  We attempt image restoration in the framework of the Baysian inference.
Recently, it has been shown that under a certain criterion the MAP (Maximum A
Posterior) estimate, which corresponds to the minimization of energy, can be
outperformed by the MPM (Maximizer of the Posterior Marginals) estimate, which
is equivalent to a finite-temperature decoding method. Since a lot of
computational time is needed for the MPM estimate to calculate the thermal
averages, the mean field method, which is a deterministic algorithm, is often
utilized to avoid this difficulty. We present a statistical-mechanical analysis
of naive mean field approximation in the framework of image restoration. We
compare our theoretical results with those of computer simulation, and
investigate the potential of naive mean field approximation.
