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Probabilistic modeling to inverse halftoning based on super resolution

On the basis of the Bayesian inference using the maximizer of the posterior marginal (MPM) estimate, we formulate the problem of inverse halftoning via the framework of super resolution for the organized dither method. Then, the Monte Carlo simulation for a set of the snapshots of the Q-Ising model clarifies that this method achieves optimal performance under the Bayes-optimal condition and that the Bayes-optimal solution reconstructs more accurately than the MAP estimate. Then, we find that the upper bound of the mean square error is inversely proportional to the number of halftone image in the procedure of inverse halftoning. Then, these results obtained by the Monte Carlo simulations are qualitatively confirmed by the analytical estimate using the infinite-range model. Further, we find that the present method is effective even for realistic images and however that false contour appears in reconstructed images, if we utilize a small number of the halftone images in the procedure of inverse halftoning.