分数傅里叶域数字水印算法

基于离散分数傅里叶变换(DFRFT)快速算法发展了一种分数傅里叶谱域图像水印算法.该算法根据分数傅里叶变换谱具有空域和频域双域信息表达能力,分别对原始图像和所加水印信息进行不同级次的分数傅里叶变换,提取水印分数傅里叶谱的低频成分并直接将其叠加到原始图像的分数傅里叶谱中的对角像元上,然后再进行逆变换得到水印图像.在JPEG压缩、图像旋转及剪切等攻击方式下,对该水印算法进行了鲁棒性分析,数值实验表明该水印算法具有良好的抗攻击性和安全性.

Fractional Fourier Domain Digital Watermarking

A fractional Fourier domain digital image watermarking scheme has been proposed based the fast discrete fractional Fourier transform (DFRFT). The algorithm takes the advantage of space and frequency double domain signal representation property of the fractional Fourier transform. The original image and the watermark sequence are firstly fractional Fourier transformed with different orders, and then only lower 'frequency' coefficients in the fractional spectrum of the watermark sequence are selected and added to the diagonal pixels in the fractional spectrum of the original image. The final watermark image is obtained by inversely transforming the joint spectra. The robustness of the watermark under different attacks such as JPEG compression, image rotation and histogram equalization has also numerically been analyzed. Numerical simulations have demonstrated that this watermarking scheme has better performances of security and anti-attack.