Transportation-theoretic image counterforensics to First Significant Digit histogram forensics

First-order statistics of First Significant Digits (FSD) have been recently exploited in multimedia forensics as a powerful tool to reveal traces of previous coding operations. As an answer, adversarial approaches aimed at modifying the FSD histogram and fooling such forensic methods have been proposed. However, the existing techniques have limitations in terms of distortion introduced in the multimedia object. In this paper, a transportation-theoretic formulation of the problem is presented which provides a close-to-optimal solution. Such strategy is tested in a well-known image forensic scenario, where FSDs of 8 × 8-DCT coefficients after single or double quantization are modified in order to restore a certain target histogram and the distortion with respect to the provided compressed image is measured in terms of MSE.