Image Steganography With Symmetric Embedding Using Gaussian Markov Random Field Model

Recent advances on adaptive steganography show that the performance of image steganographic communication can be improved by incorporating the non-additive models that capture the dependencies among adjacent pixels. In this paper, a Gaussian Markov Random Field model (GMRF) with four-element cross neighborhood is proposed to characterize the interactions among local elements of cover images, and the problem of secure image steganography is formulated as the one of minimization of KL-divergence in terms of a series of low-dimensional clique structures associated with GMRF by taking advantages of the conditional independence of GMRF. The adoption of the proposed GMRF tessellates the cover image into two disjoint subimages, and an alternating iterative optimization scheme is developed to effectively embed the given payload while minimizing the total KL-divergence between cover and stego, i.e., the statistical detectability. Experimental results demonstrate that the proposed GMRF outperforms the prior arts of model based schemes, e.g., MiPOD, and rivals the state-of-the-art HiLL for practical steganography, where the selection channel knowledges are unavailable to steganalyzers.