基于NMF及其正交投影变换的数字水印算法

A Digital Watermarking Algorithm Based on Non-Negative Matrix Factorization and Orthogonal Projection Transformation

提出一种基于非负矩阵分解(non-negative matrix factorization,NMF)及其正交投影变换的数字水印算法.利用NMF构造图像基于部分表示的基矩阵,将其正交并作为水印检测的密钥;将水印信息嵌入图像在正交基矩阵上投影的系数矩阵;再通过反变换重构图像.由于上述措施保持了NMF部分表示整体的能力,且改迭代运算为矩阵投影运算,因而算法在重构精度方面表现出明显的优势.将其应用到数字水印系统,并与文献[4]中实现的水印算法进行对比.实验结果表明,改进算法的鲁棒性更好,实用性更强.

This paper presents a watermarking algorithm based on non-negative matrix factorization （NMF） and orthogonal projection transformation. Firstly, the base matrix of an image is constructed by NMF, which is the part-based image representation. Then, the base matrix is converted perpendicularly and it is regarded as a key to extract the watermark later. The watermark is embedded into the coefficient matrix, which is made by mapping the image to the orthogonal base matrix. Finally the image is reconstructed by inverse transform of the matrix. The presented algorithm demonstrates an obvious advantage in precision of reconstruction because the basic NMF method is improved by above steps. It has been applied to the digital watermarking system and the result shows better robustness and practicability than that reported in reference .