Reti di Hopfield per il restauro di immagini

The computational properties of analogue electrical circuits, recently proposed as models for highly-interconnected networks of non-linear analogue neurons, have been found attractive in solving variational problems. The computation power of these circuits is based on the high connectivity typical of neural systems and on the convergence speed of analogue electric circuits in reaching stable states. In this paper we suggest the possibility to use the Hopfield neural netlvork model for effectively solving the problem of the restoration of blurred and noisy images. The problem, which is in general mathematically ill-posed, is reformulated as a well-posed, well-conditioned minimization problem, by imposing global smoothness constraints on the elass of solutions fitting a priori information about statistics of the noise. A possible neural network capable of finding the minimum for the prohlem is proposed, both for quadratic and non-quadratic stabilizers, and some features which could be useful for its circuital implementation are also reported. The performance of the network has been tested by means of simulations performed on serial computer; both synthetic and real images have been analysed. Given the simulation cost, images with reduced size (64x64) have been considered. The obtained results evidence the good performance of the neural network in solving image restoration problems.