Locally optimum nonlinearities for DCT watermark detection

The issue of copyright protection of digital multimedia data has attracted a lot of attention during the last decade. An efficient copyright protection method that has been gaining popularity is watermarking, i.e., the embedding of a signature in a digital document that can be detected only by its rightful owner. Watermarks are usually blindly detected using correlating structures, which would be optimal in the case of Gaussian data. However, in the case of DCT-domain image watermarking, the data is more heavy-tailed and the correlator is clearly suboptimal. Nonlinear receivers have been shown to be particularly well suited for the detection of weak signals in heavy-tailed noise, as they are locally optimal. This motivates the use of the Gaussian-tailed zero-memory nonlinearity, as well as the locally optimal Cauchy nonlinearity for the detection of watermarks in DCT transformed images. We analyze the performance of these schemes theoretically and compare it to that of the traditionally used Gaussian correlator, but also to the recently proposed generalized Gaussian detector, which outperforms the correlator. The theoretical analysis and the actual performance of these systems is assessed through experiments, which verify the theoretical analysis and also justify the use of nonlinear structures for watermark detection. The performance of the correlator and the nonlinear detectors in the presence of quantization is also analyzed, using results from dither theory, and also verified experimentally.