Digital image watermarking has become a necessity in many applications such as data authentication, broadcast monitoring on the Internet and ownership identification. Various watermarking schemes have been proposed to protect the copyright information. There are three indispensable, yet contrasting requirements for a watermarking scheme: imperceptibility, robustness and payload. Therefore, a watermarking scheme should provide a trade-off among these requirements from the information-theoretic perspective. Generally, in order to enhance the imperceptibility, robustness and payload simultaneously, the human visual system (HVS) and the statistical properties of the image signal should be fully taken into account. The statistical model-based transform domain multiplicative watermarking scheme embodies the above ideas, and therefore the detection and extraction of the multiplicative watermarks have received a great deal of attention. The performance of a statistical model-based watermark detector or decoder is highly influenced by the accuracy of the statistical model itself and the applicability of decision rule. In this paper, we firstly propose a new hidden Markov trees (HMT) statistical model in Contourlet domain, namely Cauchy mixtures-based vector HMT (vector CMM-HMT), by describing the marginal distribution with Cauchy mixture model (CMM) and grouping Contourlet coefficients into a vector, which can capture both the subband marginal distributions and the strong dependencies across scales and orientations of the Contourlet coefficients. Then, by modeling the Contourlet coefficients with vector CMM-HMT and employing locally most powerful (LMP) test, we develop a locally optimum image watermark decoder in Contourlet domain. We conduct extensive experiments to evaluate the performance of the proposed blind watermark decoder, in which encouraging results validate the effectiveness of the proposed technique, in comparison with the state-of-the-art approaches recently proposed in the literature.

数字图像水印已成为许多应用程序中的必要条件，例如数据身份验证，Internet上的广播监视和所有权标识。已经提出了各种水印方案来保护版权信息。对于水印方案，存在三个必不可少的但又相反的要求：不可感知性，鲁棒性和有效载荷。因此，从信息理论的角度来看，水印方案应该在这些要求之间进行权衡。通常，为了同时增强感知力，鲁棒性和有效载荷，应充分考虑人类视觉系统（HVS）和图像信号的统计特性。基于统计模型的变换域乘法水印方案体现了上述思想，因此，乘法水印的检测和提取受到了广泛的关注。基于统计模型的水印检测器或解码器的性能在很大程度上受到统计模型本身的准确性和决策规则的适用性的影响。本文首先通过用柯西混合模型（CMM）描述边际分布并分组Contourlet，提出了一种新的Contourlet域隐马尔可夫树（HMT）统计模型，即基于柯西混合物的矢量HMT（矢量CMM-HMT）。系数转换成向量，可以捕获子带边际分布以及Contourlet系数的各个尺度和方向的强相关性。然后，通过使用向量CMM-HMT对Contourlet系数建模并采用局部最强大的（LMP）测试，我们在Contourlet域中开发了一种局部最优的图像水印解码器。我们进行了广泛的实验，以评估所提出的盲水印解码器的性能，与最近文献中提出的最新方法相比，令人鼓舞的结果证实了所提出技术的有效性。