Transform coder identification

The widespread popularity of transform coding has made it central to a wide range of methods in forensics, quality assessment and digital restoration. However, most approaches require prior knowledge of the transform coding parameters. In this paper, we consider the challenging problem of identifying the transform matrix as well as the quantization step sizes of a transform coder, given a set of P non-overlapping N-dimensional vectors observed as its output. We formulate the problem in terms of finding the lattice with the largest determinant that contains all observed vectors and we propose an algorithm that is able to find the optimal solution. Our experimental analysis shows that the probability of success of the algorithm quickly approaches 1 for small values of (P - N). The complexity of the proposed algorithm grows linearly with the dimensionality N.