A New Statistical Detector for DWT-Based Additive Image Watermarking Using the Gauss–Hermite Expansion

Traditional statistical detectors of the discrete wavelet transform (DWT)-based image watermarking use probability density functions (PDFs) that show inadequate matching with the empirical PDF of image coefficients in view o f the fact that they use a fixed number of parameters. Hence, the decision values obtained from the estimated thresholds of these detectors provide substandard detection performance. In this paper, a new detector is proposed for the DWT-based additive image watermarking, wherein a PDF based on the Gauss-Hermite expansion is used, in view of the fact that this PDF provides a better statistical match to the empirical PDF by utilizing an appropriate number of parameters estimated from higher-order moments of the image coefficients. The decision threshold and the receiver operating characteristics are derived for the proposed detector. Experimental results on test images demonstrate that the proposed watermark detector performs better than other standard detectors such as the Gaussian and generalized Gaussian (GG), in terms of the probabilities of detection and false alarm as well as the efficacy. It is also shown that detection performance of the proposed detector is more robust than the competitive GG detector in the case of compression, additive white Gaussian noise, filtering, or geometric attack.