A predefined-time matrix-value neural network for quaternion optimization with applications to color images

Banghua Huang, Yang Liu, Kit Ian Kou, Haijun Jiang

Abstract: In this paper, we address a matrix-value optimization problem with bound constraints defined in the quaternion domain. We propose a predefined-time matrix-value projection neural network based on the quaternion matrix derivative for the quaternion optimization problem. We prove the convergence of the proposed projection neural network with derived conditions to an approximately optimal solution of quaternion optimization problem in a predefined time. We illustrate the characteristics of the approaches via two numerical examples. Furthermore, we demonstrate the effective application of the predefined-time projection neural network in color image restoration and color face recognition.