BEMD-SD Domain Image Watermarking Algorithm Using Simplified Bivariate Generalized t Distribution and Entropy Threshold Edge Detection

Balancing the relationship between imperceptibility, robustness, and watermarking capacity is a difficult challenge for digital image watermarking algorithms to overcome. In this paper, we design a well-performing statistical blind watermarking scheme to protect the copyright of digital images. First, the bidimensional empirical mode decomposition (BEMD) is combined with the Schur decomposition (SD) to construct the robust digital watermarking carrier. Then, the positionally stabilized BEMD-SD domain coefficients are selected to hide the information with the help of entropy threshold edge detection technique. Next, the simplified bivariate generalized t (SBGt) distribution is used for accurate modeling to account for the strong correlation between the coefficients, and the model parameters are computed by the inverse harmonic Newton maximum likelihood estimation (CHN-MLE) method. Finally, the digital watermark decoder is constructed to extract watermark information by combining the maximum likelihood criterion. Experimental results on a large number of test images show that the proposed blind watermarking decoder outperforms most of the state-of-the-art statistical methods and deep learning methods recently proposed in the literature. Our proposed method has excellent imperceptibility and robustness in accommodating watermarks of the same capacity.