Mean field theory of EM algorithm for Bayesian grey scale image restoration

Jun Ichi Inoue, Kazuyuki Tanaka

Research output: Contribution to journalArticle

10 Citations (Scopus)

Abstract

The EM algorithm for the Bayesian grey scale image restoration is investigated in the framework of the mean field theory. Our model system is identical to the infinite range random field script Q sign-Ising model. The maximum marginal likelihood method is applied to the determination of hyper-parameters. We calculate both the data-averaged mean square error between the original image and its maximizer of posterior marginal estimate, and the data-averaged marginal likelihood function exactly. After evaluating the hyper-parameter dependence of the data-averaged marginal likelihood function, we derive the EM algorithm which updates the hyper-parameters to obtain the maximum likelihood estimate analytically. The time evolutions of the hyper-parameters and so-called Q function are obtained. The relation between the speed of convergence of the hyper-parameters and the shape of the Q function is explained from the viewpoint of dynamics.

Original languageEnglish
Pages (from-to)10997-11010
Number of pages14
JournalJournal of Physics A: Mathematical and General
Volume36
Issue number43
DOIs
Publication statusPublished - 2003 Oct 31

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics
  • Physics and Astronomy(all)

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