The use of neural networks in bayesian image restoration

Analog neural networks present an impressive computational power due to their high connectivity, typical of neural systems, and to the convergence speed of analog electric circuits in reaching stable states. Recently, it has been suggested that these networks could be used to solve optimization problems in which a considerable computational power is often required. In the paper, we show how a hybrid neural network could be used to solve the problem of the edge preserving restoration of piecewise smooth images. For this purpose, the restoration problem is formulated, on the basis of a Bayesian approach, in such a way as to deal directly with local discontinuities. According to this approach, the image is modeled by a couple of MRF's and a posterior energy function is derived whose minimization gives the MAP estimate of the problem. The computation of the so1ution is performed through an iterative deterministic-stochastic algorithm which obeys an annealing schedule. This algorithm is inherently parallel and can be implemented by means of a hybrid architecture in which a grid of digital processors cooperates with a linear analog neural network.