Statistical-Mechanical Analysis of Inverse Digital-Halftoning

We propose a theoretical framework to investigate statistical performance of inverse digital-halftoning problems. In the context of the maximizer of the posterior marginal (MPM) estimate corresponding to the Markov random fields (MRFs) model in which each pixel takes discrete values such as 1, ..., Q, we formulate the problem of inverse digital-halftoning in which digital images are generated by the threshold constant and the so-called Bayers´ matrices. To construct the Gibbs sampler for the MRFs, we carry out Markov chain Monte Carlo (MCMC) simulations and investigate hyper-parameter dependence of the performance in terms of the mean-square error. By using the statistical-mechanical analysis, we also investigate averaged case performance of the inverse-halftoning for the corresponding analytically tractable class of the MRFs models. Both equilibrium and dynamical properties of the MPM estimation of the original grayscale images are revealed.