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中文摘要：
针对数字图像的版权保护问题,提出了一种基于非下采样剪切波变换（NSST,non-subsam-pled shearlet transform）和QR分解的零水印算法。首先,采用NSST对宿主图像进行分解;然后利用Logistic混沌系统从分解后的低频逼近分量中随机抽取出一幅子图,并将其分割成互不重叠的子块;最后对每一个子块进行QR分解,通过判断各个子块R矩阵中第1行元素向量的l1范数和所有子块R矩阵第1行元素向量l1范数的均值之间的大小关系构造零水印。实验结果表明,本文算法对添加噪声、滤波、JPEG压缩和剪切具有很强的鲁棒性,同时还能抵抗一定程度的旋转、缩放和平移（RST）几何攻击。
英文摘要：
A novel zero-watermark algorithm is proposed based on non-subsampled shearlet transform（NSST） and QR decomposition for copyright protection of digital images.In this method,the host image is processed with NSST firstly,and a sub-image is extracted from the low-frequency component randomly by the Logistic chaotic system.Then the sub-image is divided into non-overlapping sub-blocks,and each sub-block is processed with QR decomposition,so the zero-watermark is derived by judging the numerical relationship between vector l1 norm from the first row elements of each sub-block＇s R-matrix and the mean of vector l1 norms from the first row elements of all sub-blocks＇ R-matrices.Experimental results show that the method is very robust to adding noise,filtering,JPEG compression and cropping,and can resist on the geometrical attack of rotation,scaling and translations（RST） to some extent.
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