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Abstract:On the basis of statistical mechanics of the Q-Ising model, we formulate the Bayesian inference to the problem of inverse halftoning, which is the inverse process of representing gray-scales in images by means of black and white dots. Using Monte Carlo simulations, we investigate statistical properties of the inverse process, especially, we reveal the condition of the Bayes-optimal solution for which the mean-square error takes its minimum. The numerical result is qualitatively confirmed by analysis of the infinite-range model. As demonstrations of our approach, we apply the method to retrieve a grayscale image, such as standard image Lena, from the halftoned version. We find that the Bayes-optimal solution gives a fine restored grayscale image which is very close to the original. In addition, based on statistical mechanics of the QIsing model, we are sucessful in constructing a practically useful method of inverse halftoning using the Bethe approximation.PACS (2008)

On the basis of statistical mechanics formulation for problems of image restoration and errorcorrecting codes, we propose a new technique of image restoration for a binary image using the plane rotator model. In our formulation, the restored image is obtained from the equilibrium state of a ferromagnetic plane rotator model under a random field which consists of the corrupted image at finite temperature. The validity of our technique is evaluated by the dependence of overlap on the hyperparameters using the replica symmetric theory for the infinite-range model. The theory shows that our technique achieves the same optimal performance with that by the Ising spins. This statement is qualitatively confirmed by Monte Carlo simulations for two-dimensional images. Furthermore we estimate the dynamics of our technique by using Monte Carlo simulations. The simulations reveal that the convergence to the restored image is faster than that by the Ising model at low temperature.

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