Q-Ising Model Research Articles

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

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.

A Q-Ising model application for linear-time image segmentation

Abstract A computational method is presented which efficiently segments digital grayscale images by directly applying the Q-state Ising (or Potts) model. Since the Potts model was first proposed in 1952, physicists have studied lattice models to gain deep insights into magnetism and other disordered systems. For some time, researchers have realized that digital images may be modeled in much the same way as these physical systems (i.e., as a square lattice of numerical values). A major drawback in using Potts model methods for image segmentation is that, with conventional methods, it processes in exponential time. Advances have been made via certain approximations to reduce the segmentation process to power-law time. However, in many applications (such as for sonar imagery), real-time processing requires much greater efficiency. This article contains a description of an energy minimization technique that applies four Potts (Q-Ising) models directly to the image and processes in linear time. The result is analogous to partitioning the system into regions of four classes of magnetism. This direct Potts segmentation technique is demonstrated on photographic, medical, and acoustic images.

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

Abstract 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.

Controlling the dynamics of multi-state neural networks

In this paper, we first analyze the distribution of local fields (DLF) which is induced by the memory patternsin the Q-Ising model. It is found that the structure of the DLF is closely correlated with thenetwork dynamics and the system performance. However, the design rule adopted in theQ-Ising model, like the other rules adopted for multi-state neural networks with associativememories, cannot be applied to directly control the DLF for a given set of memorypatterns, and thus cannot be applied to further study the relationships between thestructure of the DLF and the dynamics of the network. We then extend a design rule,which was presented recently for designing binary-state neural networks, to make itsuitable for designing general multi-state neural networks. This rule is able tocontrol the structure of the DLF as expected. We show that controlling the DLFnot only can affect the dynamic behaviors of the multi-state neural networksfor a given set of memory patterns, but also can improve the storage capacity.With the change of the DLF, the network shows very rich dynamic behaviors,such as the ‘chaos phase’, the ‘memory phase’, and the ‘mixture phase’. Thesedynamic behaviors are also observed in the binary-state neural networks; therefore,our results imply that they may be the universal behaviors of feedback neuralnetworks.

Probabilistic inference to the problem of inverse-halftoning based on statistical mechanics of the Q-Ising model

Abstract. On the basis of statistical mechanics of the Q-Ising model on the square lattice, we apply the maximizer of the posterior marginal (MPM) estimate to the problem of inverse-halftoning for halftone images generated by the probabilistic threshold mask method. Then, the Monte Carlo simulation clarifies that the MPM estimate achieves the same performance with the conventional linear filter if we use a free prior, and that the performance of the MPM estimate is improved if we appropriately set parameters of the model prior expressed by the Boltzmann factor of the Q-Ising model on the square lattice. Furthermore, we also find that the MPM estimate shows better performance in inner areas of the Bayer's arrays than on the boundaries.

Probabilistic inference to the problem of atmospheric compensation in adaptive optics

On the basis of statistical mechanics of the Q-Ising model on the square lattice, we apply the maximizer of the posterior marginal (MPM) estimate to the problem of phase retrieval in adaptive optics. Then, using the Markov-chain Monte Carlo simulation, we estimate the performance of the MPM estimate for a typical wave-front in adaptive optics. Our method is divided into two kinds in accordance with the sensitivity of measurement by optical instruments using the shearing interferometer. The Monte Carlo simulation shows the result that the MPM estimate works effectively if we selectively choose the model of the true prior according to the sensitivity of measurement.

Statistical-mechanical approaches to the problem of phase retrieval in adaptive optics in astronomy

We construct the statistical-mechanical formulation for the problem of phase retrieval in adaptive optics for astronomy using the Q-Ising model on the square lattice. This method is based on the maximizer of the posterior marginal (MPM) estimate which is classified into two kinds selectively used according to the sensitivity of measurement. Next, using the Markov-chain Monte Carlo simulation for a typical wave-front in adaptive optics, we obtains the result that our method works well for phase retrieval if we appropriately select the model of the true prior respective of the sensitivity of measurement. Further, these results are qualitatively confirmed by the replica theory for the infinite-range model.

Statistical-Mechanical Approaches to the Problem of Phase Retrieval by theQ-Ising Model

We construct the statistical-mechanical formulation for the problem of phase retrieval by the Q-Ising model. We estimate the performance of our method using the replica theory for the infinite-range model and Monte Carlo simulation for the two-dimensional realistic model appearing in adaptive optics. We verify the result that our method works well for retrieving phases if we choose the appropriate model of the true prior respective of the sensitivity of measurement.

Probabilistic image processing by means of the Bethe approximation for theQ-Ising model

The framework of Bayesian image restoration for multi-valued images by means of the Q-Ising model with nearest-neighbour interactions is presented. Hyperparameters in the probabilistic model are determined so as to maximize the marginal likelihood. A practical algorithm is described for multi-valued image restoration based on the Bethe approximation. The algorithm corresponds to loopy belief propagation in artificial intelligence. We conclude that, in real world grey-level images, the Q-Ising model can give us good results.