摘要： 为增强水印算法的鲁棒性并兼顾其虚警率和透明性，提出一种基于低频奇异值均值的零水印算法。利用离散小波变换获得载体图像的稳定低频区域，采用离散剪切波变换提取其中较优尺度的低频分量，从而构造稳定特征区域。对该区域做分块离散余弦变换并计算奇异值矩阵，通过比较分块与整体的奇异值均值大小构建特征矩阵，并将其与水印图像进行异或运算构造零水印。构造水印时采用Arnold加密提高水印图像安全性，提取水印前则利用Radon变换校正载体图像加强算法鲁棒性。对不同纹理图像进行压缩、噪声、滤波和几何攻击，实验结果表明，在保证低虚警率和良好透明性的基础上，该算法具有较强的鲁棒性，所得到的归一化互相关函数值均高于0.98，部分可达到1.00。

关键词: 离散剪切波变换, 分块离散余弦变换, Arnold变换, 奇异值分解, Radon变换, 零水印

Abstract: To enhance the robustness as well as the transparency of the watermarking algorithm while keeping the false alarm rate at a low level,this paper proposes a zero-watermarking algorithm based on low-frequency singular mean value.The algorithm acquires stable low-frequency regions of carrier images with Discrete Wavelet Transform(DWT).On this basis,the low-frequency component at a better level is obtained with Discrete Shearlet Transform(DST) to construct a stable feature region.Block Discrete Cosine Transform(DCT) is performed on the region,and the singular value matrix is calculated.The feature matrix is built by comparing the average singular values of the block and the whole.The XOR operation is performed on the feature matrix and the watermark to obtain the zero-watermarking image.The algorithm improves the security of watermarking images with Arnold encryption,and uses Radon transform to correct carrier images before extracting the watermark,so as to enhance the robustness of the algorithm.To test the algorithm,compression,noises,wave filtering and geometric attacks are performed on images of different textures.Experimental results show that the proposed algorithm has a strong robustness,with normalized cross correlation function values all breaking 0.98 and partly reaching 1,while the transparency is good and the false alarm rate is kept at a low level.

Key words: Discrete Shearlet Transform(DST), block Discrete Cosine Transform(DCT), Arnold transform, Singular Value Decomposition(SVD), Radon transform, zero-watermarking

中图分类号: 

• TP391