Information-Theoretic Bounds for the Forensic Detection of Downscaled Signals

The detection of rescaling operations represents an important task in multimedia forensics. While many effective heuristics have been proposed, there is no theory on the forensic detectability revealing the conditions of more or less reliable detection. We study the problem of discriminating 1D and 2D genuine signals from signals that have been downscaled with the goal of quantifying the statistical distinguishability between these two hypotheses. This is done by assuming known signal models and deriving the expressions of statistical distances that are linked to the hypothesis testing theory, namely, the symmetrized form of Kullback-Leibler divergence known as the Jeffreys divergence, and the Bhattacharyya divergence. The analysis is performed for varying parameters of both the genuine signal model (variance and one-step correlation) and the rescaling process (rescaling factor, interpolation kernel, grid shift, and anti-alias filter), thus allowing us to reveal the insights on their influence and interplay. In addition to the signal itself, we consider the signal transformations (prefilter and covariance matrix estimators) that are often involved in practical rescaling detectors, showing that they yield similar results in terms of distinguishability. Numerical tests on synthetic and real signals confirm the main observations from the theoretical analysis.