Maximum likelihood hyperparameter estimation for solvable Markov random field model in image restoration

Kazuyuki Tanaka, Jun Ichi Inoue

Research output: Contribution to journalArticlepeer-review

14 Citations (Scopus)


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 hyper-parameters 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.

Original languageEnglish
Pages (from-to)546-557
Number of pages12
JournalIEICE Transactions on Information and Systems
Issue number3
Publication statusPublished - 2002 Mar


  • Bayes statistics
  • Evidence
  • Image restoration
  • Markov random fields
  • Maximum likelihood estimation

ASJC Scopus subject areas

  • Software
  • Hardware and Architecture
  • Computer Vision and Pattern Recognition
  • Electrical and Electronic Engineering
  • Artificial Intelligence


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