Statistical Mechanical Approach to Image Processing Technology Bayes-Optimal Solution to Inverse Halftoning via Super-Resolution

Abstract

We apply statistical mechanics of the Q-Ising model to a typical problem in information processing technology which is called as inverse halftoning. Here, we reconstruct an original image by making use of multiple dithered images so as to maximize the posterior marginal probability. Then, in order to clarify the validity of the present method, we estimate upper bound of the performance using the Monte Carlo simulation both for a 256-level standard image and a set of gray-level images generated by an assumed true prior. The simulation for the gray-level images finds that the lower bound of the root mean square becomes smaller with the increase in the number of dithered images and that image reconstruction is perfectly carried out, if Q kinds of dithered images are utilized, where Q is the number of the gray-levels. These properties are qualitatively confirmed by the analytical estimate using the infinite-range model. Further, we find that the performance for a 256-level image is improved by utilizing prior information on gray-level images, even if we use a small number of dithered images.