Digital watermark extraction in wavelet domain using hidden Markov model

A watermark decoder aims at extracting the hidden watermark bits from the digital data. Statistical modeling of wavelet subband coefficients has been used in watermark extraction schemes. It is known that the effectiveness of such schemes depends on how accurately the wavelet coefficients are modeled. The vector-based hidden Markov model (HMM) is a very powerful statistical model for describing 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. It is shown that the vector-basedHMM gives a better fit for the empirical data compared to the previously-used distributions. In view of this, we propose a watermark decoder using the vector-based HMM in the wavelet domain. The watermark decoder is designed based on the maximum likelihood criterion. Closed-form theoretical expression for the watermark decoder is derived. The performance of the proposed decoder is assessed using a number of test images. It is shown that the proposed decoder is superior to other decoders in terms of providing a lower bit error rate. The proposed decoder is shown to be highly robust against various kinds of attacks.