Abstract
In digital image steganography, the statistical model of an image is essential for hiding data in less detectable regions and achieving better security. This has been addressed in the literature where different cost-based and statistical model-based approaches were proposed. However, due to the usage of heuristically defined distortions and non-constrained message models, resulting in numerically solvable equations, there is no closed-form expression for security as a function of payload. The closed-form expression is crucial for a better insight into image steganography problem and also improving performance of batch steganography algorithms. Here, we develop a statistical framework for image steganography in which the cover and the stego messages are modeled as multivariate Gaussian random variables. We propose a novel Gaussian embedding model by maximizing the detection error of the most common optimal detectors within the adopted statistical model. Furthermore, we extend the formulation to cost-based steganography, resulting in a universal embedding scheme that improves empirical results of current cost-based and statistical model-based approaches. This methodology and its presented solution, by reason of assuming a continuous hidden message, remains the same for any embedding scenario. Afterward, the closed-form detection error is derived within the adopted model for image steganography and it is extended to batch steganography. Thus, we introduce Adaptive Batch size Image Merging steganographer, AdaBIM, and mathematically prove it outperforms the state-of-the-art batch steganography method and further verify its superiority by experiments.