2023-12-04T09:46:39Zhttps://eprints.lib.hokudai.ac.jp/dspace-oai/requestoai:eprints.lib.hokudai.ac.jp:2115/425392022-11-17T02:08:08Zhdl_2115_20053hdl_2115_145Bayes-optimal solution to inverse halftoning based on statistical mechanics of the Q-Ising modelSaika, YoheiInoue, Jun-IchiTanaka, HiroyukiOkada, Masatostatistical mechanicsinverse halftoningMonte Carlo simulationinfinite-range modelBethe approximationPACS=01.30.-yPACS=01.30.XxPACS=01.30.Tt421On 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 Q-Ising model, we are sucessful in constructing a practically useful method of inverse halftoning using the Bethe approximation.Versita, co-published with Springer-Verlag GmbHJournal Articleapplication/pdfhttp://hdl.handle.net/2115/42539https://eprints.lib.hokudai.ac.jp/dspace/bitstream/2115/42539/3/SaikaInoueTanakaOkada2009_authorsV.pdf1895-10821644-3608Central European Journal of Physics734444562009-09enginfo:doi/10.2478/s11534-009-0066-0The original publication is available at www.springerlink.comauthor