Affiliations: Istituto di Elaborazione della Informazione, Consiglio Nazionale delle Ricerche, Via S. Maria, 46, I-56126 Pisa, Italy. Tel.: +39 050 593400; Fax: +39 050 554342; E-mail: [email protected]
Correspondence:
[*]
Corresponding author.
Abstract: This paper proposes a neural architecture, based on two Hopfield nets interconnected with a Boltzmann Machine, for a completely data driven edge-preserving restoration of blurred and noisy images. Solving this restoration problem entails the joint estimation of the image, the degradation operator and the noise statistics, assuming that only the data are available. Since we consider the class of piecewise smooth images, modeled through a coupled Markov Random Field with an explicit, constrained line process, the hyperparameters of the image model must be estimated as well. Adopting a fully Bayesian approach, the solution can be obtained by the joint maximization of a suitable distribution with respect to the image field, the model hyperparameters, and the degradation parameters. The very high computational complexity of this joint maximization means that in most practical cases it cannot be applied, unless some approximations are adopted. In this paper, by exploiting the presence of an explicit and binary line field, we propose some approximations which are effective in computing the solution by means of an architecture based on interacting neural networks. In particular, we propose an architecture where the main computational load is supported by two Hopfield nets, one computing the intensity field, the other performing a least 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 highlight the feasibility and the efficiency of the adopted methodology.
