Multi-State Image Restoration by Transmission of Bit-Decomposed Data

We report on the restoration of gray-scale image when it is decomposed into a binary form before transmission. We assume that a gray-scale image expressed by a set of Q-Ising spins is first decomposed into an expression using Ising (binary) spins by means of the threshold division, namely, we produce (Q-1) binary Ising spins from a Q-Ising spin by the function F(\sigma_i - m) = 1 if the input data \sigma_i \in {0,.....,Q-1} is \sigma_i \geq m and 0 otherwise, where m \in {1,....,Q-1} is the threshold value. The effects of noise are different from the case where the raw Q-Ising values are sent. We investigate which is more effective to use the binary data for transmission or to send the raw Q-Ising values. By using the mean-field model, we first analyze the performance of our method quantitatively. Then we obtain the static and dynamical properties of restoration using the bit-decomposed data. In order to investigate what kind of original picture is efficiently restored by our method, the standard image in two dimensions is simulated by the mean-field annealing, and we compare the performance of our method with that using the Q-Ising form. We show that our method is more efficient than the one using the Q-Ising form when the original picture has large parts in which the nearest neighboring pixels take close values.Comment: latex 24 pages using REVTEX, 10 figures, 4 table

Infinite-range transverse field Ising models and quantum computation

We present a brief review on information processing, computing and inference via quantum fluctuation, and clarify the relationship between the probabilistic information processing and theory of quantum spin glasses through the analysis of the infinite-range model. We also argue several issues to be solved for the future direction in the research field.Comment: 13 pages, 6 figures, using svjour.cls, to appear in EPJ-Special Topic

Image restoration using the chiral Potts spin-glass

We report on the image reconstruction (IR) problem by making use of the random chiral q-state Potts model, whose Hamiltonian possesses the same gauge invariance as the usual Ising spin glass model. We show that the pixel representation by means of the Potts variables is suitable for the gray-scale level image which can not be represented by the Ising model. We find that the IR quality is highly improved by the presence of a glassy term, besides the usual ferromagnetic term under random external fields, as very recently pointed out by Nishimori and Wong. We give the exact solution of the infinite range model with q=3, the three gray-scale level case. In order to check our analytical result and the efficiency of our model, 2D Monte Carlo simulations have been carried out on real-world pictures with three and eight gray-scale levels.Comment: RevTex 13 pages, 10 figure

Statistical mechanics of image restoration and error-correcting codes

We develop a statistical-mechanical formulation for image restoration and error-correcting codes. These problems are shown to be equivalent to the Ising spin glass with ferromagnetic bias under random external fields. We prove that the quality of restoration/decoding is maximized at a specific set of parameter values determined by the source and channel properties. For image restoration in mean-field system a line of optimal performance is shown to exist in the parameter space. These results are illustrated by solving exactly the infinite-range model. The solutions enable us to determine how precisely one should estimate unknown parameters. Monte Carlo simulations are carried out to see how far the conclusions from the infinite-range model are applicable to the more realistic two-dimensional case in image restoration.Comment: 20 pages, 9 figures, ReVTe

Application of the quantum spin glass theory to image restoration

Quantum fluctuation is introduced into the Markov random fields (MRF's) model for image restoration in the context of Bayesian approach. We investigate the dependence of the quantum fluctuation on the quality of BW image restoration by making use of statistical mechanics. We find that the maximum posterior marginal (MPM) estimate based on the quantum fluctuation gives a fine restoration in comparison with the maximum a posterior (MAP) estimate or the thermal fluctuation based MPM estimate.Comment: 19 pages, 9 figures, 1 table, RevTe

Minimum entropy restoration using FPGAs and high-level techniques

One of the greatest perceived barriers to the widespread use of FPGAs in image processing is the difficulty for application specialists of developing algorithms on reconfigurable hardware. Minimum entropy deconvolution (MED) techniques have been shown to be effective in the restoration of star-field images. This paper reports on an attempt to implement a MED algorithm using simulated annealing, first on a microprocessor, then on an FPGA. The FPGA implementation uses DIME-C, a C-to-gates compiler, coupled with a low-level core library to simplify the design task. Analysis of the C code and output from the DIME-C compiler guided the code optimisation. The paper reports on the design effort that this entailed and the resultant performance improvements

Naive mean field approximation for image restoration

We attempt image restoration in the framework of the Baysian inference. Recently, it has been shown that under a certain criterion the MAP (Maximum A Posterior) estimate, which corresponds to the minimization of energy, can be outperformed by the MPM (Maximizer of the Posterior Marginals) estimate, which is equivalent to a finite-temperature decoding method. Since a lot of computational time is needed for the MPM estimate to calculate the thermal averages, the mean field method, which is a deterministic algorithm, is often utilized to avoid this difficulty. We present a statistical-mechanical analysis of naive mean field approximation in the framework of image restoration. We compare our theoretical results with those of computer simulation, and investigate the potential of naive mean field approximation.Comment: 9 pages, 11 figure