Abstract
An algorithm for restoration of images degraded by Poisson noise is proposed. The algorithm belongs to the family of Markov chain Monte Carlo methods with auxiliary variables. We explicitly use the fact that medical images consist of finitely many, often relatively few, grey-levels. The continuous scale of grey-levels is discretized in an adaptive way, so that a straightforward application of the Swendsen–Wang (Phys. Rev. Lett. 58 (1987) 86) algorithm becomes possible. Partial decoupling method due to Higdon (J. Am. Statist. Assoc. 93 (1998) 442, 585) is also incorporated into the algorithm. Simulation results suggest that the algorithm is reliable and efficient.
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