Blind image watermark decoder in NSST-FPCET domain using Weibull Mixtures-HMT

Balancing imperceptibility, robustness, and data payload is a key topic in digital watermarking technology. Many contributions point to statistical modeling as an effective solution to this problem. On the basis of this, in this paper, we devise a hybrid domain image watermark decoder based on Weibull mixtures based hidden Markov tree (Weibull Mixtures-HMT) model. In the embedding phase, Otsu-Canny edge detection method is used to map the positions of high entropy blocks to the target subband obtained by non-subsampled shearlet transform (NSST), and fast polar complex exponential transform (FPCET) is computed in the target blocks to obtain the NSST-FPCET domain. The watermark signals are embedded into NSST-FPCET magnitudes by a linear method. In the extraction phase, NSST-FPCET magnitude coefficients are modeled by Weibull Mixtures-HMT model, which describes the distribution characteristics as well as the dependencies of NSST-FPCET magnitudes. The efficient variance reduced stochastic expectation maximization method is employed for estimating the parameters of Weibull Mixtures-HMT model. A statistical image watermark decoder in NSST-FPCET domain is finally achieved by the maximum likelihood decision. Massive experiments are performed so as to confirm the superiority of the designed scheme in trade-off among the data payload, imperceptibility, and robustness.