A Novel Statistical Detector for Contourlet Domain Image Watermarking Using 2D-GARCH Model

Abstract

In this paper, we propose a novel watermark detector in contourlet domain using likelihood ratio test (LRT). Since the accuracy of an LRT based watermark detector is dependent on the efficiency of the applied statistical model, first, we study the statistical properties of the contourlet coefficients. Using different tests, we demonstrate that the marginal distribution of contourlet coefficients is heavy-tailed and heteroscedasticity exists in these coefficients. All of the previously proposed models for contourlet coefficients assume that these coefficients are identically distributed, so they can not capture the characteristics of the contourlet coefficients. To overcome this problem, we propose using two dimensional generalized autoregressive conditional heteroscedasticity (2D-GARCH) model for contourlet coefficients that provides an efficient structure for the dependencies of these coefficients. Based on using 2D-GARCH model, a novel LRT based heteroscedastic watermark detector is designed in contourlet domain. Experimental results confirm the efficiency of the proposed watermark detector under different types of attacks and its outperformance compared with alternative watermarking methods.