四元数调制重叠变换及其在双彩色图像数字水印中的应用

Modulated quaternion lapped transform and its application in dual color image watermarking

为了整体处理彩色图像,基于四元数彩色图像表示方法和四元数代数理论,定义了四元数调制重叠变换(MQLT),将传统的主要针对灰度图像的复数调制重叠变换(MCLT)推广应用于彩色图像处理中.然后,通过建立MQLT系数与彩色图像三通道传统MCLT系数之间的关系,分析了MQLT系数的对称特性,并基于MQLT变换及其系数对称特性,结合Arnold变换和冗余嵌入策略,提出了一种鲁棒的双彩色图像盲水印算法.为了避免水印能量损失,修改系数嵌入水印时遵循了系数的对称性.所提算法充分利用了四维频域空间,将有意义的彩色水印嵌入到彩色载体图像中.实验结果表明,所提算法在不可见性和鲁棒性2个方面均明显优于采用传统三通道分别处理思想的MCLT算法.

In order to process color images holistically,by using the quaternion representation of col-or images and the algebra of quaternion,modulated quaternion lapped transform （MQLT）is defined to generalize the conventional modulated complex lapped transform （MCLT）for gray images and applied into the process of color images.Then,the symmetric properties of the MQLT coefficients are analyzed after the establishment of the relationships between the MQLT coefficients and the MCLT coefficients of three channels.Finally,combining with the Arnold transform and multiple re-dundant embedding strategy,a robust blind dual color image watermarking algorithm is proposed based on MQLT and its symmetric property.In order to avoid watermark energy loss,the MQLT coefficients are modified to embed watermarks according to their symmetric properties.The proposed algorithm fully utilizes four-dimensional MQLT domain and embeds a meaningful color watermark into a color host image.The experimental results show that the proposed algorithm is superior to the conventional component-wise algorithm based on the MCLT in terms of invisibility and robustness.