There are three indispensable, yet contrasting requirements for a watermarking scheme: imperceptibility, robustness, and payload. Therefore, it is a challenge to obtain a tradeoff among above requirements in image watermark detection. In this paper, we propose a new statistical watermark decoder in discrete non-separable Shearlet transform (DNST) domain using singular values and Gaussian-Cauchy mixture-based vector hidden Markov tree (HMT). Our method can obtain great performance in imperceptibility, robustness and payload, and it is necessary for image copyright protection. We first perform DNST on the host image, and apply singular value decomposition (SVD) to the significant DNST domain high entropy blocks. We then embed the digital watermark into the DNST high entropy blocks by modifying the robust singular values. At the receiver, by combining the Gaussian-Cauchy mixture-based vector HMT and maximum likelihood (ML) decision, we propose a new blind image watermark decoder in DNST domain. Here, robust DNST domain singular values are firstly modeled by using Gaussian-Cauchy mixture-based vector HMT, where the Gaussian-Cauchy mixture marginal distribution and various strong dependencies of DNST domain singular values are incorporated. Then the statistical model parameters of Gaussian-Cauchy mixture-based vector HMT are estimated using parameter-expanded expectation–maximization (PXEM) approach. And finally, a blind image watermark decoder is developed using Gaussian-Cauchy mixture-based vector HMT and ML decision rule. The major contribution of this paper is the use of singular value, Gaussian-Cauchy mixture-based vector HMT and PXEM algorithms, which enhances the performance of watermarking scheme. Experimental results on some test images and comparison with well-known existing methods demonstrate the efficacy and superiority of the proposed method.

对于水印方案，有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，在图像水印检测中在上述要求之间取得折衷是一个挑战。在本文中，我们提出了一种新的统计水印解码器，该算法使用奇异值和基于高斯-考奇混合的矢量隐藏马尔可夫树（HMT）在离散不可分Shearlet变换（DNST）域中。我们的方法在不易察觉性，鲁棒性和有效载荷方面都可以取得很好的性能，并且对于图像版权保护是必要的。我们首先在主机映像上执行DNST，然后将奇异值分解（SVD）应用于重要的DNST域高熵块。然后，通过修改鲁棒的奇异值，将数字水印嵌入到DNST高熵块中。在接收方，通过结合基于高斯-考奇混合的矢量HMT和最大似然（ML）决策，我们提出了一种新的DNST域盲图像水印解码器。在此，首先使用基于高斯-考奇混合的矢量HMT对鲁棒的DNST域奇异值进行建模，其中结合了高斯-考奇混合边际分布和DNST域奇异值的各种强相关性。然后使用参数扩展期望最大化（PXEM）方法估计基于高斯-考奇混合向量的HMT的统计模型参数。最后，利用基于高斯-考奇混合的矢量HMT和ML决策规则，开发了一种盲图像水印解码器。本文的主要贡献是使用奇异值，基于高斯-考奇混合的矢量HMT和PXEM算法，从而提高了水印方案的性能。在一些测试图像上的实验结果以及与已知的现有方法的比较证明了该方法的有效性和优越性。