面向小波域的加权分数阶微积分图像数字水印新算法

针对现有加密技术易被破解，算法缺乏初值敏感性的问题，提出了一种采用分数阶微分和交换小波变换系数的图像数字水印的新算法。该算法充分利用了分数阶微分阶次具有极强的敏感性的特点，首先采用分数阶Cauchy公式对正弦信号做两个不同阶次的微分，同时将微分信号分别采样后加权叠加成伪随机序列；然后用此伪随机序列置乱水印，通过交换Haar小波分解的载体图像的高频系数将置乱水印嵌入载体图像。实验结果表明，提出的新算法能经受多种常见图像处理的攻击，具有较强的鲁棒性和较好的不可见性，能够实现较好的图像数字水印效果。

New image digital watermark algorithm with weighted fractional calculus based on wavelet coefficients

In this paper, a novel digital watermark algorithm, based on fractional calculus and wavelet transform, for still images is proposed. It makes fully use of the characteristic of the fractional order that is highly sensitive. The algorithm makes sinusoidal signal by fractional Cauchy formula with two differential orders. The sampled signals of the differential signals were superimposed as the pseudo-random sequence which is used to scramble the watermark. By exchanging the high-frequency coefficients of the carrier image, the scrambled watermark was embedded into the carrier image. Several experiments to verify the proposed method are given and the results show that this novel algorithm is robust to a number of regular geometric attacks and other image processing operations. The new method has a good performance on both robustness and invisibility.