L. Bedini et al., A MIXED-ANNEALING ALGORITHM FOR EDGE-PRESERVING IMAGE-RECONSTRUCTION USING A LIMITED NUMBER OF PROJECTIONS, Signal processing, 32(3), 1993, pp. 397-408
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 ad
vantages of considering the image discontinuities explicitly in order
to reduce the excessively smooth appearance of the reconstructions pro
duced by global smoothness constraints. The use of Markov Random Field
models means that it is possible to describe the local behaviour of t
he image and, in particular, to enforce constraints on possible config
urations of its discontinuities. In a Bayesian setting, additional kno
wledge in the form of Gibbs priors is combined with the observed data
and the reconstructed image is computed as the mode of the resulting p
osterior. Due to the large dimensions and the non-convexity of the pro
blem, algorithms based on simulated annealing techniques should be use
d; these algorithms have an enormous computational load and several te
chniques have been proposed in order to reduce the computational costs
. A particular annealing schedule is proposed here that finds the solu
tion iteratively by means of a sequence in which deterministic steps a
lternate with probabilistic ones. The algorithm is suitable for a para
llel implementation in a hybrid architecture made up of a grid of digi
tal 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 proje
ctions are available.