A Random Matrix Approach to the Forensic Analysis of Upscaled Images

Abstract

The forensic analysis of resampling traces in upscaled images is addressed via subspace decomposition and random matrix theory principles. In this context, we derive the asymptotic eigenvalue distribution of sample autocorrelation matrices corresponding to genuine and upscaled images. To achieve this, we model genuine images as an autoregressive random field and we characterize upscaled images as a noisy version of a lower dimensional signal. Following the intuition behind Marcenko-Pastur law, we show that for upscaled images, the gap between the eigenvalues corresponding to the low-dimensional signal and the ones from the background noise can be enhanced by extracting a small number of consecutive columns/rows from the matrix of observations. In addition, using bounds provided by the same law for the eigenvalues of the noise space, we propose a detector for exposing traces of resampling. Finally, since an interval of plausible resampling factors can be inferred from the position of the gap, we empirically demonstrate that by using the resulting range as the search space of existing estimators (based on different principles), a better estimation accuracy can be attained with respect to the standalone versions of the latter.