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Bayes-optimal solution to inverse halftoning based on statistical mechanics of the Q-Ising model

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Saika Y., Inoue J.-i., Tanaka H., Okada M.
Open Physics
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2009
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vol. 7
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issue 3
444-456
EN
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 Q-Ising model, we are sucessful in constructing a practically useful method of inverse halftoning using the Bethe approximation.
2
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Environmental dependence of stellar velocity dispersion in the Main galaxy sample of SDSS DR10

100%
Deng X.-F.
Open Physics
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2015
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vol. 13
|
issue 1
EN
The aim of this work is to examine the environmental dependence of stellar velocity dispersion in local galaxies. In studies that likely suffer from the radial selection effect, one has a preference for the use of volumelimited samples. Two volume-limited samples with different redshift and luminosity ranges were constructed from the Main galaxy data of the Sloan Digital Sky Survey Data Release 10 (SDSS DR10). Considering some drawbacks of volume-limited samples, the apparent magnitude-limited Main galaxy sample was also applied. Statistical analyses in these different galaxy samples can reach the same conclusion: galaxies with large stellar velocity dispersions exist preferentially in high density regimes, while galaxies with small stellar velocity dispersions are located preferentially in low density regions, which is inconsistent with that obtained at intermediate redshifts.
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