Yohei Saika

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

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.

Bayesian inference in optical measurement due to remote sensing to synthetic aperture radar interferometry

We investigated the Bayesian inferences using the maximize a posteriori (MAP) estimation for the problem of phase unwrapping in remote sensing using the synthetic aperture radar (SAR) interferometry. Then, in order to clarify performance of the Bayesian inference estimate, we carried out Monte Carlo simulation for a set of wave-fronts generated by an assumed true prior. Then, we clarified that optimal performance was achieved under the Bayes-optimal condition within statistical uncertainty. Then, we clarified that the present method was effective even for an artificial wave-front in remote sensing due to SAR interferometry. Also, we found that the Bayesian inference via the conjugate gradient method to derive the MAP solution for this problem. Using the numerical simulation for the wave-front, we found that the MAP estimation using the conjugate gradient method was effective for phase unwrapping as well as the MPM estimate approximately.

Probabilistic modeling to inverse halftoning based on super resolution

On the basis of the Bayesian inference using the maximizer of the posterior marginal (MPM) estimate, we formulate the problem of inverse halftoning via the framework of super resolution for the organized dither method. Then, the Monte Carlo simulation for a set of the snapshots of the Q-Ising model clarifies that this method achieves optimal performance under the Bayes-optimal condition and that the Bayes-optimal solution reconstructs more accurately than the MAP estimate. Then, we find that the upper bound of the mean square error is inversely proportional to the number of halftone image in the procedure of inverse halftoning. Then, these results obtained by the Monte Carlo simulations are qualitatively confirmed by the analytical estimate using the infinite-range model. Further, we find that the present method is effective even for realistic images and however that false contour appears in reconstructed images, if we utilize a small number of the halftone images in the procedure of inverse halftoning.

Generalized statistical smoothing to the problem of inverse-halftoning for error diffusion

In order to reconstruct a gray-level image from the halftone image generated by the error diffusion method, we introduce the generalized parameter scheduling into the parameters for edge enhancement procedure in the statistical smoothing and tune the parameters to reconstruct the original gray-level image with high accuracy. Then, we numerically estimate both the static and dynamic properties of the present method based on the PSNR, the gray-level histogram and the gray-level on the segment across the edges. The simulations clarify that the generalized statistical smoothing improves the performance by introducing the generalized parameter scheduling into the edge enhancement procedure, and that the edges of the original images are accurately reconstructed by the present method, although the small peaks appear in the histogram of the gray-level.

Probabilistic Inference to the Problem of Inverse-halftoning based on Statistical Mechanics of Spin Systems

On the basis of statistical mechanics of spin systems, we formulate the problem of inverse-halftoning using the maximizer of the posterior marginal (MPM) estimate for halftone images which are generated both by the threshold mask method and the clustered-dot dither method. Then, the Monte Carlo simulation for a halftone image clarifies that the MPM estimate works well for inverse-halftoning, if we appropriately set parameters of the Boltzmann factor of the ferromagnetic Q-Ising model used for the model prior. Also, we reveal the result that inverse-halftoning is achieved in inner area of the threshold mask more accurately than on the boundary

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.

Probabilistic Inference to the Problem of Inverse-halftoning based on Statistical Mechanics of the Q-Ising Model

On the basis of statistical mechanics of the Q-Ising model, we formulate the problem of inverse-halftoning using the maximizer of the posterior marginal (MPM) estimate for halftone images obtained by the threshold mask method. Then, we estimate the performance of the method in terms of the mean square error and the histogram of the gray-level using the Markov-chain Monte Carlo simulation. The simulation for a set of snapshots of the Q-Ising model reveals the results that the MPM estimate works effectively for the problem of inverse-halftoning, if we appropriately set the parameters of the model prior expressed by the Boltzmann factor of the Q-Ising model. We then clarify that the model prior shifts the gray-level images from both sides to the middle range of the gray-level in the procedure of inverse-halftoning. Also, these properties are confirmed by the MCMC method even for real-world images.

Quantum mean-field decoding algorithm for error-correcting codes

We numerically examine a quantum version of TAP (Thouless-Anderson-Palmer)-like mean-field algorithm for the problem of error-correcting codes. For a class of the so-called Sourlas error-correcting codes, we check the usefulness to retrieve the original bit-sequence (message) with a finite length. The decoding dynamics is derived explicitly and we evaluate the average-case performance through the bit-error rate (BER).

Dynamics of predicting temperature-humidity index and power consumption in small-scale system utilizing Bayesian inference via the EAP estimation

By making use of environmental quantities, such as temperature and relative humidity, we search optimal conditions on thermal index called as the temperature-humidity index (THI) at each sampling point and power consumption due to air conditioning, both of which are estimated by repeating the Bayesian inference using the EAP estimation with an increase in the ratio of the coefficient of the model prior as to that of the likelihood. Then, we estimate static property of the Bayesian inference and dynamic property of the iterative method by making use of numerical calculations for several cases. Numerical results show that the iterative method succeeds in searching the optimal conditions on the environmental variables, if we increase the ratio up to its optimum respective of the choice of observed variables. These results are confirmed by the mean-field theory for the full-connected model.

Bayesian inference using the expected a posterior estimation for predicting comfort environment and effective usage of power based on thermal index via the temperature-humidity index

By making use of Bayesian inference using the expected a posterior (EAP) estimation, we construct an information technique for providing temperature and relative humidity so as to realize effective usage of electric power under comfortable environment based on the temperature-humidity index (THI) at a small-scale target system. In this method, we estimate the temperature and the relative humidity as expectations which are averaged over the posterior probability composed of the model of the true prior generating a set of ideal environments at the target room and the likelihood rewriting each original ideal environment to a realistic one observed at the target room. Numerical calculations find that we succeed in providing the temperature and the relative humidity both of which lead to comfortable environment and effective usage of power due to air conditioning at the target room, if we tune parameters appropriately. Also, we find that upper bound of the overlap is realized, if we use the assumed true prior and the transition probability from the original to observed states.