Determination of parameters in an image recovery by statistical-mechanical means

Morita, Tohru; Tanaka, Kazu.

doi:10.1016/0378-4371(95)00276-6

Cited by 31 publications

(8 citation statements)

References 8 publications

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“…The method of Ref. 11 or the method of maximization of the marginal likelihood [13] Step 2: By solving Eqs. (22) to (25) for the obtained estimate, 〈σ (2) (x)〉 and 〈σ 1 (2) (x)〉 are obtained and are used as the estimates for σ (2) (x) / (2|L|) and σ 1 (2) (x) / (2|L|), respectively.…”

Section: Summary Of the Proposed Methodsmentioning

confidence: 99%

“…10, the values obtained by evaluating the original image x are used for σ where p is estimated from the degraded image y. Since the formulation in this paper is essentially based on the microcanonical distribution, it seems a very natural strategy to apply the hyperparameter estimation based on the microcanonical distribution for the binary image which was proposed by Morita and Tanaka [11]. On the other hand, there exists a method of maximization of the marginal likelihood which is the general hyperparameter estimation method in the statistics.…”

Section: Framework Of Gray-level Image Restoration Based On Microcanomentioning

confidence: 99%

“…One is the method given in Ref. 11 and the other is a method using maximization of the marginal likelihood [13].…”

Section: Framework Of Gray-level Image Restoration Based On Microcanomentioning

confidence: 99%

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Automatic hyperparameter estimation in probabilistic image restoration algorithm based on Gibbs microcanonical distribution

Tanaka

2004

Syst. Comp. Jpn.

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SUMMARYFor an original image given as an 8-gray-level image, the framework for image restoration is composed of Bayes statistics for the a priori probability distribution based on the microcanonical distribution. In this process, the a priori probability distribution serving as the microcanonical distribution is formulated on the basis of the variables characterizing the spatial flatness and smoothness of the image in terms of the number of nearest pixel pairs with different gray levels and the number of nearest pixel pairs with gray levels differing by 1. In the present paper, we propose a new method of estimation, from a degraded image, of the number of nearest pixel pairs with different gray levels and the number of nearest pixel pairs with gray levels differing by 1 in the original image. Then, based on that formulation, an iterative computation algorithm for the restoration of a 256-gray-level image is presented from the viewpoint of statistical mechanics. Through some numerical experiments, we investigate how the proposed method can improve the quality of the restored image.

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Section: Summary Of the Proposed Methodsmentioning

confidence: 99%

Section: Framework Of Gray-level Image Restoration Based On Microcanomentioning

confidence: 99%

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Automatic hyperparameter estimation in probabilistic image restoration algorithm based on Gibbs microcanonical distribution

Tanaka

2004

Syst. Comp. Jpn.

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“…Igarashi and Kawato [8] have shown that the Markov random field model can be derived from the regularization theory. A major problem in the Markov random field model is how to estimate the global parameters, and hence various methods for the estimation have been considered [46,8,12,13]. In particular, Morita and Tanaka [12] have considered an image restoration problem under the assumption that the total number of pairs of nearest-neighbor sites, which have different values of pixels in the original image, is accurately known.…”

Section: Introductionmentioning

confidence: 99%

Quantum statistical-mechanical iterative method in image restoration

Tanaka

Horiguchi

2000

Electron. Comm. Jpn. Pt. III

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“…Geman and Geman applied this to the recovery of corrupted images by using simulated annealing of a spin-S Ising model. After that, Gidas [9] proposed a new method based on a combination of the renormalization group technique and the simulated annealing procedure; then, Zhang [10] introduced Mean-Field Annealing to treat the image reconstruction problem, while Tanaka and Morita [11,12] applied the cluster variation method. Methods of statistical mechanics have also been used to study combinatorial optimization problems (see, e.g., [13] and references therein).…”

Section: Introductionmentioning

confidence: 99%

Statistical mechanics approach to the phase unwrapping problem

Stramaglia

Refice

Guerriero

2000

Physica A: Statistical Mechanics and its Applications

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The use of Mean-Field theory to unwrap principal phase patterns has been recently proposed. In this paper we generalize the Mean-Field approach to process phase patterns with arbitrary degree of undersampling. The phase unwrapping problem is formulated as that of finding the ground state of a locally constrained, finite size, spin-L Ising model under a non-uniform magnetic field. The optimization problem is solved by the Mean-Field Annealing technique. Synthetic experiments show the effectiveness of the proposed algorithm

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Determination of parameters in an image recovery by statistical-mechanical means

Cited by 31 publications

References 8 publications

Automatic hyperparameter estimation in probabilistic image restoration algorithm based on Gibbs microcanonical distribution

Automatic hyperparameter estimation in probabilistic image restoration algorithm based on Gibbs microcanonical distribution

Quantum statistical-mechanical iterative method in image restoration

Statistical mechanics approach to the phase unwrapping problem

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