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Digital watermarking of images is an essential method for copyright protection and image security. This paper presents an innovative, robust watermarking system for color images based on moment and wavelet transformations, algebraic decompositions, and chaotic systems. First, we extended classical Charlier moments to quaternary Charlier moments (QCM) using quaternion algebra. This approach eliminates the need to decompose color images before applying the discrete wavelet transform (DWT), reducing the computational load. Next, we decompose the resulting DWT matrix using QR and singular value decomposition (SVD). To enhance the system's security and robustness, we introduce a modified version of Henon's 2D chaotic map. Finally, we integrate the arithmetic optimization algorithm to ensure dynamic and adaptive watermark insertion. Our experimental results demonstrate that our approach outperforms current color image watermarking methods in security, storage capacity, and resistance to various attacks, while maintaining a high level of invisibility.
Tahiri et al. (Fri,) studied this question.