L'uso di reti neurali per la ricostruzione di immagini in presenza di discontinuità

In this paper, the edge-preserving reconstruction of piecewise smooth images is formulated within a probabilistic approach, where the image is modelled as two coupled Markov Random Fields, one representing the intensity and the other the discontinuities. In this way, prior knowledge about global and local features of the image can be introduced in the form of a Gibbs prior and a Maximum A Posteriori estimate can be assumed as the solution of the original problem. Since the posterior probability often presents local maxima, very expensive stochastic relaxation algorithms should be used to obtain the global maximizer. In order to reduce execution times, we propose a mixedannealing algorithm, which obtains the solution iteratively by means of a sequence in which deterministic steps alternate with probabilistic ones. In particular, each deterministic step is designed to minimize a quadratic function of the intensity only, while each probabilistic step updates the discontinuities, using the Gibbs sampler. This algorithm can exploit the computational power of neural networks solving optimization problems; indeed, it can be implemented on a hybrid architecture made up of a grid of digital processors interacting with a linear neural network which supports most of the computational costs. Such a computational scheme can be adopted both for image restoration and for image reconstruction from projections, where the large size of the neighbourhoods would prevent the use of the Gibbs sampler.