A Highly Robust Reversible Watermarking Scheme Using Embedding Optimization and Rounded Error Compensation

The robust reversible watermarking (RRW) requires high robustness and capacity on the condition of reversibility and imperceptibility, which still remains a big challenge nowadays. In this paper, we propose a two-stage RRW scheme that improves robustness and capacity through embedding optimization and rounded error compensation. The first stage inserts a robust watermark into the selected Pseudo-Zernike moments (PZMs) by using an adaptive normalization method and an optimized embedding strategy. Specifically, the adaptive normalization method achieves both an invariance to pixel amplitude variation and a balance between robustness and imperceptibility, and the optimized embedding strategy reduces embedding distortions remarkably. The watermarked PZMs are inversely transformed to generate the robustly watermarked image, in which rounded errors caused in the inverse transformation is compensated elaborately and thus a larger capacity can be obtained at the same embedding distortion. The second stage embeds a reversible watermark consisting of errors between the robust watermark embedded image and the original one, aiming at achieving the reversibility in case of no attacks. Extensive experimental simulations show that the proposed scheme provides strong robustness against common signal processing, including AWGN, salt-and-pepper noise, JPEG, JPEG2000, median filtering, mean filtering, geometrical transformations involving rotation and scaling, and a compressive sensing attack exemplified by two-dimensional compressive sensing, which outperforms the state-of-the-art schemes. Our code is available at https://github.com/yichao-tang/PZMs-RRW.