Abstract
We have investigated the relaxation dynamics of image restoration through a Bayesian approach. The relaxation dynamics is much faster at zero temperature than at the Nishimori temperature where the pixel-wise error rate is minimized in equilibrium. At low temperature, we observed non-monotonic development of the overlap. We suggest that the optimal performance is realized through premature termination in the relaxation processes in the case of the infinite-range model. We also performed Markov chain Monte Carlo simulations to clarify the underlying mechanism of non-trivial behaviour at low temperature by checking the local field distributions of each pixel.
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