Supervised learning of smoothing parameters in image restoration by regularization under cellular neural networks framework

Estimation of the smoothing parameters is one of the difficult problems in using regularization techniques for image restoration. The paper shows how cellular neural networks (CNNs) incorporated with a learning algorithm can be useful in adaptive learning of the smoothing parameters of regularization. A CNN model is designed to minimize the regularization cost function which is in a quadratic form. The connection weights of this CNN are obtained by comparing the cost function with a Lyapunov function. Unlike the common approaches in the literature, instead of using the learning connection weights of the neural networks, we propose supervised learning of the regularization smoothing parameters by a modified version of the recurrent perceptron learning algorithm (RPLA) which is developed for completely stable CNNs operating in a bipolar binary output mode. It is concluded that CNNs with the RPLA provides a set of suitable smoothing parameters resulting in a robust restoration of noisy images. For comparison, experimental results obtained by a median filter are also reported.