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收稿：2018-07-10，
修回：2018-8-13，
纸质出版：2019-01-16
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目的
2
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
$$β$$
，需要进行大量的实验来获取且存在随机性的问题，提出一种增强奇异值分解的自适应零水印算法。
方法
2
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
$$β$$
，更好地解决奇异值分解（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
2
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
2
利用BAS算法自适应地确定BN-SVD中参数
$$β$$
，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。
Objective
2
Parameter
$$β$$
is the most commonly used anti-attack scaling ratio in boost normed singular value decomposition (BN-SVD). However
it requires numerous experiments to obtain and has randomness. Thus
an adaptive zero-watermarking algorithm based on BN-SVD was proposed. Using this parameter presents three advantages. First
the singular value of the image is enlarged
the sensitivity of the image to attacks is reduced
and the robustness of the algorithm is improved to some extent. Second
singular values are limited to a certain range. The diagonal distortion problem can be solved by equalizing the grayscale in the diagonal direction. Third
a singular value vector is specialized
and the corresponding relation between a singular value vector and an image is specialized to one
such that singular values can represent the features of the image. Thus
the problem of false alarm error is solved.
Method
2
First
the original image was divided into non-overlapping blocks. Then
slant transform (ST) was performed on each block matrix. BN-SVD was used on each block matrix after ST to achieve a maximum singular value
and a feature vector was created by comparing the maximum singular value with the average maximum singular value. The watermarked image was processed by Arnold transformation and logistic mapping to obtain an encrypted and scrambled double-encrypted watermarked image. Finally
the zero watermark was constructed using the feature vector
and the double-encrypted watermarked image was used for XOR operation. During optimization
parameter
$$β$$
was determined by training and updating continuously through the BAS fitness function. Similar to genetic algorithm
particle swarm optimization
and so on
the proposed algorithm does not need to know the specific function form and gradient information. The optimization process can be realized independently
and its characteristics were single individual
less computation
and faster optimization speed. The algorithm was inspired by beetle search behavior. The biological principle is as follows:the beetle relies 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 detected a higher concentration of odors
the beetles turn in that direction. According to this simple principle
the beetle can effectively find food.
Results
2
Under JPEG compression
rotation
filtering
clipping
and other attacks
the normalized coefficients of the extracted watermarked images and the original watermarked exceeded 98%. Lena
Baboon
and Bridge were selected as the original grayscale image
and two different sizes of "Liaoning Technical University" were chosen as binary watermarking images. Several sets of experiments were conducted. In the experiment
a normalized correlation coefficient (NC) was used to analyze the similarity between the original watermark and the extracted watermark
and the optimal parameters
$$β$$
for the 16×16 pixels and 32×32 pixels watermarked images were found by the BAS optimization algorithm. The optimum parameter
$$β$$
values of the three gray images of Lena
Baboon
and Bridge were 0.298 3
0.642 4
and 0.533 2 for the 16×16 pixels watermarked images and 0.737 0
0.991 4
and 0.873 5 for the 32×32 pixels watermarked images. The experimental results revealed that with the increase in attack intensity and mixed attacks
the NC value of the watermark is affected. However
most NC values exceeded 0.99. The NC value of the watermark extracted after geometric attacks
such as clipping and rotation
was close to 1. Given that the original gray image was rotated
and some pixels were lost in the clipping process
the watermark generated was incomplete. A larger compression attack parameter corresponded to a larger NC value
indicating that the algorithm had better resistance to JPEG compression. For all kinds of noise attacks
the NC value of the extracted watermark can exceed 0.99.
Conclusion
2
BAS algorithm can be used to adaptively determine parameters
$$β$$
in BN-SVD. The optimal scale of scaling enhanced the singular value of the image and reduced the sensitivity of the image matrix when attacked. The problems of diagonal distortion and false alarm error caused by singular value decomposition were solved effectively
and the robustness of the watermarking algorithm was improved. Compared with other traditional optimization algorithms
the BAS algorithm presented the advantages of short training time
fast convergence speed
and good robustness. By integrating the concept of zero watermark
the contradiction between robustness and invisibility of the watermark is solved. Thus
the robustness of the watermarking algorithm was improved.
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