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首页> 外文期刊>Physica, A. Statistical mechanics and its applications >Physical consideration of an image in image restoration using Bayes' formula
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Physical consideration of an image in image restoration using Bayes' formula

机译：使用贝叶斯公式进行图像恢复时对图像的物理考虑

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摘要

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.
机译：我们通过贝叶斯公式考虑图像恢复，并从以下两个角度研究图像与先验概率之间的关系：超参数估计和恢复图像的准确性。贝叶斯公式采用Q-Ising模型作为先验概率。不是Q-Ising能量，而是Potts能量在超参数估计中起着重要作用。从超参数估计的观点来看，自然图像和先验概率之间的关系通过波兹能量和图像的磁化来表征。图像的Potts能量和磁化强度由图像的一组像素状态定义。自然图像的Potts能量和磁化强度在先验概率下越接近平均Potts能量和磁化强度，则从降级图像得出的超参数估计值就越接近超参数的真实值。为了恢复图像的准确性，具有较小Q-Ising能量的图像可以通过由Q-Ising先验组成的贝叶斯公式更好地恢复。对于更复杂的先验概率，期望对图像和先验概率之间的关系的考虑是有效的。

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