Statistical image watermark decoder using NSM-HMT in NSCT-FGPCET magnitude domain

The image watermarking technology is an effective technology for protecting image copyright at present. Image watermarking techniques have a constraint relationship between imperceptibility, robustness, and watermark capacity. Balancing imperceptibility, robustness, and watermark capacity becomes a tricky problem. This paper proposes a statistical image watermarking scheme using nonsubsampled Contourlet transform (NSCT) domain fast generic polar complex exponential transform (FGPCET) magnitudes and nonsymmetric mixtures (NSM) based hidden Markov tree (HMT). In the embedding part, to enhance robustness and imperceptibility, we insert the watermark signal into the robust local NSCT domain FGPCET magnitudes through the multiplicative method. In the decoding part, a statistical image watermarking decoder is designed using the NSM-HMT model and maximum likelihood criterion. Here, marginal characteristics and strong correlations of local NSCT domain FGPCET magnitudes are described by NSM-HMT. In addition, the generalized expectation-maximization (GEM)-clusterized method of moments (CMM) approach is used for accurate parameters. Extensive Monte Carlo ex-periments validate the better performance of the proposed image watermarking method compared to other well-known methods.