PSO-based Quaternion Fourier Transform steganography: Enhancing imperceptibility and robustness through multi-dimensional frequency embedding

This paper presents a novel steganography technique using the Quaternion Fourier Transform (QFT) in the 4D frequency domain to enhance imperceptibility and robustness in digital image embedding. Steganography, the art of hiding information within media, faces challenges in balancing security, imperceptibility, and robustness. To address this, we leverage the multi-dimensional properties of quaternions, enabling the embedding of secret data in both grayscale and color images. For grayscale images, two quaternion dimensions are utilized for intensity and secret data, while for color images, all four dimensions are employed with one reserved for metadata. The research question centers on how to maximize spatial dispersion and color similarity while maintaining high imperceptibility and robustness against attacks. Experimental results show that the proposed method improves visual imperceptibility by more than 4 % and exhibits a 13 % increase in robustness against common steganalysis attacks compared to the best state-of-the-art existing technique. These advancements highlight the potential of this method for applications in secure communication, digital watermarking, and copyright protection. By combining the quaternion mathematical framework with a novel optimization strategy, this approach significantly improves upon traditional steganography methods.