Statistical-mechanical analysis of dynamical properties of algorithms for image restoration
| Project/Area Number |
14084201
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| Research Category |
Grant-in-Aid for Scientific Research on Priority Areas
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| Allocation Type | Single-year Grants |
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| Review Section |
Science and Engineering
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| Research Institution | Hokkaido University |
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Principal Investigator |
INOUE Jun-ichi Hokkaido University, Graduate School of Information Science and 'Technology, Associate Professor, 大学院情報科学研究科, 助教授 (30311658)
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| Project Period (FY) |
2002 – 2005
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| Project Status |
Completed (Fiscal Year 2005)
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| Budget Amount *help |
¥7,900,000 (Direct Cost: ¥7,900,000)
Fiscal Year 2005: ¥1,800,000 (Direct Cost: ¥1,800,000)
Fiscal Year 2004: ¥1,900,000 (Direct Cost: ¥1,900,000)
Fiscal Year 2003: ¥1,800,000 (Direct Cost: ¥1,800,000)
Fiscal Year 2002: ¥2,400,000 (Direct Cost: ¥2,400,000)
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| Keywords | Probabilistic image processing / Statistical mechanics of information / Bavesian Statistics / EM algorithm / Replica method / Non-extensive statistical mechanics / Quantum fluctuation / Evaluation of statistical performance / 統計力学 / 情報科学 / 画像修復 / ダイナミックス / マルコフ連鎖モンテカルロ法 / 確率的情報処理 / フラストレートした格子模型 / 量子スピングラス / 量子アニーリング / アルゴリズムの平均的性能評価 / ランダムスピン系 / 平均場理論 / ベーテ近似 / 非加法的エントロピー / ベイズ推定 / ダイナミックス解析 / 不完全データからの最尤推定 |
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| Research Abstract |
In this research project, we investigated the dynamical properties of Bayesian image restoration for the blapk-while binary and gray-scaled images represented by the Ising and the Q-Ising models, respectively. We introduced the mean-field model to evaluate the accuracy or the speed of the convergence for EM algorithm and gradient descent method to obtain the maximum likelihood estimate for the hyper-parameters. We found that EM algorithm is superior to the gradient descent method in the speed of the convergence. Moreover, our analysis made it clear that the dynamical behavior of the hyper-parameters shows a kind of the "oscillating phenomena " before they converge to their true values if the time to wait until the system reaches to the equilibrium states is not enough.
We also proposed a new-type of the deterministic annealing EM algorithm which was extended by means of non-extensive statistical mechanics. The method was applied to the problem of Traveling salesman and the statistical performance was investigated extensively.
We also presented several applications of quantum spin glasses (random field Ising model, Shermgton-KJrkpatrick model, Ising spin glasses with p-body interaction in a transverse field) to probabilistic information processing, especially to the problems of image restoration and error-correcting codes. As a related optimization method, quantum annealing was also introduced to these research fields and its performance was investigated by using the quantum Markov chain Monte Carlo method. The Nishimori-Wong condition, on which the best possible performance of the quantum MPM estimation is achieved, was derived as a condition on the effective amplitude of the transverse field.
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Report
(5 results)
Research Products
(27 results)
