BGGMM-HMT based locally optimum image watermark detector in high-order NSST difference domain

Imperceptibility, robustness and data payload are three main requirements of any image watermarking systems to guarantee desired functionalities, but there is a tradeoff among them from the information-theoretic perspective. How to achieve this balance is a major challenge. In this paper, we propose a new statistical image watermarking scheme, which is based on the high-order difference coefficients in nonsubsampled Shearlet transform (NSST) domain and the bounded generalized Gaussian mixture model-based hidden Markov tree (BGGMM-HMT). In the watermark embedding process, we use a nonlinear embedding approach to hide the digital watermark into the robust high-order difference coefficients, which can achieve better imperceptibility. In the watermark detection process, high-order difference coefficients are accurately modeled by using BGGMMHMT, where the distribution characteristics of high-order difference coefficients can be captured through BGGMM, and the scale dependencies of high-order difference coefficients can be captured through HMT. Statistical model parameters are then estimated by combining the approach of minimizing the higher bound on data negative log-likelihood function and upward-downward algorithm. Finally, an image watermark detector based on BGGMM-HMT is developed using the locally optimum (LO) decision rule. For the proposed detector, the receiver operating characteristic (ROC) expression is derived in detail. We evaluate the proposed scheme from different aspects and compare it with the state-of-the-art schemes. After a large number of experimental tests, the encouraging results obtained prove the effectiveness of our watermarking scheme.