Detection of JSteg algorithm using hypothesis testing theory and a statistical model with nuisance parameters

Abstract

This paper investigates the statistical detection of data hidden within DCT coefficients of JPEG images using a Laplacian distribution model. The main contributions is twofold. First, this paper proposes to model the DCT coefficients using a Laplacian distribution but challenges the usual assumption that among a sub-band all the coefficients follow are independent and identically distributed (i.i.d). In this paper it is assumed that the distribution parameters change from DCT coefficient to DCT coefficient. Second this paper applies this model to design a statistical test, based on hypothesis testing theory, which aims at detecting data hidden within DCT coefficient with the JSteg algorithm. The proposed optimal detector carefully takes into account the distribution parameters as nuisance parameters. Numerical results on simulated data as well as on numerical images database show the relevance of the proposed model and the good performance of the ensuing test.