Her变换的数字水印算法

经对目前数字水印变换域算法的研究,发现常用的变换大多都是正交变换（如DCT和DWT等）。作者通过对Haar函数系、Haar类函数系和Walsh函数系这三大类正交函数系的研究,找到了与之对应的三类性能优良的正交变换,Her类正交变换就是其中的一种。由于Her函数系所对应的Her矩阵不是归一化的正交矩阵,所以不能像DCT等矩阵一样直接应用于数字水印技术,通过对Her连续函数的采样,得出了其对应的离散矩阵,然后通过一系列的实验数据和理论证明,成功的将其应用于数字水印中。最后,提出一种新颖的、鲁棒的Her域盲水印算法。实验结果表明该算法计算简单,且具有良好的不可见性,通过与传统DCT水印的对比表明,该算法在抵抗噪声和和滤波等方面具有较强的鲁棒性。

Watermarking algorithm based on Her transform

Most transformations used for digital watermarking in transformation domain are orthogonal transformations, such as DCT and DWT. Three types of orthogonal transformation with excellent performance are found by studying three systems of orthogonal functions: Haar function system, Haar type function system and Walsh function system. Her transformation is one of the three transformations. Her function system can not be used directly in digital watermarking as DCT matrix being used, since Her matrix of Her function system is not normalized orthogonal matrix. The corresponding discrete matrix is obtained by sampling Her continuous functions, and successfully used in digital watermarking with a series of experiments and theoretical analysis. A digital watermarking algorithm based on Her transformation is proposed. Experimental results show that the algorithm is simple and good at perceptual transparency as well as robustness of watermarking extraction. In addition, the experimental results of comparing with the traditional DCT watermarking show that this algorithm is of good robustness against noise and filtering.