Multiplicative Watermark Decoder in Contourlet Domain Using the Normal Inverse Gaussian Distribution

In recent years, many works on digital image watermarking have been proposed all aiming at protection of the copyright of an image document or authentication of data. This paper proposes a novel watermark decoder in the contourlet domain . It is known that the contourlet coefficients of an image are highly non-Gaussian and a proper distribution to model the statistics of the contourlet coefficients is a heavy-tailed PDF. It has been shown in the literature that the normal inverse Gaussian (NIG) distribution can suitably fit the empirical distribution. In view of this, statistical methods for watermark extraction are proposed by exploiting the NIG as a prior for the contourlet coefficients of images. The proposed watermark extraction approach is developed using the maximum likelihood method based on the NIG distribution. Closed-form expressions are obtained for extracting the watermark bits in both clean and noisy environments. Experiments are performed to verify the robustness of the proposed decoder. The results show that the proposed decoder is superior to other decoders in terms of providing a lower bit error rate. It is also shown that the proposed decoder is highly robust against various kinds of attacks such as noise, rotation, cropping, filtering, and compression.