Coefficient difference based watermark detector in nonsubsampled contourlet transform domain

Abstract Imperceptibility and robustness are two main requirements of any image watermarking systems to guarantee desired functionalities, but there is a tradeoff between them from the information–theoretic perspective. It is a challenging work to design a high performance digital watermarking scheme to keep a trade-off between imperceptibility and robustness. By modeling the nonsubsampled Contourlet transform (NSCT) coefficient differences with ranked set sample (RSS) based Cauchy distribution and employing locally most powerful (LMP) test, we propose a locally optimum image watermark detector in NSCT domain. In the proposed scheme, we first compute the robust coefficient differences according to the inter-scale dependency between NSCT coefficients, and then embed the digital watermark into the significant NSCT coefficient difference subband. At the watermark receiver, robust NSCT coefficient differences are firstly modeled by employing the Cauchy distribution, where the statistical properties of NSCT coefficient differences are captured accurately. Then the RSS approach is introduced to estimate the location parameter and shape parameter of Cauchy distribution. And finally an optimal detector for multiplicative watermarking is developed using the LMP decision rule and RSS-based Cauchy distribution. Also, we utilize the statistical model to derive the closed-form expressions for the watermark detector. Experimental results demonstrate the high efficiency of our watermarking scheme, which can provide better imperceptibility and outstanding robustness against various attacks, in comparison with the state-of-the-art approaches recently proposed in the literature.