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Physical consideration of an image in image restoration using Bayes’ formula

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  • Kiwata, Hirohito

Abstract

We consider image restoration by Bayes’ formula and investigate the relationship between an image and a prior probability from the following two viewpoints: hyperparameter estimation and the accuracy of a restored image. The Q-Ising model is adopted as a prior probability in Bayes’ formula. Not the Q-Ising energy, but the Potts energy plays an important role in the hyperparameter estimation. From the viewpoint of the hyperparameter estimation, the relationship between a natural image and a prior probability is characterized through the Potts energy and magnetization of an image. The Potts energy and magnetization of an image are defined by a set of pixels’ state of an image. The closer to the average Potts energy and magnetization over a prior probability the Potts energy and magnetization of a natural image is, the closer to the true value of a hyperparameter the estimated value of a hyperparameter from a degraded image is. For the accuracy of a restored image, the image which has a smaller Q-Ising energy is better restored by Bayes’ formula composed of the Q-Ising prior. The consideration for the relationship between an image and a prior probability is expected to be valid for a more complicated prior probability.

Suggested Citation

  • Kiwata, Hirohito, 2012. "Physical consideration of an image in image restoration using Bayes’ formula," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(6), pages 2215-2224.
    • Handle: RePEc:eee:phsmap:v:391:y:2012:i:6:p:2215-2224
    DOI: 10.1016/j.physa.2011.11.025
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    References listed on IDEAS

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    1. Stramaglia, Sebastiano & Refice, Alberto & Guerriero, Luciano, 2000. "Statistical mechanics approach to the phase unwrapping problem," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 276(3), pages 521-534.
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    Cited by:

    1. Ma, Tinghuai & Li, Lu & Ji, Sai & Wang, Xin & Tian, Yuan & Al-Dhelaan, Abdullah & Al-Rodhaan, Mznah, 2014. "Optimized Laplacian image sharpening algorithm based on graphic processing unit," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 416(C), pages 400-410.

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