MATLAB Implementation of Digital Watermarking with Hypercomplex Frequency Domain Algorithm

For color carrier images, we propose a new watermarking algorithm operating in the hypercomplex frequency domain. The algorithm processes color images using Fast Hypercomplex Fourier Transform (FHFT), where MATLAB implementation involves: 1) Converting RGB images to quaternion representation (using quaternion() function) 2) Applying FHFT via dedicated hypercomplex transformation libraries 3) Selecting appropriate frequency bands for watermark embedding 4) Modifying symmetric coefficients while preserving spectral properties The MATLAB code ensures watermarked images remain transmittable through standard RGB channels. Analytical results demonstrate that inverse hypercomplex Fourier transform effectively distributes watermark-induced errors across the entire image and disperses them among red, green, and blue components. This implementation achieves an optimal balance between digital watermark imperceptibility and security. Additionally, we introduce a "cross-redundant embedding" rule in the MATLAB implementation, where watermark data is distributed using interleaving algorithms across multiple frequency components. This redundancy approach significantly enhances the watermark's robustness against attacks. Experimental results conducted through MATLAB simulations validate the algorithm's superiority in terms of PSNR metrics, robustness tests, and visual quality assessments compared to conventional methods. The code includes systematic testing modules for performance evaluation under various image processing operations.