A hidden Markov model-based blind detector for multiplicative watermarking

Nowadays, transmission of data via Internet has made illegal data distribution a major problem in digital world. Watermarking is known as a possible solution to protect digital data. In this work, we propose a blind detector for multiplicative watermarking of images in the wavelet domain. To this end, the vector-based hidden Markov model (HMM) is employed as a prior model for the wavelet coefficients of the host image. This model is known to provide an accurate fit to the distribution of the wavelet coefficients by capturing both their heavy-tailed marginal statistics and their inter-subbands and cross-orientations dependencies. Analytical expressions for the proposed watermark detector such as the mean and variance of the log-likelihood ratio test are derived and used to evaluate its performance. The performance of the proposed detector is shown to outperform that of the other detectors by providing higher detection rate and better imperceptibility of the embedded watermark. It is also shown that the proposed vector-based HMM detector under various attacks such as compression, rotation, filtering and noise, is more robust than other existing detectors.