Image restoration with a truncated Gaussian model

Hiroyuki Tanaka, Keiji Miura, Masato Okada

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)

Abstract

The Gaussian model for image restoration has the problem of positive probability densities for pixels outside the realistic range. To solve this problem, we introduce a truncated Gaussian model (TG model). In this model, the tails of the Gaussian distribution are cut off at upper and lower bounds and are replaced by δ peaks at the cut boundaries. We analytically obtain the average performance of the TG model in a mean-field system by solving exactly the infinite-range model and using the replica method. We also compare the infinite-range model to the more realistic two-dimensional case by Monte Carlo simulations. When modeling the TG model, we introduce a generalized prior probability. This prior probability includes the Gaussian, Ising, Q-Ising spin, and TG model as special cases. Thus, we can choose an appropriate model depending on the statistical properties of the images.

Original languageEnglish
Article number034003
Journaljournal of the physical society of japan
Volume77
Issue number3
DOIs
Publication statusPublished - 2008 Mar 1

Keywords

  • Bayesian estimation
  • Image restoration
  • Replica method
  • Statistical mechanics
  • Truncated Gaussian models

ASJC Scopus subject areas

  • Physics and Astronomy(all)

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