Statistical mechanical iterative method for inverse halftoning using multiple halftone images

On the basis of the statistical mechanics of the Q-Ising model, we formulate the problem of inverse halftoning using multiple halftone images and the maximizer of the posterior marginal (MPM) estimate based on Bayesian inference. Using Monte Carlo simulation for a set of snapshots of the Q-Ising model, we demonstrated that estimation performance is improved by introducing prior information on the original images into the MPM estimate and that optimal performance is achieved around the Bayes-optimal condition within statistical uncertainty. These properties were qualitatively confirmed by analytical estimation using the mean-field model. Further, we constructed a practical and useful inverse halftoning method using the statistical mechanical iterative method via Bethe approximation. Monte Carlo simulation using a 256-grayscale standard image showed that Bethe approximation works as well as MPM estimation if the parameters are set appropriately.