Quaternion Hilbert transform and its applications in color image encryption

This paper proposes the Quaternion Hilbert Transform (QHT) and applies it to the encryption of color red, green and blue (RGB) images. Firstly, by decomposing an arbitrary quaternion signal into the linear sum of two complex signals and based on the Hilbert transform of complex signals, a Hilbert transform suitable for quaternion signals is constructed. Secondly, various commonly used properties satisfied by the Quaternion Hilbert Transform are derived. Finally, color RGB images are represented as quaternion signals, and a color RGB image encryption method based on the Quaternion Hilbert Transform is proposed. Experiments show that the proposed method has excellent visual effects and index performance, exhibits robustness against attacks such as noise and cropping, and has high sensitivity to keys, which verifies its effectiveness.