矩阵三角分解在数字水印中的应用

将非奇异矩阵进行三角分解是一种将复杂矩阵变换为简单矩阵的方法，也是分析矩阵特性的方法。而数字图像也可以看作矩阵，根据图像的这一特点结合小波变换提出一种鲁棒性较好的水印算法。首先对图像进行离散小波分解，分解的尺度由水印信息量大小决定；然后计算分解后最高尺度的细节矩阵的方差，选择方差最大的一个进行预处理，若其是奇异矩阵，通过一个置换矩阵将其转换为非奇异矩阵，这里置换矩阵可以当作密钥；然后对其进行LU分解，得到两个具有良好分布特性的三角矩阵；最后将置乱后的水印信息嵌入到两个矩阵的非零像素值中。实验结果证明该算法简单易行，具有较好的鲁棒性和安全性。

Gray scale watermarking algorithm based on LU factorization

The method to decompose the non-singular matrix into two triangulars is a approach that can transform complex matrix into a simple matrix,and it is also the method of analyzing the characteristics of matrix.The digital image can be seen as a matrix,based on the characteristics of the LU Factorization,this paper presents a novel robust watermarking algorithm in wavelet domain of digital image.Firstly,the original image will be transformed into wavelet domain by DWT,and the level of which is decided by the vo...