分数阶傅里叶变换在数字水印中的应用
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摘要
传统的图像水印技术是基于离散余弦变换,只适用于处理平稳的信号,并且离散余弦变换属于有损的数据压缩过程。而分数阶傅里叶变换可以用来处理非平稳的信号,通过对连续型分数阶傅里叶变换进行离散化采样,得到适合数值计算的离散形式,然后在频率域对幅度中间的系数使用一个随机的正态分布序列进行修改,再经过逆变换,就得到了加入水印的图像。由此提出了改进的基于分数阶傅里叶变换的随机序列水印算法。仿真结果验证了所提出的算法显著地提高了在各种攻击下水印的健壮性。
The traditional image watermarking technology is based on discrete cosine transform,the block of image is needed to add watermark,it directly results in the high complexity of the algorithm. The idea is that a 2D discrete fractional Fourier transform of the image is the computing. Then the inverse transform is applied to give the watermarked image. So it is proposed based on fractional Fourier transform of the random sequence watermark algorithm,by introducing a threshold to detect the watermark. The simulation results verify the correctness and effectiveness of the conclusion.
The traditional image watermarking technology is based on discrete cosine transform,the block of image is needed to add watermark,it directly results in the high complexity of the algorithm. The idea is that a 2D discrete fractional Fourier transform of the image is the computing. Then the inverse transform is applied to give the watermarked image. So it is proposed based on fractional Fourier transform of the random sequence watermark algorithm,by introducing a threshold to detect the watermark. The simulation results verify the correctness and effectiveness of the conclusion.
引文
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[5]李宏伟,袁保宗.高阶模糊函数的收敛性分析[J].电子学报,2000,2(1):8-12.
[6]刘庆云,李志瞬,李海英,梁红.多分量多项式相位信号的参数估计[J].电子学报,2004,2(3):4-7.
[7]冀辰宇,阚一凡,焦圣喜.基于颜色提取方法的仪表彩色指针识别[J].东北电力大学学报,2012,6(3):80-82.
[8]侯一民,贺广文,张娜,白佳文.基于能量图匹配的步态识别方法研究[J].东北电力大学学报,2012,6(3):65-67.
[2]Pan R,Prabhakar B,Psounis K,Wischik D.SHRiNK:A Method for Enabling Scaleable Performance Prediction and Efficient Network Simulation[J].IEEE/ACM Transactions on Networking[J],2005,13(5):975-988.
[3]C.Stein.Estimation of the mean of a multivariate normal distribution.Ann.Statist,1981,9(4):1135-1151.
[4]傅里叶变换离散化的研究进展[J].中国科学,2008,3(2):1-5.
[5]李宏伟,袁保宗.高阶模糊函数的收敛性分析[J].电子学报,2000,2(1):8-12.
[6]刘庆云,李志瞬,李海英,梁红.多分量多项式相位信号的参数估计[J].电子学报,2004,2(3):4-7.
[7]冀辰宇,阚一凡,焦圣喜.基于颜色提取方法的仪表彩色指针识别[J].东北电力大学学报,2012,6(3):80-82.
[8]侯一民,贺广文,张娜,白佳文.基于能量图匹配的步态识别方法研究[J].东北电力大学学报,2012,6(3):65-67.