中文摘要：

图像加密技术一直是图像处理中的热点问题,把分数阶微积分引入图像加密技术中更是当代前沿研究课题.本文基于分数阶微积分及分数阶Fourier变换的方法,提出了一种新的数字水印算法.该算法在分数阶傅里叶域嵌入水印,分数阶微积分阶次以及分数阶Fourier变换的变换阶数为数字水印的安全性提供了保证.随后作者用相关性检测的方法来提取水印.最后作者通过对算法仿真以及加密图像的抗攻击性能进行测试,发现本文提出的数字水印算法有较好的不可感知性,且对噪声、旋转、剪切等攻击具有良好的鲁棒性.

英文摘要：

This article focuses on image encryption,which has been a hot topic in image processing area for a long time.A digital watermarking algorithm is proposed based on fractional calculus and discrete fractional Fourier transform.In this algorithm,watermarks are embedded in the fractional Fourier domain,and it is extracted by correlation detection method.The operational order of fractional calculus and the fractional Fourier transform underlie the security of the digital watermark.By simulations and tests of anti-attack performance,the invisibility of the algorithm on robust to noise,crop,rotation and other attacks are verified.