Maximum Likelihood Hyperparameter Estimation for Solvable Markov Random Field Model in Image Restoration
Summary :
We propose a new solvable Markov random field model for Bayesian image processing and give the exact expressions of the marginal likelihood and the restored image by using the multi-dimensional Gaussian formula and the discrete Fourier transform. The proposed Markov random field model includes the conditional autoregressive model and the simultaneous autoregressive model as a special case. The estimates of hyperparameters are obtained by maximizing the marginal likelihood. We study some statistical properties of the solvable Markov random field model. In some numerical experiments for standard images, we show that the proposed Markov random field model is useful for practical applications in image restorations. The investigation of probabilistic information processing by means of a solvable probabilistic model is recently in progress not only for image processing but also for error correcting codes and so on. The solvable probabilistic model gives us some important aspects for the availability of probabilistic computational systems.
- Publication
- IEICE TRANSACTIONS on Information Vol.E85-D No.3 pp.546-557
- Publication Date
- 2002/03/01
- Publicized
- Online ISSN
- DOI
- Type of Manuscript
- PAPER
- Category
- Image Processing, Image Pattern Recognition
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Kazuyuki TANAKA, Jun-ichi INOUE, "Maximum Likelihood Hyperparameter Estimation for Solvable Markov Random Field Model in Image Restoration" in IEICE TRANSACTIONS on Information,
vol. E85-D, no. 3, pp. 546-557, March 2002, doi: .
Abstract: We propose a new solvable Markov random field model for Bayesian image processing and give the exact expressions of the marginal likelihood and the restored image by using the multi-dimensional Gaussian formula and the discrete Fourier transform. The proposed Markov random field model includes the conditional autoregressive model and the simultaneous autoregressive model as a special case. The estimates of hyperparameters are obtained by maximizing the marginal likelihood. We study some statistical properties of the solvable Markov random field model. In some numerical experiments for standard images, we show that the proposed Markov random field model is useful for practical applications in image restorations. The investigation of probabilistic information processing by means of a solvable probabilistic model is recently in progress not only for image processing but also for error correcting codes and so on. The solvable probabilistic model gives us some important aspects for the availability of probabilistic computational systems.
URL: https://global.ieice.org/en_transactions/information/10.1587/e85-d_3_546/_p
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@ARTICLE{e85-d_3_546,
author={Kazuyuki TANAKA, Jun-ichi INOUE, },
journal={IEICE TRANSACTIONS on Information},
title={Maximum Likelihood Hyperparameter Estimation for Solvable Markov Random Field Model in Image Restoration},
year={2002},
volume={E85-D},
number={3},
pages={546-557},
abstract={We propose a new solvable Markov random field model for Bayesian image processing and give the exact expressions of the marginal likelihood and the restored image by using the multi-dimensional Gaussian formula and the discrete Fourier transform. The proposed Markov random field model includes the conditional autoregressive model and the simultaneous autoregressive model as a special case. The estimates of hyperparameters are obtained by maximizing the marginal likelihood. We study some statistical properties of the solvable Markov random field model. In some numerical experiments for standard images, we show that the proposed Markov random field model is useful for practical applications in image restorations. The investigation of probabilistic information processing by means of a solvable probabilistic model is recently in progress not only for image processing but also for error correcting codes and so on. The solvable probabilistic model gives us some important aspects for the availability of probabilistic computational systems.},
keywords={},
doi={},
ISSN={},
month={March},}
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TY - JOUR
TI - Maximum Likelihood Hyperparameter Estimation for Solvable Markov Random Field Model in Image Restoration
T2 - IEICE TRANSACTIONS on Information
SP - 546
EP - 557
AU - Kazuyuki TANAKA
AU - Jun-ichi INOUE
PY - 2002
DO -
JO - IEICE TRANSACTIONS on Information
SN -
VL - E85-D
IS - 3
JA - IEICE TRANSACTIONS on Information
Y1 - March 2002
AB - We propose a new solvable Markov random field model for Bayesian image processing and give the exact expressions of the marginal likelihood and the restored image by using the multi-dimensional Gaussian formula and the discrete Fourier transform. The proposed Markov random field model includes the conditional autoregressive model and the simultaneous autoregressive model as a special case. The estimates of hyperparameters are obtained by maximizing the marginal likelihood. We study some statistical properties of the solvable Markov random field model. In some numerical experiments for standard images, we show that the proposed Markov random field model is useful for practical applications in image restorations. The investigation of probabilistic information processing by means of a solvable probabilistic model is recently in progress not only for image processing but also for error correcting codes and so on. The solvable probabilistic model gives us some important aspects for the availability of probabilistic computational systems.
ER -
English
