基于菲涅耳变换与全变分分解的鲁棒水印算法

为了兼顾水印算法的透明性与抗几何变换能力，引入光学加密方法，提出了基于相位截断菲涅耳变换与全变分分解的鲁棒水印算法。引入Logistic映射，通过对其迭代来获取混沌序列，以构建一个随机掩码；基于Fresnel变换，联合随机掩码，对水印信息完成光学加密；再利用相位截断机制，得到2个私钥。借助全变分分解方法来处理宿主图像，获取卡通与纹理部分；引入离散小波变换(DWT)，分别对加密水印与纹理部分实施分解，输出各自对应的子带信息；并将这些子带信息进行融合，通过可逆DWT方法，获取嵌入水印后的纹理信息；通过组合水印纹理部分与初始的卡通部分，形成水印图像。设计水印检测机制，在水印图像中检索出编码水印，借助2个私钥来复原水印。测试数据显示：所提算法兼顾了理想的水印透明性与鲁棒性，在多种几何变换下，所复原的水印失真较小，对应的相关系数维持在0.9以上。

Robust watermarking based on Fresnel transform and total variational decomposition

In order to take into account the transparency and anti-geometric transformation ability of watermarking algorithm, by introducing the optical encryption method, the robust watermarking algorithm based on phase truncated Fresnel transform and total variational decomposition is proposed. Logistic mapping is introduced to obtain a set of chaotic sequences by iteration for constructing a random mask. Based on Fresnel transform and random mask, the optical encryption of watermarking information is completed. And then two private keys are obtained by using phase truncation mechanism. The host image is processed by total variational decomposition to obtain the cartoon and texture parts. The Discrete Wavelet Transform(DWT) is introduced to decompose the encrypted watermarking and texture parts, and the corresponding sub-band information are obtained. These sub-band information are fused and texture information embedded in watermarking is obtained by reversible DWT method. The watermarking image is formed by combining the watermarking texture part with the original cartoon part. The watermarking extraction method is designed to detect the encrypted watermarking information from the watermarking image, and two private keys are adopted to decrypt the encrypted watermarking information. The test data show that this algorithm takes into account the ideal transparency and robustness of watermarking, and under various geometric transformations, the reconstructed watermarking distortion is small with corresponding correlation coefficient above 0.9.