Staistical-mechanical Iterative Algorithm by means of Cluster Variation Method in Compound Gauss-Markov Random Field Model

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  • Tanaka Kazuyuki
    Department of Computer and Mathematical Sciences, Graduate School of Information Sciences, Tohoku University

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  • 結合ガウス・マルコフ確率場モデルに対するクラスター変分法による統計力学的反復計算アルゴリズム
  • ケツゴウ ガウス マルコフ カクリツバ モデル ニ タイスル クラスター ヘン ブンホウ ニ ヨル トウケイ リキガクテキ ハンプク ケイサン アルゴリズム

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Compound Gauss-Markov random field model is one of Markov random field models for natural image restorations. An optimization algorithm was constructed by means of mean-field approximation, which is a familiar techniques for analyzing massive probabilistic models approximately in the statistical mechanics. Cluster variation method was proposed as an extended version of the mean-field approximation in the statistical mechanics. Though the mean-field approximation treat only the marginal probability distribution for every single pixel, the cluster variation method can take acount into the correlation between pixels by treating the marginal probability distribution for every nearest neighbor pair of pixels. In this paper, we propose a newstatistical-mechanical iterative algorithm by means of the cluster variation method for natural image restorations in the compound Gauss-Markov random field model. In some numerical experiments, it is investigate howthe proposed algorithm improves the quality of restored images by comparing it with the algorithm constructed from the mean-field approximation.

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