基于快速曲波变换的数字水印算法

第二代曲波理论采用了新的框架结构，参数减少，实现更加简单。基于非均匀采样的快速Fourier变换（usfft算法）和基于特殊选择的Fourier采样的卷绕(wrapping算法)是第二代曲波理论的两种快速数值实现方法。为适应大图像的数字水印，本文结合快速曲波算法的特点和人类视觉特征，设计了一种快速的数字水印算法。仿真研究结果表明，基于usfft算法和基于wrapping算法的数字水印算法都能较好的保证了数字水印的鲁棒性和不可见性之间的统一，并且基于wrapping算法在提高了运行速度方面效果更加显著。

Digital Image Watermark Algorithm Based on the Fast Curvelet Transform

The second generation curvelet theory adopted a new framework which had the reduction parameter and the simple realization. It had two fast numerical implementations. The first digital transformation was based on unequally-spaced fast Fourier transform while the second was based on the wrapping of specially selected Fourier samples. To meet the large image watermark, this paper designed a fast watermark algorithm according to the characteristics of the fast curvelet algorithm and the human visual. The experimental results demonstrate that the digital image watermark algorithm based on either the usfft algorithm or the wrapping algorithm all ensures a fine unification of robustness and invisibility, and the digital image watermark algorithm based on wrapping algorithm is more significant in improving the running speed.