Locally optimum watermark decoder in NSST domain using RSS-based Cauchy distribution

Abstract

It is important to consider the tradeoff between imperceptibility and robustness requirements in developing an image-watermarking technique, some statistical model-based image watermarking schemes have been designed in the past decade. The effectiveness of a statistical watermark decoder depends highly on the modeling of the transform-domain coefficients and the use of hypothesis testing. In this study, a multiplicative image watermarking scheme is proposed in the nonsubsampled Shearlet transform (NSST) domain, where NSST coefficients are modeled by ranked set sample (RSS) based Cauchy statistical distribution and locally most powerful (LMP) test criterion is applied. Digital image watermarking technique consists of two parts, namely, embedding and extracting. In the embedding process, to achieve relatively good imperceptibility and robustness, watermark data is inserted into the significant NSST directional subband that has the highest energy value, by modifying nonlinearly the significant NSST coefficients. In the extracting phase, a scheme is proposed for designing a blind NSST domain watermark decoder incorporating the RSS based Cauchy statistical distribution and LMP test criterion. Here, the RSS method is used to estimate the location parameter and shape parameter of Cauchy statistical distribution instead of traditional maximum-likelihood (ML) method, which can provide the Cauchy model with higher precision parameters. Experimental results on a set of standard test images show significant improvements in imperceptibility and robustness using the proposed method compared with the best known state-of-the-art approaches.