Contourlet domain locally optimum image watermark decoder using Cauchy mixtures based vector HMT model

Digital image watermarking has become a necessity in many applications such as data authentication, broadcast monitoring on the Internet and ownership identification. Various watermarking schemes have been proposed to protect the copyright information. There are three indispensable, yet contrasting requirements for a watermarking scheme: imperceptibility, robustness and payload. Therefore, a watermarking scheme should provide a trade-off among these requirements from the information-theoretic perspective. Generally, in order to enhance the imperceptibility, robustness and payload simultaneously, the human visual system (HVS) and the statistical properties of the image signal should be fully taken into account. The statistical model-based transform domain multiplicative watermarking scheme embodies the above ideas, and therefore the detection and extraction of the multiplicative watermarks have received a great deal of attention. The performance of a statistical model-based watermark detector or decoder is highly influenced by the accuracy of the statistical model itself and the applicability of decision rule. In this paper, we firstly propose a new hidden Markov trees (HMT) statistical model in Contourlet domain, namely Cauchy mixtures-based vector HMT (vector CMM–HMT), by describing the marginal distribution with Cauchy mixture model (CMM) and grouping Contourlet coefficients into a vector, which can capture both the subband marginal distributions and the strong dependencies across scales and orientations of the Contourlet coefficients. Then, by modeling the Contourlet coefficients with vector CMM–HMT and employing locally most powerful (LMP) test, we develop a locally optimum image watermark decoder in Contourlet domain. We conduct extensive experiments to evaluate the performance of the proposed blind watermark decoder, in which encouraging results validate the effectiveness of the proposed technique, in comparison with the state-of-the-art approaches recently proposed in the literature.