Two Matrix-Type Projection Neural Networks for Matrix-Valued Optimization with Application to Image Restoration

In recent years, matrix-valued optimization algorithms have been studied to enhance the computational performance of vector-valued optimization algorithms. This paper presents two matrix-type projection neural networks, continuous-time and discrete-time ones, for solving matrix-valued optimization problems. The proposed continuous-time neural network may be viewed as a significant extension to the vector-type double projection neural network. More importantly, the proposed discrete-time projection neural network is suitable for parallel implementation in terms of matrix state spaces. Under pseudo-monotonicity and Lipschitz continuous conditions, the proposed two matrix-type projection neural networks are guaranteed to be globally convergent to the optimal solution. Finally, the proposed matrix-type projection neural network is effectively applied to image restoration. Computed examples show that the two proposed matrix-type projection neural networks are much superior to the vector-type projection neural networks in terms of computation speed.