A mixed-annealing algorithm for edge preserving image reconstruction using a limited number of projections

Abstract

The use of a priori information in image reconstruction has been shown effective in improving the quality of the solutions, especially when a small set of noisy data is available. Many authors have shown the advantages of considering the image discontinuities explicitly in order to reduce the excessively smooth appearance of the reconstructions produced by global smoothness constraints. The use of Markov Random Field models means that it is possible to describe the local behaviour of the image and, in particular, to enforce constraints on possible configurations of its discontinuities. In a Bayesian setting, additional knowledge in the form of Gibbs priors is combined with the observed data and the reconstructed image is computed as the mode of the resulting posterior. Due to the large dimensions and the non-convexity of the problem, algorithms based on simulated annealing techniques should be used; these algorithms have an enormous computational load and several techniques have been proposed in order to reduce the computational costs. A particular annealing schedule is proposed here that finds the solution iteratively by means of a sequence in which deterministic steps alternate with probabilistic ones. The algorithm is suitable for a parallel implementation in a hybrid architecture made up of a grid of digital processors interacting with a linear neural network which supports most of the computational costs. The proposed method has been applied to the problem of tomographic reconstruction from projections. It is shown to give good solutions even when a limited number of noisy projections are available.