Bayesian and regularization methods for hyperparameter estimation in image restoration

Rafael Molina*, Aggelos K. Katsaggelos, Javier Mateos

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

162 Scopus citations


In this paper, we propose the application of the hierarchical Bayesian paradigm to the image restoration problem. We derive expressions for the iterative evaluation of the two hyperparameters applying the evidence and maximum a posteriori (MAP) analysis within the hierarchical Bayesian paradigm. We show analytically that the analysis provided by the evidence approach is more realistic and appropriate than the MAP approach for the image restoration problem. We furthermore study the relationship between the evidence and an iterative approach resulting from the set theoretic regularization approach for estimating the two hyperparameters, or their ratio, defined as the regularization parameter. Finally the proposed algorithms are tested experimentally.

Original languageEnglish (US)
Pages (from-to)231-246
Number of pages16
JournalIEEE Transactions on Image Processing
Issue number2
StatePublished - 1999


  • Hierarchical bayesian models
  • Image restoration
  • Parameter estimation
  • Regularization

ASJC Scopus subject areas

  • Software
  • Computer Graphics and Computer-Aided Design


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