Locally optimum image watermark detector based on statistical modeling of SWT-EFMs magnitudes

Abstract

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. Improving the ability of imperceptibility, watermark capacity, and robustness at the same time has been a challenge for all image watermarking algorithms. The statistical model-based transform domain multiplicative watermarking is an effective way to achieve the tradeoff among imperceptibility, robustness and data payload. In this paper, we propose a locally optimum statistical image watermark detector by incorporating stationary wavelet transform (SWT), exponent-Fourier moments (EFMs), and locally optimum (LO) decision rule. SWT has many characteristics, such as high redundancy, high reconstruction accuracy, low time complexity and multi-resolution representation, and EFMs can provide the excellent robustness. In order to obtain valuable samples, we first decompose the digital image by using SWT, and then perform EFMs calculation in the corresponding frequency domain. These robust frequency-domain EFMs magnitudes are treated as the basis for the following research work. In our scheme, the watermark is hidden into the target location of frequency-domain EFMs magnitudes by using multiplicative embedding method. These magnitudes at the target location are abbreviated as SWT-EFMs magnitudes for the convenience of subsequent description. We analyze the statistical characteristics of SWT-EFMs magnitudes in detail. In order to achieve accurate statistical modeling of SWT-EFMs magnitudes, the Beta Generalized Weibull mixtures-based hidden Markov tree (BGWM-HMT) model is constructed in SWT-EFMs magnitudes. The expectation-conditional maximization either (ECME) and the upward–downward algorithms are used to obtain model parameters. Our proposed statistical model can simultaneously capture the special distribution characteristics of SWT-EFMs magnitudes and the dependencies between scales. At the receiver, a statistical watermark detector based on the LO decision rule and BGWM-HMT model is developed in SWT-EFMs magnitudes. We derive closed-form expressions about the LO statistic and analyze the receiver operating characteristic (ROC) of the proposed detector. In addition, we measure the proposed scheme in terms of robustness, invisibility and time complexity. Experimental results on some test images and comparison with well-known existing methods demonstrate the efficacy and superiority of the proposed statistical image watermark detector.