Statistical models for digital watermarking

Abstract

This thesis is directed towards the study of the likelihood ratio (LR) detection method in detecting invisible watermark in images. LR detection method based on Bayes' decision theory has been considered for image watermarking in transform domain. The Neyman-Pearson criterion is used to derive a decision threshold. In order to achieve an optimum behavior of the LR detector, a probability distribution function (PDF) that models the distribution of the transform coefficients is required. We propose using the generalized Gaussian PDF and Laplacian PDF to model transform coefficients of discrete wavelet transform (DWT), and the generalized gamma PDF to model coefficients of discrete Fourier transform (DFT). Decision rule and closed-form decision threshold are derived for all proposed models. New estimators are introduced for parameters of the generalized Gaussian and generalized gamma distributions. Our numerical experiments reveal that the proposed models can produce better LR detection.