A Nonlinear Noise-Resistant Zeroing Neural Network Model for Solving Time-Varying Quaternion Generalized Lyapunov Equation and Applications to Color Image Processing

The time-varying Lyapunov equation (TVLE) plays a crucial role in control design and system stability. However, there has been limited research conducted on the time-varying generalized Lyapunov equation in the quaternion field. To tackle the time-varying quaternion generalized Lyapunov equation, a nonlinear noise-resistant zeroing neural network (NNR-ZNN) model with a novel power activation function (NPAF) is devised. The issue of non-commutativity within quaternion is circumvented by utilizing the real representation. The theoretical analyses provide a sufficient explanation for the global stability, fixed-time convergence, and robustness of the NNR-ZNN model. Under several different kinds of noises, the exceptional robustness of the NNR-ZNN model is highlighted by comparison with other existing models. In the end, the successful applications of the NNR-ZNN model to color image fusion and color image denoising confirm the practical value of the NNR-ZNN model.