Design and Analysis of Quaternion-Valued Artificial Neural Networks for Image Encryption/Decryption

This paper addresses the exponential projective synchronization (EPSYN) and exponential quasi-projective synchronization (EQPSYN) of quaternion-valued artificial neural networks (QVANNs) featuring dual-sided coefficients with time-delay effects. Separating the QVANNs is generally accompanied by a more complicated derivation process, and the non-decomposition method is strategically used to directly process the raw system parameters. Through the construction of applicable Lyapunov functions and an effective dual-sided controller, the sufficient conditions have been established for EPSYN of the considered QVANNs. Furthermore, by relaxing the original controller, a result on EQPSYN with easily verifiable conditions is derived, and the error bound of QVANNs is estimated. Finally, three numerical examples are simulated to verify the effectiveness and feasibility of the proposed scheme, along with a discussion on its application in image encryption/decryption. The information entropy (IE) of the encrypted images is very close to the ideal value of 8, which indicates that the encryption algorithms possess robust security.