A Robust Multibit Multiplicative Watermark Decoder Using a Vector-Based Hidden Markov Model in Wavelet Domain

The vector-based hidden Markov model (HMM) is a powerful statistical model for characterizing the distribution of the wavelet coefficients, since it is capable of capturing the subband marginal distribution as well as the inter-scale and cross-orientation dependencies of the wavelet coefficients. In this paper we propose a scheme for designing a blind multibit watermark decoder incorporating the vector-based HMM in wavelet domain. The decoder is designed based on the maximum likelihood criterion. A closed-form expression is derived for the bit error rate and validated experimentally with Monte Carlo simulations. The performance of the proposed watermark detector is evaluated using a set of standard test images and shown to outperform the decoders designed based on the Cauchy or generalized Gaussian distributions without or with attacks. It is also shown that the proposed decoder is more robust against various kinds of attacks compared with the state-of-the-art methods.