Transform coder identification with double quantized data

The analysis of chains of double transform coders has been recently addressed in the image forensic literature, especially for the case of double JPEG compression. In that case, the transform is assumed to be known a priori (e.g., 2D-DCT), whereas the quantization steps of the first coder need to be determined. In this work, we generalize the analysis to the challenging case in which nothing is known about the first coder, but that the transform is orthonormal. Given a set of vectors observed as output of a chain of two transform coders, we identify both the transform and the quantizer of the first. The key idea is to denoise the observed vectors exploiting the constraints imposed by the first quantizer and then apply our previously proposed method, which successfully performs transform identification in the case of noiseless observations. Experiments on real images validate the proposed approach.