A neural architecture for fully data driven edge-preserving image restoration

This paper proposes a neural architecture, based on two Hopfield nets inter connected with a Boltzmann Machine, for a completely data driven edge-prese rving restoration of blurred and noisy images. Solving this restoration pro blem entails the joint estimation of the image, the degradation operator an d the noise statistics, assuming that only the data are available. Since we consider the class of piecewise smooth images, modeled through a coupled M arkov Random Field with an explicit, constrained line process, the hyperpar ameters of the image model must be estimated as well. Adopting a fully Baye sian approach, the solution can be obtained by the joint maximization of a suitable distribution with respect to the image field, the model hyperparam eters, and the degradation parameters. The very high computational, complex ity of this joint maximization means that in most practical cases it cannot be applied, unless some approximations are adopted. In this paper, by expl oiting the presence of an explicit and binary line field, we propose some a pproximations which are effective in computing the solution by means of an architecture based on interacting neural networks. In particular, we propos e an architecture where the main computational load is supported by two Hop field nets, one computing the intensity field, the other performing a feast square estimation of the blur coefficients. The Boltzmann Machine is used following two modalities: running and learning. In the running modality, it updates the binary line process; in the learning modality, it performs the ML estimation of the hyperparameters, which are interpreted as the weights of cliques of interconnected neurons. Simulation results are provided to h ighlight the feasibility and the efficiency of the adopted methodology.