基于分数阶傅里叶变换和扩展变换抖动调制的鲁棒数字水印算法

Robust Watermarking Algorithm Based on Fractional Fourier Transform and Spread Transform Dither Modulation

针对现有分数阶傅里叶变换水印算法在透明性和鲁棒性等方面的不足,提出了一种基于分数阶傅里叶变换和扩展变换抖动调制的鲁棒数字水印算法。首先对载体图像进行提升小波分解,将低频子带均匀分割,并对各子块进行分数阶傅里叶变换。然后,从频率角度构造载体向量,选择幅值系数的中低频系数构成每个子块的载体向量。在水印嵌入时,先对载体向量进行投影变换,再根据水印信息对投影后所得数据进行抖动调制。水印的提取过程采用了最小距离检测,实现了水印的盲检测。实验结果表明,该算法不仅具有很好的透明性,而且对JPEG压缩、滤波、噪声、剪切等常见的图像攻击具有良好的鲁棒性。此外,所提算法水印的安全性和实用性也优于常见算法。

Aiming at the existent algorithms＇ defects in transparency and robustness,a new robust image watermarking algorithm based on fractional Fourier transform and spread transform dither modulation was presented in this paper.First,lifting wavelet transform is performed on the original image.The lowpass subband is segmented into non-overlapping blocks,and each block is transformed by the fractional Fourier transform.Then,the low-frequency coefficients of the amplitude information are chosen to construct the host vectors depending on frequency.In the process of embedding watermark,spread transform is performed on the host vectors to obtain the projected host vectors,and then the binary watermark is embedded using dither modulation.A minimum distance decoder is used to decode the watermark.The experimental results show that the proposed algorithm can obtain better transparency as well as robustness against common image attacks such as JPEG compression,filtering,noisy,cropping and so on.Compared with previous similar schemes,the presented method achieves higher practicality and reliability.