Contourlet based image watermarking using optimum detector in the noisy environment

In this paper, a new multiplicative image watermarking system is presented. As human visual system is less sensitive to the image edges, watermarking is applied in the contourlet domain, which represents image edges sparsely. In the presented scheme, watermark data is embedded in the most energetic directional subband. By modeling general gaussian distribution (GGD) for the contourlet coefficients, the distribution of watermarked noisy coefficients is analytically calculated. At the receiver, based on the maximum likelihood (ML) decision rule, the optimal detector is proposed. Experimental results show the imperceptibility and high robustness of the proposed method against Additive White Gaussian Noise (AWGN) and JPEG compression attacks.