A neural network model for linear and non-linear image restoration

The computational properties or analogue electrical circuits, recently proposed as models for highly-interconnected networks or non-linear analogue neurons, have been found attractive in solving variational problems. The computation power or these circuits is based on the high connectivity typical or neural systems and on the convergence speed of analogue electric circuits in reaching stable states. In this paper, we suggest that the Hopfield neural network model could be used to restore blurred and noisy images. The problem, which is usually mathematically ill-posed, is reformulated as a well-posed, well-conditioned minimization problem by imposing global smoothness constrains on the class of solutions fitting a priori information. A neural network capable of finding the minimum for the problem is proposed, for both quadratic and highly non-quadratic stabilizers, and some features which could be useful in its circuital implementation are also reported.