A new watermark decoder in DNST domain using singular values and gaussian-cauchy mixture-based vector HMT

Abstract 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.