Abstract: In order to solve the problem of perceptible quality degradation and the inherent conflict between imperceptibility and robustness, a novel image watermark algorithm based on Non-negative Matrix Factorization（NMF） and Discrete Wavelet Transform（DWT） is proposed in this paper. The processes of watermark embedding include three steps：the original image is divided to not-overlap image blocks and then decomposable coefficients are obtained by three-level DWT in every image blocks. Secondly the low-frequency coefficients of block images are selected and then approximately represented as a product of a base matrix and a coefficient matrix using NMF. Finally the feature vector represent original image is obtained by quantizing coefficient matrix, and then the copyright information is embedding by calculating the watermark and feature vector. Experimental results show that the scheme is robust against common signal processing attacks, meanwhile security of the algorithm is guaranteed by using secret keys.

Key words: digital watermarking, zero-watermarking, discrete wavelet transform, non-negative matrix factorization, robust

摘要： 为了解决现有数字水印中鲁棒性和不可感知性之间的矛盾，设计了一种基于非负矩阵分解和离散小波变换的图像零水印算法。原始图像进行不重叠分块，分别对每子块图像进行3级小波分解得到低频近似分量；对细节分量作非负矩阵分解得到可近似表示子块图像的基矩阵和系数矩阵；将系数矩阵量化得到特征向量，通过特征向量和水印的运算得到原始图像的版权信息。实验结果表明该方案对常见信号处理具有很强的鲁棒性，同时密钥的使用保障了算法的安全性。

关键词: 数字水印, 零水印, 离散小波变换, 非负矩阵分解, 鲁棒性