Statistical Distribution Index of Modulation

Digital watermarks are usually embedded in the still images’ frequency domain. The DWT/DCT coefficients are usually modelled by the Generalized Gaussian Distribution, while the DFT coefficients are modelled by the Weibull Distribution. The idea of this paper is to use statistical properties of the host signal. The watermark is embedded through the modification of the distribution of host signal X. The advantage of this idea is that a sequence of pseudo-random data looks more natural and makes it much easier to hide information. Let F0, ..., Fm−1 be m different distributions and F = ∪Fi. To watermark the host signal X with mark i, X is modified to follow the distribution Fi. The detection method is given. Kullback-Leibler(K-L) distance(relative entropy) and Chernoff information are used for the design reference. The K-L distance and the Chernoff information of the Generalized Gaussian Distribution and Weibull Distribution are discussed.