This paper proposes the trinion Hartley Transform (THT) and presents its commonly used properties, such as linearity, cyclic shift property, convolution theorem, and so on. In addition, the relationship between THT and Fourier Transform is derived, and a fast computation for THT based on FFT is proposed. Finally, based on the proposed THT and its fast computation, encryption and decryption methods suitable for color images are proposed, and the effectiveness of the proposed methods are verified by simulation results.

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.