A Blind Watermark Decoder in Nonsubsampled Shearlet Domain Using Bivariate Weibull Distribution

Digital image watermarking has become a necessity in many applications such as data authentication, broadcast monitoring on the Internet and ownership identification. There are three indispensable, yet contradictory requirements for a watermarking scheme: perceptual transparency, watermark capacity, and robustness against attacks. Therefore, a watermarking scheme should provide a trade-off among these requirements from the information-theoretic perspective. Improving the ability of imperceptibility, watermark capacity, and robustness at the same time has been a challenge for all image watermarking algorithms. In this paper, we propose a novel digital image watermark decoder in the nonsubsampled Shearlet transform (NSST) domain, wherein a PDF (probability density function) based on the bivariate Weibull distribution is used. In the presented scheme, we construct the nonlinear monotone function based adaptive high-order watermark embedding strength functions by employing the human visual system (HVS) properties, and embed watermark data into the singular values of high entropy NSST coefficients blocks. At the watermark receiver, the singular values of high entropy NSST coefficients blocks are firstly modeled by employing the bivariate Weibull distribution according to their inter-scale dependencies, then the statistical model parameters of bivariate Weibull distribution are estimated effectively, and finally a blind watermark extraction approach is developed using the maximum likelihood method based on the bivariate Weibull distribution. The experimental results show that the proposed blind watermark decoder is superior to other decoders in terms of imperceptibility and robustness.