Hyperparameter estimation in image restoration problems with partially known blurs

Nikolas P. Galatsanos, Vladimir Z. Mesarović, Rafael Molina, Aggelos K. Katsaggelos, Javier Mateos

Research output: Contribution to journalArticlepeer-review

47 Scopus citations


This work is motivated by the observation that it is not possible to reliably estimate simultaneously all the necessary hyperparameters in an image restoration problem when the point-spread function is assumed to be the sum of a known deterministic and an unknown random component. To solve this problem we propose to use gamma hyperpriors for the unknown hyperparameters. Two iterative algorithms that simultaneously restore the image and estimate the hyperparameters are derived, based on the application of evidence analysis within the hierarchical Bayesian framework. Numerical experiments are presented that show the benefits of introducing hyperpriors for this problem.

Original languageEnglish (US)
Pages (from-to)1845-1854
Number of pages10
JournalOptical Engineering
Issue number8
StatePublished - Aug 2002


  • Bayesian estimation
  • Gamma hyperpriors
  • Hyperparameter estimation
  • Image restoration
  • Partially known blur

ASJC Scopus subject areas

  • Atomic and Molecular Physics, and Optics
  • Engineering(all)


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