联合非下采样Contourlet变换与奇异值分解的多水印算法

Multiple watermarks algorithm based on nonsubsampled Contourlet transform and singular value decomposition

为解决最近报道的Contourlet变换域基于奇异值分解的水印算法存在的高虚警率问题,提出一种多水印算法。对Arnold置乱后的水印图像进行奇异值分解,将其中一个正交矩阵嵌入原始图像非下采样Contourlet域的两个高频方向子带中,并利用奇异值来调整原始图像非下采样Contourlet域剩余子带的系数矩阵,通过逆变换得到含水印图像。抽取水印时首先计算从待检测图像抽出的正交矩阵和真实水印正交矩阵的相似度,与阈值进行比较,以决定抽取过程是否进行。由于非下采样Contourlet变换的高冗余性,最终可抽取出多个水印图像。实验表明,算法较好地克服了高虚警率问题。一系列的攻击实验证明算法具有较好的鲁棒性。

In order to solve the high false alarm rate flaw in Contourlet transform domain based on singular value decomposition watermarking algorithms reported recently, this paper proposed a multiple watermarks algorithm. Arnold scrambled watermark image was decomposed with singular value decomposition, then an orthogo-nal matrix was embedded into the two high frequency directional subbands of original image in the nonsubsampled Contourlet domain. By using the singular values to adjust the rest nonsubsampled Contourlet transform coefficient matrices of the original image, the inverse transformation was done to obtain the watermarked image. Similarity of the extracted orthogonal matrix from the image to be inspected and the real or- thogonal matrix was calculated and compared to a given threshold, to decide whether the process of extracting should proceed or not. Multiple watermark images were finally extracted due to the high redundancy of the nonsubsampled Contourlet trans- form. Experiments show that, the algorithm can solve the problem of high false alarm rate flaw. A series of experiments prove that the proposed algorithm is robustness to commom attacks.