Hidden messages in heavy-tails: DCT-domain watermark detection using alpha-stable models

This paper addresses issues that arise in copyright protection systems of digital images, which employ blind watermark verification structures in the discrete cosine transform (DCT) domain. First, we observe that statistical distributions with heavy algebraic tails, such as the alpha-stable family, are in many cases more accurate modeling tools for the DCT coefficients of JPEG-analyzed images than families with exponential tails such as the generalized Gaussian. Motivated by our modeling results, we then design a new processor for blind watermark detection using the Cauchy member of the alpha-stable family. The Cauchy distribution is chosen because it is the only non-Gaussian symmetric alpha-stable distribution that exists in closed form and also because it leads to the design of a nearly optimum detector with robust detection performance. We analyze the performance of the new detector in terms of the associated probabilities of detection and false alarm and we compare it to the performance of the generalized Gaussian detector by performing experiments with various test images.