algorithm; however, the general natural signal is not absolutely sparse, and requires Perform sparse representation on a certain sparse basis, that is, sparse;

本实施方式采用二值数字图像作为水印信息，即二值数字图像水印信息，由于图像信息本身稀疏性不佳，需要稀疏变换提高图像信息稀疏性，离散余弦变换是一种很好的稀疏变换方式，对二值数字图像水印信息进行离散余弦变换可以达到很好的稀疏化效果；In this embodiment, a binary digital image is used as watermark information, that is, binary digital image watermark information. Since the image information itself is not sparse enough, sparse transformation is needed to improve the image information sparsity. Discrete cosine transform is a very good sparse transformation method. , the discrete cosine transform of the binary digital image watermark information can achieve a very good sparse effect;

首先，读取二值数字图像水印信息W=(w_s,q)_S×Q，二值数字图像水印信息W是大小为S×Q的矩阵，w_s,q为二值数字图像水印信息W的第s行、第q列位置上的元素，w_i,j∈{0,1}；First, read the binary digital image watermark information W=(w_s,q )_S×Q , the binary digital image watermark information W is a matrix of size S×Q, w_s,q is the binary digital image watermark information W The element at the sth row and qth column position of , w_i,j ∈ {0,1};

对二值数字图像水印信息W进行逐列扫描，即从左面第一列信息开始，到右边最后一列信息为止，首尾相连将二值数字图像水印信息W转换成一维水印信息一维水印信息C^w是一维列向量，共有L行，L=S×Q；The binary digital image watermark information W is scanned column by column, that is, from the first column information on the left to the last column information on the right, end-to-end to convert the binary digital image watermark information W into one-dimensional watermark information The one-dimensional watermark information C^w is a one-dimensional column vector, with a total of L rows, L=S×Q;

一维水印信息C^w经过离散余弦变换，得到离散余弦变换域信息即稀疏化的一维水印信息稀疏化的一维水印信息D^w是一维列向量，共有L行；The one-dimensional watermark information C^w undergoes the discrete cosine transform to obtain the discrete cosine transform domain information, that is, the sparse one-dimensional watermark information The sparse one-dimensional watermark information D^w is a one-dimensional column vector with a total of L rows;

设定稀疏化一维水印信息的稀疏度K，0<K＜＜1，采样数据量为K*L，保留K值；K值越小说明稀疏度越好，采样数据量也就越小，二值图像水印信息的可压缩性就越强，保留K值以便提取水印时使用，结束步骤1；Set the sparsity K of the sparse one-dimensional watermark information, 0<K<<1, the amount of sampled data is K*L, and keep the value of K; the smaller the value of K, the better the sparsity, and the smaller the amount of sampled data. The more compressible the binary image watermark information is, the K value is reserved for use when extracting the watermark, and step 1 is ended;

步骤2：构造测量矩阵，将测量矩阵作为密钥，用密钥对步骤1确定的稀疏化的一维水印信息进行测量，实现对一维水印信息的压缩和加密；Step 2: Construct a measurement matrix, use the measurement matrix as a key, and use the key to measure the sparse one-dimensional watermark information determined in step 1, so as to realize the compression and encryption of the one-dimensional watermark information;

测量矩阵的作用：通过测量矩阵得到被测量信号的测量值，而这个测量值的数据量要比被测量信号小很多，从而实现压缩的目的，解压过程需要已知测量矩阵才能恢复被测量信号，因此，压缩过程也是加密过程；The function of the measurement matrix: the measurement value of the measured signal is obtained through the measurement matrix, and the data volume of this measurement value is much smaller than the measured signal, so as to achieve the purpose of compression. The decompression process requires a known measurement matrix to restore the measured signal. Therefore, the compression process is also an encryption process;

构造测量矩阵必须满足两个条件：一个是测量矩阵必需满足有限等距准则(Restricted Isometry Principle,RIP)，另一个条件是测量值采样个数必须大于某一数值才能精确重构原始信号；Two conditions must be met to construct the measurement matrix: one is that the measurement matrix must satisfy the Restricted Isometry Principle (RIP), and the other condition is that the number of samples of measured values must be greater than a certain value in order to accurately reconstruct the original signal;

研究表明，如果测量矩阵与稀疏变换矩阵是不相干的，则二者乘积在很大概率上满足有限等距准则；高斯随机矩阵与贝努力随机矩阵都能保证同大部分的稀疏变换矩阵都不相干；然而，在处理数字图像压缩感知时，高斯随机矩阵或者贝努力随机矩阵并不是很适用，因为一幅图像的列向量的维数是非常大的，高斯随机矩阵或者贝努力随机矩阵构造的测量矩阵更是非常巨大，这就造成测量过程需要很大的内存空间和计算量，复杂度极高，不利于硬件设备的实现，难以实用化；Studies have shown that if the measurement matrix and the sparse transformation matrix are irrelevant, the product of the two satisfies the finite isometric criterion with a high probability; Gaussian random matrix and Bernoulli random matrix can guarantee that most of the sparse transformation matrices Coherent; however, when dealing with compressed sensing of digital images, Gaussian random matrices or Bernoulli random matrices are not very suitable, because the dimension of the column vector of an image is very large, Gaussian random matrices or Bernoulli random matrices constructed The measurement matrix is very large, which requires a large amount of memory space and calculations in the measurement process, and the complexity is extremely high, which is not conducive to the realization of hardware devices and is difficult to be practical;

本实施方式将一种适用于图像的乱序哈德马集(Scrambled Block HadamardEnsemble，SBHE)作为测量矩阵Φ应用于水印处理，其构造方法如下：In this embodiment, a Scrambled Block Hadamard Ensemble (SBHE) suitable for images is used as a measurement matrix Φ for watermark processing, and its construction method is as follows:

首先，将P个大小为b×b的哈德马矩阵块H_Block按照如下公式组成H：First, P Hadamard matrix blocks H_Blocks of size b×b are combined to form H according to the following formula:

式中，P和b均为整数，取值满足：P*b=L；In the formula, both P and b are integers, and the value satisfies: P*b=L;

然后，对矩阵H的列向量进行随机排序，再对行向量进行随机排序；Then, randomly sort the column vectors of the matrix H, and then randomly sort the row vectors;

最后，抽取排序后矩阵H中的任意L_cs行组成测量矩阵测量矩阵Φ是大小为L_cs×L的矩阵，为测量矩阵Φ的第l_cs行、第l列位置上的元素，L_cs满足条件：L_cs＜＜L，L_cs∈[K*L,L)；Finally, any L_cs row in the sorted matrix H is extracted to form a measurement matrix The measurement matrix Φ is a matrix of size L_cs ×L, It is the element in the l_cs row and l column of the measurement matrix Φ, L_cs satisfies the condition: L_cs ＜<L, L_cs ∈[K*L,L);

将上述测量矩阵Φ作为密钥保存；Save the above measurement matrix Φ as a key;

用密钥Φ的每个行向量分别与稀疏化的一维水印信息做内积，得到一维水印信息在密钥上的投影，即测量值可以用公式描述为：Use the inner product of each row vector of the key Φ with the sparse one-dimensional watermark information to obtain the projection of the one-dimensional watermark information on the key, that is, the measured value It can be described by the formula:

Y^w=Φ·D^wY^w = Φ·D^w

式中，测量值Y^w是一维列向量，共L_cs行，密钥Φ是大小L_cs×L的矩阵，稀疏化的一维水印信息D^w是一维列向量，共有L行；In the formula, the measured value Y^w is a one-dimensional column vector with L_cs rows in total, the key Φ is a matrix of size L_cs ×L, and the sparse one-dimensional watermark information D^w is a one-dimensional column vector with L rows in total;

因为稀疏化的一维水印信息D^w的总数据量为L，测量值Y^w的总数据量为L_cs，L_cs＜＜L，所以测量过程实现了数据压缩，又因为在未知密钥Φ的情况下，压缩过程不可逆，所以压缩过程也是加密过程，同时，压缩过程也是信号采样过程，采样率为Because the total data volume of the sparse one-dimensional watermark information D^w is L, and the total data volume of the measurement value Y^w is L_cs , L_cs <<L, so the measurement process realizes data compression, and because the unknown key Φ In the case of , the compression process is irreversible, so the compression process is also an encryption process. At the same time, the compression process is also a signal sampling process, and the sampling rate is

步骤3：读取待进行版权保护的数字图像，将其作为原始载体图像信息，保留一份原始载体图像信息的备份，对原始载体图像信息进行离散余弦变换并对变换后得到的离散余弦变换域信息进行分块，将步骤2处理后的水印信息嵌入到载体图像中得到含水印图像；Step 3: Read the digital image to be protected by copyright, use it as the original carrier image information, keep a backup of the original carrier image information, perform discrete cosine transform on the original carrier image information and transform the discrete cosine transform domain The information is divided into blocks, and the watermark information processed in step 2 is embedded into the carrier image to obtain a watermarked image;

待进行版权保护的数字图像信息就是原始载体图像信息A=(a_m,n)_M×N，原始载体图像信息A是大小为M×N的矩阵，a_m,n为原始载体图像A的第m行、第n列位置上的元素；The digital image information to be protected by copyright is the original carrier image information A=(am_,n )_M×N , the original carrier image information A is a matrix with a size of M×N, and a_m,n is the first element of the original carrier image A The element at the position of row m and column n;

原始载体图像信息A逐列进行扫描，即从左面第一列信息开始，依次扫描，到右边最后一列信息为止，各列信息首尾相连转换成一维的原始载体图像C^A是一维列向量，共有L_A行，L_A=M×N；The original carrier image information A is scanned column by column, that is, starting from the first column of information on the left, scanning in turn, and ending with the last column of information on the right, each column of information is connected end to end and converted into a one-dimensional original carrier image C^A is a one-dimensional column vector with a total of L_A rows, L_A =M×N;

对一维的原始载体图像C^A做离散余弦变换，得到原始载体图像的离散余弦变换域信息原始载体图像的离散余弦变换域信息D^A是一维列向量，共有L_A行，D^A中列的位置处于低位的元素主要表现原始载体图像空间域低频信息，反之，列的位置处于高位的元素主要表现原始载体图像空间域高频信息，根据人眼视觉特性，人眼对低频信息的辨识能力低，因此，水印信息应当尽量嵌入到低频信息中；Perform discrete cosine transform on the one-dimensional original carrier image C^A to obtain the discrete cosine transform domain information of the original carrier image The discrete cosine transform domain information D^A of the original carrier image is a one-dimensional column vector, which has a total of L_A rows. The elements in the low position of the column in D^A mainly represent the low-frequency information of the original carrier image in the space domain, otherwise, the columns in the high position Elements mainly represent the high-frequency information in the spatial domain of the original carrier image. According to the visual characteristics of the human eye, the ability of the human eye to identify low-frequency information is low. Therefore, the watermark information should be embedded in the low-frequency information as much as possible;

将原始载体图像的离散余弦变换域信息D^A低频部分分割成大小为B×1的矩阵块，每个矩阵块是一个列向量，B是矩阵块的行数，β为伸缩系数，β∈(代,代.5]，用来调节B的大小，使得分块更加集中于低频部分，原始载体图像的离散余弦变换域信息D^A总共被分割成块，分块完成之后，总块数等于L_cs+1，前L_cs个分块主要集中在低频部分，每个分块是大小为B×1的矩阵块，最后一个分块是大小为(L_A-L_cs*B)×1的矩阵块，最后一块信息主要集中在高频部分，不应该在最后一块中嵌入任何信息；Divide the discrete cosine transform domain information D^A of the original carrier image into matrix blocks of size B×1, each matrix block is a column vector, B is the number of rows of the matrix block, β is the expansion coefficient, β∈(generation, generation.5] is used to adjust the size of B, so that the block is more concentrated in the low-frequency part, and the discrete cosine transform domain information D^A of the original carrier image total is divided into Block, after the block is completed, the total number of blocks Equal to L_cs +1, the first L_cs blocks are mainly concentrated in the low frequency part, each block is a matrix block with a size of B×1, and the last block is a size of (L_A -L_cs *B)×1 The matrix block of , the information of the last block is mainly concentrated in the high-frequency part, and no information should be embedded in the last block;

将水印信息测量值嵌入到原始载体图像离散余弦变换域信息D^A前L_cs个分块的每个分块第一行数据中，公式为：Measure the watermark information Embedded into the first line of data of each sub-block of the first L_cs sub-blocks of the discrete cosine transform domain information D^A of the original carrier image, the formula is:

式中，α∈(0,1)是调节嵌入强度的权值，α越大嵌入强度越大，对原始载体图像信息的改变也就越大，从而引起图像质量的下降也就越加严重，但水印信息的鲁棒性会增强，反之，α越小嵌入强度越小，原始载体图像信息的改变也就越小，图像更加保真，水印信息的鲁棒性减弱；由以上过程求得含水印的载体图像离散余弦变换域信息为一维列向量，行数为L_A；In the formula, α∈(0,1) is the weight to adjust the embedding strength, the greater the α, the greater the embedding strength, the greater the change to the original carrier image information, and the more serious the degradation of the image quality will be. However, the robustness of the watermark information will be enhanced. On the contrary, the smaller the α, the smaller the embedding strength, the smaller the change of the original carrier image information, the more fidelity the image, and the weakened robustness of the watermark information; Watermarked carrier image discrete cosine transform domain information is a one-dimensional column vector, and the number of rows is L_A ;

含水印的载体图像离散余弦变换域信息做离散余弦逆变换，得到一维含水印的图像信息一维含水印的图像信息是一维列向量，共有L_A行；将一维含水印的图像信息按照逐列扫描的逆过程复原成大小为M×N的含水印图像为含水印图像的第m行、第n列位置上的元素；Watermarked carrier image discrete cosine transform domain information Do inverse discrete cosine transform to get one-dimensional watermarked image information One-dimensional watermarked image information Is a one-dimensional column vector, with a total of L_A rows; the one-dimensional watermarked image information According to the reverse process of column-by-column scanning, it is restored to a watermarked image of size M×N for watermarked images The element at the mth row and nth column position of ;

水印嵌入过程结束，含水印图像可公开发布使用，将水印嵌入过程中计算和产生的数据：稀疏度K、密钥Φ、伸缩系数β、权值α以及原始载体图像的备份进行保存，版权所有者保留以上数据，在提取水印的过程中需要使用。The watermark embedding process is over, and the watermarked image It can be released and used publicly. The data calculated and generated during the watermark embedding process: sparsity K, key Φ, expansion coefficient β, weight α, and the backup of the original carrier image are saved. The copyright owner retains the above data and extracts the watermark need to be used in the process.

当出现版权纠纷等问题，版权所有者需要证明版权的合法性时，可以提取水印信息，基于压缩感知的数字图像水印提取方法，其流程如图2所示，包括以下步骤：When issues such as copyright disputes arise and the copyright owner needs to prove the legitimacy of the copyright, the watermark information can be extracted. The digital image watermark extraction method based on compressed sensing, its process is shown in Figure 2, including the following steps:

步骤1：分别读入含水印图像和原始载体图像的备份，对两者分别做离散余弦变换，得到含水印图像离散余弦变换域信息和原始载体图像离散余弦变换域信息，计算一维水印信息测量值；Step 1: Read in the watermarked image and the backup of the original carrier image respectively, and perform discrete cosine transform on them respectively to obtain the discrete cosine transform domain information of the watermarked image and the discrete cosine transform domain information of the original carrier image, and calculate the one-dimensional watermark information measurement value;

在出现版权纠纷或者版权所有者需要提取数字图像水印信息的时候，读取含水印图像信息含水印图像信息是大小为M×N的矩阵，为含水印图像信息的第m行、第n列位置上的元素；载入原始载体图像的备份信息，即原始载体图像信息A=(a_m,n)_M×N，原始载体图像信息A是大小为M×N的矩阵，a_m,n为原始载体图像信息A的第m行、第n列位置上的元素；对原始载体图像信息A逐列进行扫描，即从左面第一列信息开始，依次扫描，到右边最后一列信息为止，将原始载体图像信息A转换成一维的原始载体图像C^A是一维列向量，共有L_A行，L_A=M×N；对含水印图像信息运用同样的方法逐列进行扫描，将其转换成一维含水印图像信息是一维列向量，共有L_A行；When there is a copyright dispute or the copyright owner needs to extract the digital image watermark information, read the watermarked image information Watermarked image information is a matrix of size M×N, for watermarked image information Elements at the mth row and nth column position of ; load the backup information of the original carrier image, that is, the original carrier image information A=(a_m,n )_M×N , the original carrier image information A is M×N in size The matrix of a_m,n is the element on the mth row and the nth column of the original carrier image information A; the original carrier image information A is scanned column by column, that is, starting from the first column information on the left, scanning in turn, to Up to the last column of information on the right, the original carrier image information A is converted into a one-dimensional original carrier image C^A is a one-dimensional column vector, with a total of L_A rows, L_A =M×N; for image information containing watermark Use the same method to scan column by column and convert it into one-dimensional watermarked image information Is a one-dimensional column vector with a total of L_A rows;

一维原始图像信息C^A做离散余弦变换得到原始载体图像的离散余弦变换域信息原始载体图像的离散余弦变换域信息D^A是一维列向量，共有L_A行；The one-dimensional original image information C^A performs discrete cosine transform to obtain the discrete cosine transform domain information of the original carrier image The discrete cosine transform domain information D^A of the original carrier image is a one-dimensional column vector with a total of L_A rows;

一维含水印图像信息做离散余弦变换得到含水印的载体图像离散余弦变换域信息为一维列向量，行数为L_A；One-dimensional watermarked image information Do the discrete cosine transform to obtain the discrete cosine transform domain information of the watermarked carrier image is a one-dimensional column vector, and the number of rows is L_A ;

将原始载体图像的离散余弦变换域信息D^A和含水印的载体图像离散余弦变换域信息分别进行分块，每个分块为一个行数为B的列向量，B为每个分块的行数，L_cs是密钥Φ的行数，可由密钥Φ求得，β为嵌入过程中保留的伸缩系数；原始载体图像的离散余弦变换域信息D^A和含水印的载体图像离散余弦变换域信息分别被分割成块；将二者前L_cs个分块的第一个数据对应求差值，公式为：The discrete cosine transform domain information D^A of the original carrier image and the discrete cosine transform domain information of the watermarked carrier image Carry out blocks separately, each block is a column vector with the number of rows B, B is the number of rows of each block, L_cs is the number of rows of the key Φ, which can be obtained from the key Φ, β is the expansion coefficient reserved during the embedding process; the discrete cosine transform domain information D^A of the original carrier image and the Watermarked carrier image discrete cosine transform domain information are divided into block; the difference between the first data of the first L_cs blocks of the two is correspondingly calculated, and the formula is:

${\stackrel{<span><span>^</span>^</span>}{\mathrm{<span><span>y</span>the\; y</span>}}}_{\mathrm{<span><span>j</span>j</span>}<span><span>+</span>+</span>\mathrm{<span><span>1</span>1</span>}}^{\mathrm{<span><span>w</span>w</span>}}<span><span>=</span>=</span>\frac{{\stackrel{<span><span>^</span>^</span>}{\mathrm{<span><span>d</span>d</span>}}}_{\mathrm{<span><span>B</span>B</span>}<span><span>*</span>*</span>\mathrm{<span><span>j</span>j</span>}<span><span>+</span>+</span>\mathrm{<span><span>1</span>1</span>}}^{\mathrm{<span><span>A</span>A</span>}}<span><span>-</span>-</span>{\mathrm{<span><span>d</span>d</span>}}_{\mathrm{<span><span>B</span>B</span>}<span><span>*</span>*</span>\mathrm{<span><span>j</span>j</span>}<span><span>+</span>+</span>\mathrm{<span><span>1</span>1</span>}}^{\mathrm{<span><span>A</span>A</span>}}}{\mathrm{<span><span>\&alpha;</span>\&alpha;</span>}}<span><span>,</span>,</span><span><span>(</span>(</span>\mathrm{<span><span>j</span>j</span>}<span><span>=</span>=</span>\mathrm{<span><span>0,1</span>0,1</span>}<span><span>,</span>,</span><span><span>.</span>.</span><span><span>.</span>.</span><span><span>.</span>.</span><span><span>,</span>,</span>{\mathrm{<span><span>L</span>L</span>}}_{\mathrm{<span><span>cs</span>cs</span>}}<span><span>-</span>-</span>\mathrm{<span><span>1</span>1</span>}<span><span>)</span>)</span><span><span>;</span>;</span>$

式中，α为水印嵌入过程中保存的权值α，通过以上公式计算得到一维水印信息测量值一维水印信息测量值是一维列向量，共L_cs行；In the formula, α is the weight α saved in the watermark embedding process, and the one-dimensional watermark information measurement value is calculated by the above formula Measured value of one-dimensional watermark information is a one-dimensional column vector with a total of L_cs rows;

步骤2：调入密钥，对一维水印信息进行解压缩；Step 2: Call in the key to decompress the one-dimensional watermark information;

一维水印信息测量值解压的过程即公式：Y^w=Φ·D^w中，已知一维水印信息测量值Y^w和密钥Φ，求原稀疏化一维水印信息D^w的过程；该解压过程需要应用子空间追踪算法，子空间追踪算法作为一种解压缩算法，有着计算速度快，恢复精度高的优点，需要输入信号为：一维水印信息测量值密钥Φ、稀疏化一维水印信息的稀疏度K；具体描述如下；The process of decompressing the measured value of one-dimensional watermark information is the formula: Y^w = Φ·D^w , given the measured value Y^w of one-dimensional watermark information and the key Φ, the process of finding the original sparse one-dimensional watermark information D^w ; The decompression process needs to apply the subspace tracking algorithm. As a decompression algorithm, the subspace tracking algorithm has the advantages of fast calculation speed and high recovery accuracy. The required input signal is: one-dimensional watermark information measurement value The key Φ, the sparsity K of the sparse one-dimensional watermark information; the specific description is as follows;

输入信号：测量矩阵一维水印信息测量值稀疏度K，索引集Γ⁰=φ；Input signal: measurement matrix Measured value of one-dimensional watermark information Sparsity K, index set Γ⁰ = φ;

输出信号：重构的稀疏化的一维水印信息Output signal: reconstructed sparse one-dimensional watermark information

(1)初始化；索引Γ⁽⁰⁾={Φ^TY^w中绝对值最大K个元素所对应的索引集}，${Y_r}^w=Y^w-{\mathrm{\&Phi;}}_{{\mathrm{\&Gamma;}}^{\left(0\right)}}{\left({\mathrm{\&Phi;}}_{{\mathrm{\&Gamma;}}^{\left(0\right)}}^T{\mathrm{\&Phi;}}_{{\mathrm{\&Gamma;}}^{\left(0\right)}}\right)}^{-1}{\mathrm{\&Phi;}}_{{\mathrm{\&Gamma;}}^{\left(0\right)}}^T{Y}^w,D^{\left(0\right)}={\left({\mathrm{\&Phi;}}_{{\mathrm{\&Gamma;}}^{\left(0\right)}}^T{\mathrm{\&Phi;}}_{{\mathrm{\&Gamma;}}^{\left(0\right)}}\right)}^{-1}{\mathrm{\&Phi;}}_{{\mathrm{\&Gamma;}}^{\left(0\right)}}^T{Y_r}^w,n=0;$(1) Initialization; index Γ⁽⁰⁾ = {the index set corresponding to the K elements with the largest absolute value in Φ^T Y^w },${Y_r}^w=Y^w-{\mathrm{\&Phi;}}_{{\mathrm{\&Gamma;}}^{\left(0\right)}}{\left({\mathrm{\&Phi;}}_{{\mathrm{\&Gamma;}}^{\left(0\right)}}^T{\mathrm{\&Phi;}}_{{\mathrm{\&Gamma;}}^{\left(0\right)}}\right)}^{-1}{\mathrm{\&Phi;}}_{{\mathrm{\&Gamma;}}^{\left(0\right)}}^T{Y}^w,{\mathrm{D.}}^{\left(0\right)}={\left({\mathrm{\&Phi;}}_{{\mathrm{\&Gamma;}}^{\left(0\right)}}^T{\mathrm{\&Phi;}}_{{\mathrm{\&Gamma;}}^{\left(0\right)}}\right)}^{-1}{\mathrm{\&Phi;}}_{{\mathrm{\&Gamma;}}^{\left(0\right)}}^T{Y_r}^w,\mathrm{no}=0;$

(2)若Y_r^w=0，则停止迭代，并输出重建信号否则继续，n=n+令，Λ={Φ^TY_r^w中最大K个元素所对应的索引集}，更新索引集Γ⁽ⁿ⁾=Γ^(n-1)∪Λ；(2) If Y_r^w =0, stop the iteration and output the reconstruction signal Otherwise, continue, n=n+order, Λ={the index set corresponding to the largest K elements in Φ^T Y_r^w }, update the index set Γ⁽ⁿ⁾ =Γ^(n-1) ∪Λ;

(3)应用最小二乘法求得近似解，即(3) Apply the least squares method to obtain an approximate solution, namely

(4)选出中最大的K个元素所对应的索引集，即索引Γ⁽ⁿ⁾={中最大的K个元素所对应的索引集}；(4) elected The index set corresponding to the largest K elements in , that is, the index Γ⁽ⁿ⁾ ={ The index set corresponding to the largest K elements in };

(5)更新残量${{\tilde{Y}}_r}^w=Y^w-{\mathrm{\&Phi;}}_{{\mathrm{\&Gamma;}}^{\left(n\right)}}{\left({\mathrm{\&Phi;}}_{{\mathrm{\&Gamma;}}^{\left(n\right)}}^T{\mathrm{\&Phi;}}_{{\mathrm{\&Gamma;}}^{\left(n\right)}}\right)}^{-1}{\mathrm{\&Phi;}}_{{\mathrm{\&Gamma;}}^{\left(n\right)}}^T{Y}^w;$(5) Update residual${{\tilde{Y}}_r}^w=Y^w-{\mathrm{\&Phi;}}_{{\mathrm{\&Gamma;}}^{\left(\mathrm{no}\right)}}{\left({\mathrm{\&Phi;}}_{{\mathrm{\&Gamma;}}^{\left(\mathrm{no}\right)}}^T{\mathrm{\&Phi;}}_{{\mathrm{\&Gamma;}}^{\left(\mathrm{no}\right)}}\right)}^{-1}{\mathrm{\&Phi;}}_{{\mathrm{\&Gamma;}}^{\left(\mathrm{no}\right)}}^T{Y}^w;$

(6)判断是否满足停止迭代的条件：若则终止迭代，并输出否则令转到步骤(2)继续迭代过程。(6) Judging whether the condition for stopping the iteration is met: if then the iteration is terminated and the output Otherwise order Go to step (2) to continue the iterative process.

应用以上描述的子空间追踪算法解压信息，解压完成后，重构出稀疏化的一维水印信息为一维列向量，行数为L；Apply the subspace tracking algorithm described above to decompress the information. After the decompression is completed, reconstruct the sparse one-dimensional watermark information is a one-dimensional column vector, and the number of rows is L;

步骤3：稀疏化后的一维水印信息恢复成二值数字图像水印信息；Step 3: The sparse one-dimensional watermark information is restored to binary digital image watermark information;

对稀疏化的一维水印信息进行离散余弦逆变换，转换成一维水印信息一维水印信息是一维列向量，共有L行；For sparse one-dimensional watermark information Perform inverse discrete cosine transform and convert to one-dimensional watermark information One-dimensional watermark information is a one-dimensional column vector with a total of L rows;

将一维水印信息按照逐列扫描的逆过程还原成二值数字图像水印信息二值数字图像水印信息是大小为S×Q的矩阵，为二值数字图像水印信息的第s行、第q列位置上的元素，由于重构过程中，二值数字图像水印信息可能出现误差，为此，可以设置适当阈值，对误差进行校正，如设定阈值为0.5，当时，将0赋值于当将1赋值于w_s,q，得到最终结果至此，水印的提取过程结束，提取出的二值数字图像水印即可用来证明版权所有者的合法性，Restore one-dimensional watermark information to binary digital image watermark information according to the reverse process of column-by-column scanning Binary digital image watermark information is a matrix of size S×Q, Watermark information for binary digital images The elements at the s-th row and q-th column position of , due to the error may occur in the binary digital image watermark information during the reconstruction process, for this reason, an appropriate threshold can be set to correct the error, such as setting the threshold to 0.5, when , assign 0 to when Assign 1 to w_s,q to get the final result At this point, the watermark extraction process is over, and the extracted binary digital image watermark can be used to prove the legitimacy of the copyright owner.

下面结合实验数据和实验结果以及附图来说明本实施方式的优越性：The superiority of this embodiment is described below in conjunction with experimental data, experimental results and accompanying drawings:

实验采用5令该×5令该lena灰度图像作为原始载体图像，如附图3(a)所示，水印图像采用二值字母图像，如附图3(b)所示，信号采样率为0.7，由本实施方式算法嵌入水印后得到的含水印图像如附图3(c)所示，直接从中提取水印如附图3(d)所示；The experiment uses the lena grayscale image of 5 order × 5 order as the original carrier image, as shown in Figure 3(a), the watermark image uses binary letter image, as shown in Figure 3(b), the signal sampling rate is 0.7, the watermarked image obtained after embedding the watermark by the algorithm of this embodiment is shown in Figure 3 (c), and the watermark is directly extracted from it as shown in Figure 3 (d);

计算含水印图像与原始图像的PSNR(最大峰值信噪比)为：44.1289dB，直接从中提取水印的NC(归一化相关系数)值为：1。The calculated PSNR (maximum peak signal-to-noise ratio) of the watermarked image and the original image is: 44.1289dB, and the NC (normalized correlation coefficient) value of directly extracting the watermark from it is: 1.

在水印技术领域，通常PSNR值大于36dB被认作图像质量保真效果好，本实施方式的PSNR在44.1289dB，已经达到了很好的图像保真效果，人眼无法直接辨识含水印图像与原始载体图像的差异；In the field of watermarking technology, usually a PSNR value greater than 36dB is considered to have a good image quality fidelity effect. The PSNR of this embodiment is 44.1289dB, which has achieved a very good image fidelity effect. The human eye cannot directly distinguish between the watermarked image and the original Differences in carrier images;

附图4(a)和附图4(b)是在不同的采样率下含水印图像与原始图像的PSNR以及NC情况；Accompanying drawing 4 (a) and accompanying drawing 4 (b) are PSNR and NC situation of watermarked image and original image under different sampling rates;

由图可以看出在采样率小于0.4之后NC值才开始出现缓慢下降，但NC值始终能维持在0.98以上，具有很强的可压缩能力；采样率越小，压缩后的水印信息对原始载体图像的图像质量影响越小，当采样率为0.4时，PSNR已经达到47dB以上，分别高出文献“TsaiP,HuYC,and Yeh H L.Reversible image hiding scheme using predictive coding andhistogram shifting[J].Signal Processing,2009,89(6):1129-1143”与文献“Jun Lang，Zheng-Guang Zhang.Blind digital watermarking method in the fractional Fouriertransform domain[J].Optics and Lasers in Engineering,2013,4(53):112-121”中描述的算法10dB和7dB，由此可见，本实施方式含水印图像的图像质量比其他算法显著增强。It can be seen from the figure that the NC value begins to decline slowly after the sampling rate is less than 0.4, but the NC value can always be maintained above 0.98, which has a strong compressibility; the smaller the sampling rate, the compressed watermark information is more important to the original carrier. The image quality of the image is less affected. When the sampling rate is 0.4, the PSNR has reached more than 47dB, which is higher than the literature "TsaiP, HuYC, and Yeh H L. Reversible image hiding scheme using predictive coding and histogram shifting [J]. Signal Processing ,2009,89(6):1129-1143" and the literature "Jun Lang, Zheng-Guang Zhang. Blind digital watermarking method in the fractional Fouriertransform domain[J]. Optics and Lasers in Engineering, 2013,4(53):112 The algorithm described in -121" is 10dB and 7dB. It can be seen that the image quality of the watermarked image in this embodiment is significantly enhanced compared with other algorithms.

下面分别用多种常见的攻击方式对含水印图像进行攻击实验：The following uses a variety of common attack methods to conduct attack experiments on watermarked images:

对含水印图像进行0.005(密度)的椒盐噪声攻击，攻击后的含水印图像如图5(a)，攻击后的图像与原始图像的PSNR下降为：27.6366dB，提取水印的NC值为：0.98769，如图5(b)所示。Carry out a 0.005 (density) salt and pepper noise attack on the watermarked image. The watermarked image after the attack is shown in Figure 5(a). The PSNR of the attacked image and the original image is reduced to: 27.6366dB, and the NC value of the extracted watermark is: 0.98769 , as shown in Figure 5(b).

对含水印图像进行70(品质因数)的JPEG压缩攻击，攻击后的含水印图像如图6(a)，攻击后的图像与原始图像的PSNR下降为：31.9435dB，提取水印的NC值为：0.96705，如图6(b)所示。Perform a JPEG compression attack of 70 (quality factor) on the watermarked image. The watermarked image after the attack is shown in Figure 6(a). The PSNR between the attacked image and the original image is reduced to: 31.9435dB, and the NC value of the extracted watermark is: 0.96705, as shown in Figure 6(b).

对含水印图像进行0.005(均方差)的高斯白噪声攻击，攻击后的含水印图像如图7(a)，攻击后的图像与原始图像的PSNR下降为：23.1053dB，提取水印的NC值为：0.96024，如图7(b)所示。Carry out a Gaussian white noise attack of 0.005 (mean square error) on the watermarked image. The watermarked image after the attack is shown in Figure 7(a). The PSNR between the attacked image and the original image is reduced to: 23.1053dB, and the NC value of the extracted watermark is : 0.96024, as shown in Figure 7(b).

对含水印图像进行64×64(像素)的剪切攻击，攻击后的含水印图像如图8(a)，攻击后的图像与原始图像的PSNR下降为：20.4162dB，提取水印的NC值为：0.95671，如图8(b)所示。Carry out a 64×64 (pixel) clipping attack on the watermarked image. The watermarked image after the attack is shown in Figure 8(a). The PSNR between the attacked image and the original image is reduced to: 20.4162dB, and the NC value of the extracted watermark is : 0.95671, as shown in Figure 8(b).

由以上实验结果可知，本实施方式的水印算法对多种常见攻击方式都有较好的抵抗能力，具有一定的鲁棒性，而目前采用压缩感知理论的数字图像水印算法如文献“赵春辉，刘巍.基于压缩感知的交互支持双水印算法[J].电子学报，2012，40(4)：609-617”，文献“林婉娟.压缩感知重建算法及其在数字水印中的应用[D].北京：北京交通大学，2011.”及文献“陈国法，郭树旭，李杨等.基于压缩感知的数字图像水印算法[J].现代电子技术，2012，35(13)：98-100”中均未实现对多种常见攻击方式的全面抵抗。由此可见，本算法比现有压缩感知水印算法存在优越性；From the above experimental results, it can be seen that the watermarking algorithm in this embodiment has good resistance to many common attack methods and has certain robustness. However, the current digital image watermarking algorithm using compressive sensing theory such as the literature "Zhao Chunhui, Liu Wei. Interactive support double watermarking algorithm based on compressed sensing [J]. Electronic Journal, 2012, 40(4): 609-617", literature "Lin Wanjuan. Compressed sensing reconstruction algorithm and its application in digital watermarking [D]. Beijing: Beijing Jiaotong University, 2011." and "Chen Guofa, Guo Shuxu, Li Yang, etc. Digital Image Watermarking Algorithm Based on Compressive Sensing [J]. Modern Electronic Technology, 2012, 35(13): 98-100". Realize comprehensive resistance to many common attack methods. It can be seen that this algorithm has advantages over existing compressive sensing watermarking algorithms;

对含水印图像进行噪声、压缩、剪切等多种类型，多种强度的攻击，测试鲁棒性，实验结果汇总如表1所示：Various types of attacks, such as noise, compression, and shearing, etc., are performed on watermarked images to test the robustness. The experimental results are summarized in Table 1:

表1为实验结果汇总表Table 1 is the summary table of experimental results

从实验结果可以看出，本算法对各种常见攻击方式都可以保证提取的水印NC值在0.9以上，甚至绝大多数的NC值高于0.95，具有较好的鲁棒性。It can be seen from the experimental results that this algorithm can guarantee the NC value of the extracted watermark to be above 0.9 for various common attack methods, and even most of the NC values are higher than 0.95, which has good robustness.

虽然以上描述了本发明的具体实施方式，但是本领域内的熟练的技术人员应当理解，这些仅是举例说明，可以对这些实施方式做出多种变更或修改，而不背离本发明的原理和实质,本发明的范围仅由所附权利要求书限定。Although the specific embodiments of the present invention have been described above, those skilled in the art should understand that these are only examples, and various changes or modifications can be made to these embodiments without departing from the principles and principles of the present invention. In essence, the scope of the invention is limited only by the appended claims.

Claims (2)

1. a digital image watermark embedding method based on compressed sensing, it is characterised in that: comprise the following steps:

Step 1: binary digital image watermark information is carried out LS-SVM sparseness, obtains the one-dimensional watermark information of rarefaction；

Read binary digital image watermark information W=(w_s,q)_S×Q, binary digital image watermark information W be size be the square of S × QBattle array, wherein, the row of S representing matrix, the row of Q representing matrix, w_s,qS row, q row position for binary digital image watermark information WThe element put, w_s,q∈{0,1}；

Binary digital image watermark information W is scanned by column, converts thereof into one-dimensional watermark informationOne-dimensional watermark information C^wIt is a dimensional vector, total L row, and have L=S × Q；W represents binary digital image watermark information, isThe abbreviation of watermark；

One-dimensional watermark information C^wThrough discrete cosine transform, obtain the One-Dimensional Water official seal of the i.e. rarefaction of discrete cosine transform domain informationBreathThe one-dimensional watermark information D of rarefaction^wIt is a dimensional vector, total L row；

Setting degree of rarefication K, the 0 ＜ K ＜ ＜ 1 of the one-dimensional watermark information of rarefaction, sampled data output is K*L, retains K value；

Step 2: structure calculation matrix, using calculation matrix as key, with the one-dimensional watermark of the rarefaction that double secret key step 1 determinesInformation measures, it is achieved compression and the encryption to one-dimensional watermark information；

By the Ha Dema matrix-block H that P size is b × b_BlockAccording to equation below composition H:

In formula, P and b is integer, and value meets: P*b=L；The column vector of matrix H is carried out randomly ordered, then to row toAmount carries out randomly ordered, any L in matrix H after extraction sequence_csRow composition calculation matrixCalculation matrix ΦBe size be L_csThe matrix of × L,L for calculation matrix Φ_csElement on row, l column position, L_csMeet condition: L_cs＜ ＜ L, L_cs∈[K*L,L)；Cs represents compressed sensing, is the abbreviation of Compressive sensing；

Above-mentioned calculation matrix Φ is preserved as key；

By each row vector of key Φ, one-dimensional watermark information with rarefaction does inner product respectively, obtains one-dimensional watermark information closeProjection on key, i.e. measured valueMeasured value Y^wIt is a dimensional vector, L altogether_csOK；Because One-Dimensional WaterThe total amount of data of official seal breath is L, and the total amount of data of measured value is L_cs, L_cs＜ ＜ L, so measurement process achieves data compression,Again because in the case of unknown key Φ, compression process is irreversible, so compression process is also the ciphering process to data；

Step 3: read the digital picture of pending copyright protection, as initial carrier image information, retains a originalCarrier image information backup, carries out discrete cosine transform and to the discrete cosine obtained after conversion to initial carrier image informationTransform domain information carries out piecemeal, and the watermark information after step 2 being processed is embedded in carrier image and obtains containing watermarking images；

Read the digital image information of pending copyright protection, i.e. initial carrier image information A=(a_m,n)_M×N, initial carrier figureAs information A be size be the matrix of M × N, wherein, M represents capable, and N represents row, a_m,nFor initial carrier image A m row, n-thElement on column position；

Initial carrier image information A is scanned by column, converts thereof into one-dimensional initial carrier imageC^AIt is a dimensional vector, total L_AOK, L_A=M × N；

To one-dimensional initial carrier image C^ADo discrete cosine transform, obtain the discrete cosine transform domain information of initial carrier imageDiscrete cosine transform domain information D of initial carrier image^AIt is a dimensional vector, total L_AOK；

By discrete cosine transform domain information D of initial carrier image^AThe low frequency part matrix-block that is divided into size to be B × 1,In formulaFor rounding downwards symbol, B is the line number of matrix-block, and β is coefficient of dilatation, and have β ∈ (0,0.5],It is used for regulating the size of piecemeal, discrete cosine transform domain information D of initial carrier image^AAltogether it is divided intoBlock,For the symbol that rounds up；

Then by watermark information measured valueIt is embedded into the discrete cosine transform domain of initial carrier imageInformation D^AFront L_csIn each piecemeal the first row data of individual piecemeal, this process can be described as:

In formula, step (1)Be equivalent to all of elementSeparately save asRepresent D^AIn element；α ∈ (0,1) is the weights of regulation embedment strength, and α is the biggest, and embedment strength is the biggest, and watermark robustness is the strongest, embeds waterAfter print, carrier image quality decrease is the biggest, otherwise, α is the least, and watermark robustness is the most weak, and after embedding watermark, carrier picture quality is moreGood；The carrier image discrete cosine transform domain information containing watermark is obtained after embedding watermarkIt is oneDimensional vector, line number is L_A；Represent watermark information measured value Y^wIn element；RepresentIt isIn element；

Carrier image discrete cosine transform domain information containing watermarkDo inverse discrete cosine transform, obtain the one-dimensional image containing watermarkInformationThe one-dimensional image information containing watermarkIt is a dimensional vector, total L_AOK；

By the one-dimensional image information containing watermarkAccording to the inverse process scanned by column be recovered to size be M × N containing watermarking imagesFor containing watermarking imagesM row, element on the n-th column position；

The telescopiny of watermark terminates, and step 1, step 2 and step 3 need to retain the sparse of the one-dimensional watermark information of rarefaction respectivelyDegree K, key Φ, coefficient of dilatation β, weights α and the backup of initial carrier image.

2. a digital image watermark extraction method based on compressed sensing, processes the digital watermarking figure obtained to claim 1As processing, it is characterised in that: comprise the following steps:

Step 1: read in containing watermarking images and initial carrier backup image respectively, both are done respectively discrete cosine transform, obtainsContaining watermarking images discrete cosine transform domain information and initial carrier image discrete cosine transform domain information, calculate one-dimensional watermark informationMeasured value；

Read containing watermarking imagesContaining watermarking imagesBe size be the matrix of M × N,For containing watermarking imagesM row, element on the n-th column position；

Read the backup of initial carrier image information, initial carrier image information A=(a_m,n)_M×NBe size be the matrix of M × N,a_m,nFor the element on the m row of initial carrier image information A, the n-th column position；

Initial carrier image information A is scanned by column, converts thereof into one-dimensional initial carrier imageC^AIt is a dimensional vector, total L_AOK, L_A=M × N；

To containing watermarking images informationIt is scanned by column, converts thereof into one-dimensional containing watermarking images informationIt is a dimensional vector, total L_AOK；

One-dimensional original image information C^ADo discrete cosine transform and obtain the discrete cosine transform domain information of initial carrier imageDiscrete cosine transform domain information D of initial carrier image^AIt is a dimensional vector, total L_AOK；

One-dimensional containing watermarking images informationDo discrete cosine transform and obtain the carrier image discrete cosine transform domain information containing watermarkBeing a dimensional vector, line number is L_A；

By discrete cosine transform domain information D of initial carrier image^AWith the carrier image discrete cosine transform domain information containing watermarkCarrying out piecemeal respectively, piecemeal size is B × 1 matrix, and B is identical, i.e. with the value of B in watermark telescopiny hereinB is the line number of matrix-block,It is to round downwards symbol, L_csBeing the line number of key Φ, can be tried to achieve by key Φ, β is flexible systemNumber, β is used for regulating the size of piecemeal, and the value of β is identical with the β value in telescopiny；The discrete cosine of initial carrier image becomesChange domain information D^AWith the carrier image discrete cosine transform domain information containing watermarkIt is divided into respectivelyBlock；It is upwardsRound symbol；

Will the two front L_csEach piecemeal the first row data correspondence of individual piecemeal seeks difference, and formula is:

${\hat{y}}_{j+1}^w=\frac{{\hat{d}}_{B*j+1}^A-d_{B*j+1}^A}{\mathrm{\&alpha;}},(j=0,1,\mathrm{...},L_{cs}-1);$

In formula,RepresentIn element；Represent D^AIn B*j+1 (j=0,1 ..., L_cs-1) individual element；RepresentIn B*j+1 (j=0,1 ..., L_cs-1) individual element；α is the weights α preserved in watermark telescopiny, by calculatingObtain one-dimensional watermark information measured valueOne-dimensional watermark information measured valueIt is a dimensional vector,L altogether_csOK；

Step 2: call in key, decompresses one-dimensional watermark information；

One-dimensional watermark information is decompressed by application subspace tracing algorithm, reconstructuring water-mark information:

Subspace tracing algorithm needs the signal of input to be respectively as follows: one-dimensional watermark information measured valueKey Φ, degree of rarefication K,Application subspace tracing algorithm decompression reconstructs the one-dimensional watermark information of rarefaction；

Step 3: the one-dimensional watermark information after rarefaction reverts to binary digital image watermark information；

The one-dimensional watermark information of rarefaction is carried out inverse discrete cosine transform, is converted into one-dimensional watermark information, then by one-dimensional watermarkInformation is recovered to, according to the inverse process scanned by column, the digital figure watermark information that size is M row N row.