Statistical image watermark decoder based on local frequency-domain Exponent-Fourier moments modeling

There are three indispensable, yet contrasting 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. In this paper, we propose a statistical image watermark decoder based on the local frequency-domain Exponent-Fourier moments modeling, which can achieve the tradeoff among imperceptibility, robustness and data payload. The frequency-domain EFMs magnitudes are first generated by combining stationary wavelet transform (SWT) and Exponent-Fourier moments (EFMs). We divide the target region to select local frequency-domain EFMs magnitudes, which are planned to embed watermarks, statistical modeling, and extract watermarks. In order to achieve an accurate modeling process, we conduct the comprehensive statistical analyses of local frequency-domain EFMs magnitudes and establish the powerful Beta Generalized Weibull mixtures-based hidden Markov tree (BGW-HMT) model, which can take into account the non-Gaussian distribution characteristic and the interscale dependency at the same time. The Expectation/Conditional Maximisation Either (ECME) algorithm and upward–downward algorithm are successfully applied to estimate the parameters of BGW-HMT model. At the receiver, the BGW-HMT model is used in the design process of watermark decoder. The decoder structure is developed by using the maximum likelihood decision. In order to prove the effectiveness of proposed watermarking scheme, multi-angle performance tests are performed, including imperceptibility, robustness, watermark capacity and time complexity. The corresponding experimental results from the above four perspectives are inspiring. Compared with the state-of-the-art schemes, our statistical decoder is significantly superior to other statistical decoders .