目的 针对增强奇异值分解（BN-SVD）中引入最抗攻击缩放比例的参数，需要进行大量的实验来获取且具有随机性的问题，提出一种增强奇异值分解的自适应零水印算法。方法 首先对原始图像进行不重叠分块，每一个子块都做斜变换处理，再分别对斜变换后得到的每一个块矩阵进行增强奇异值分解，依据每一个块矩阵的最大奇异值与整体最大奇异值均值的大小关系构成特征向量；对水印图像进行Arnold变换和混沌映射得到二次加密的水印图像；最后利用特征向量与二次加密后的水印图像做异或运算构造零水印；利用天牛须优化算法(BAS)中的适应度函数循环迭代自适应确定参数，更好的解决SVD算法在水印的提取时存在的虚警率和对角线失真的问题。结果 仿真实验结果表明，在JPEG压缩、噪声、滤波、旋转、剪切以及混合攻击下，提取水印图像与原水印图像的归一化系数NC值均可达到98%以上，性能较好结论 利用BAS算法自适应地确定BN-SVD中参数，找到最佳抗攻击缩放比例，增强了图像的奇异值，降低了图像矩阵在受到攻击时的敏感性。有效地解决奇异值分解带来的对角线失真和虚警错误的问题，最终提高了算法的鲁棒性。
Adaptive Zero-watermarking algorithm based on Boost normed singular value decomposition
Xiao Zhenjiu,Jiang Dong,Zhang Han,Tang Xiaoliang,Chen Hong(College of Software，Liaoning Technical University，Huludao 125105，China)
Object To solve the problem that the parameter β, which is the most anti-attack scaling ratio introduced in boost normed singular value decomposition (BN-SVD), needs a lot of experiments to obtain and has randomness, An adaptive zero-watermarking algorithm based on boost normed singular value decomposition (BN-SVD) is proposed.By using this parameter has three advantages.The first one, the singular value of the image is enlarged,the sensitivity of the image to attack is reduced, and the robustness of the algorithm is improved to some extent.The second one, singular values are limited to a certain range. The diagonal distortion problem can be solved by equalizing the gray scale in the diagonal direction.The last one, singular value vector is specialized and the corresponding relation between singular value vector and image is specialized to one. So that singular values can represent the features of the image. Thus, the problem of false alarm error is solved .Method First, the original image is divided into non-overlapping blocks, and then the slant transform(ST) is utilized to each block matrix. Boost normed singular value decomposition(BN-SVD) was used to each block matrix after slant transformation to achieve a maximum singular value and a feature vector was created by comparing the maximum singular value with the average of the maximum singular value the maximum singular value. The watermark image was processed by Arnold transformation and Logistic map to obtain an encrypted and scrambling double-encrypted watermark image. Finally, the zero watermark is constructed by using the feature vector and the double-encrypted watermark image to do XOR operation. In the process of optimization, the parameter β was determined by training and updating continuously through BAS fitness function.This algorithm is similar to genetic algorithm, particle swarm optimization and so on, and it does not need to know the specific function form and gradient information. The optimization process can be realized independently, and its characteristics are as follows: single individual, less computation and faster optimization speed. The algorithm is inspired by beetle search behavior. The biological principle is: the beetle is based on the strength of the food smell to find food. Two antennae were randomly used to search nearby areas. When the antennae on one side detect a higher concentration of odors, the beetles turn in direction. According to this simple principle, the beetle can find food effectively.Results Under jepg compression, rotation, filtering, clipping and other attacks, the normalized coefficients of the extracted watermark image and the original watermark image are above 98%. Selecting Lena，Baboon and as the original grayscale image, two different sizes "Liaoning Technical University" are selected as binary watermarking images and made several sets of experiments.In the experiment, normalized correlation coefficient (NC) is used to analyze the similarity between the original watermark and the extracted watermark, and the optimal parameters β of size 16 × 16 and 32 × 32 watermark images are found by BAS optimization algorithm.For the two different size watermarked images , the optimum parameter β of three gray images of Lena, Baboon and Bridge is 0.2983，0.6424，0.5332 and 0.7370、0.9914，0.8735 by using BAS .Experimental results show that with the increase of attack intensity and the increase of mixed attack, the NC value of watermark is affected, but most NC values are above 0.99. The NC value of watermark extracted after geometric attacks such as clipping and rotation is close to 1. Because the original gray image is rotated and some pixels are lost in the process of clipping, so the watermark generated is not complete.The larger the compression attack parameter, the larger the NC value, which indicates that the algorithm has better resistance to JEPG compression.For all kinds of noise attacks, the NC value of extracting watermark can reach above 0.99.Conclusion By using BAS algorithm to adaptively determine parameters β in BN-SVD.The optimal scale of scaling is found to enhance the singular value of the image and reduce the sensitivity of the image matrix when it is attacked.The problem of diagonal distortion and false alarm error caused by singular value decomposition is solved effectively and the robustness of watermarking algorithm is improved. Compared with other traditional optimization algorithms, the BAS algorithm has the advantages of short training time and fast convergence speed. It has good robustness. Combining the idea of zero watermark, the contradiction between robustness and invisibility of watermark is solved. In addition, compared with other conventional optimization algorithms, the BAS algorithm has the advantages of shorter training time and faster convergence speed. It has better robustness.Finally, the robustness of the watermarking algorithm is improved.