Demystifying histograms of multi-quantised DCT coefficients

JPEG compression artefacts are among the most prominent features in the forensic analysis of digital images. Here, we focus on the spectral analysis of histograms of single- and multi-quantised DCT coefficients. We present a model of the frequency response of finite-support histograms, which explains position and magnitude of characteristic quantisation peaks with reasonable precision and gives valuable insights into the formation of quantisation artefacts in general. We derive a set of practical rules for the efficient analysis of single- and multi-compressed images and discuss applications in the estimation of quantisation tables.