Design and Analysis of Quaternion-Valued Neural Networks for Associative Memories

This paper addresses the problem of designing associative memories based on quaternion-valued neural networks (QVNNs). A system designing procedure for QVNNs is developed by employing quaternion matrix decomposition, and a given set of states can be assigned as the equilibrium points of the designed QVNNs. Moreover, some sufficient conditions for the asymptotic stability of the equilibrium points are obtained via Lyapunov's direct method. Numerical simulations manifest that the constructed QVNNs work efficiently on storing and retrieving blurred gray-scale and true color images.