ABSTRACT This paper presents alternative continuous- and discrete-time neural networks for image restoration in real time by introducing new vectors and transforming its optimization conditions into a system of double projection equations. The proposed neural networks are shown to be stable in the sense of Lyapunov and convergent for any starting point. Compared with the existing neural networks for image restoration, the proposed models have the least neurons, a one-layer structure and the faster convergence, and is suitable to parallel implementation. The validity and transient behaviour of the proposed neural network is demonstrated by numerical examples.

中文翻译：

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用于图像恢复的替代连续和离散时间神经网络

摘要 本文通过引入新向量并将其优化条件转换为双投影方程系统，提出了用于实时图像恢复的替代连续和离散时间神经网络。所提出的神经网络在李雅普诺夫意义上是稳定的，并且对于任何起点都是收敛的。与现有的用于图像恢复的神经网络相比，所提出的模型具有最少的神经元、一层结构和更快的收敛速度，适合并行实现。数值例子证明了所提出的神经网络的有效性和瞬态行为。