Stochastic quaternion-valued fuzzy cellular neural networks with a mixture of time delays: mean-square stability of measure pseudo almost automorphic solutions with application to image denoising.

This paper addresses a family of stochastic quaternion-valued fuzzy cellular neural networks with a mixture of time delays in a measure-theoretic framework. By combining the Banach fixed-point theorem with the Lebesgue-Radon-Nikodym theorem, sufficient conditions are established to guarantee existence and uniqueness of measure pseudo almost automorphic solutions. Furthermore, new criteria ensuring the mean-square stability of the considered system are derived. The proposed analysis provides a rigorous framework for studying the dynamical behavior of delayed stochastic quaternion-valued neural networks in measurable spaces. Numerical simulations are performed to corroborate the theoretical results and illustrate the validity of the theoretical stability results. Moreover, the proposed stochastic quaternion-valued fuzzy cellular neural network model is applied to image denoising, where its performance is validated through both qualitative visual assessment and quantitative evaluation metrics, showing its ability to effectively remove noise while preserving key image details. The main novelty of this study lies in integrating quaternion-valued dynamics, fuzzy interactions, stochastic perturbations, mixed time delays, and measure pseudo-almost automorphic behavior into a unified cellular neural network framework. The theoretical results extend existing stability analyses and demonstrate the applicability of the proposed model to multidimensional signal processing.