An original Continuous Hopfield Network for optimal images restoration

Image restoration is a very important task in image processing. The Artificial Neural Network (ANN) approach was used to solve this problem, especially the Discrete Hopfield Network (DHN). This approach suffers from the fluctuation problem due to the use of the hard limit function as activation function. To overcome this shortcoming, we use in this work the Continuous Hopfield Network (CHN) that uses a probabilistic density as activation function. Indeed, this kind of function avoids the fluctuation behaviour and permits to extend the research area of the solution. In this regard, we propose our own energy function with appropriate parameters to obtain feasible equilibrium points. The performance of our method is demonstrated by several computational tests. Key-Words: Artificial neural network, Image restoration problem, Degraded image, Continuous Hopfield network, Discrete Hopfield network, Linear filtering, Fluctuation problem.