Nonlinear Discrete Optimisation of Reversible Steganographic Coding

Authentication mechanisms are at the forefront of defending the world from various types of cybercrime. Steganography can serve as an authentication solution by embedding a digital signature into a carrier object to ensure the integrity of the object and simultaneously lighten the burden of metadata management. However, steganographic distortion, albeit generally imperceptible to human sensory systems, might be inadmissible in fidelity-sensitive situations. This has led to the concept of reversible steganography. A fundamental element of reversible steganography is predictive analytics, for which powerful neural network models have been effectively deployed. As another core aspect, contemporary reversible steganographic coding is based primarily on heuristics and therefore worth further study. While attempts have been made to realise automatic coding with neural networks, perfect reversibility is still unreachable via such an unexplainable intelligent machinery. Instead of relying on deep learning, we aim to derive an optimal coding by means of mathematical optimisation. In this study, we formulate reversible steganographic coding as a nonlinear discrete optimisation problem with a logarithmic capacity constraint and a quadratic distortion objective. Linearisation techniques are developed to enable mixed-integer linear programming. Experimental results validate the near-optimality of the proposed optimisation algorithm benchmarked against a brute-force method.