Blind deconvolution using a variational approach to parameter, image, and blur estimation

Rafael Molina*, Javier Mateos, Aggelos K. Katsaggelos

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

184 Scopus citations


Following the hierarchical Bayesian framework for blind deconvolution problems, in this paper, we propose the use of simultaneous autoregressions as prior distributions for both the image and blur, and gamma distributions for the unknown parameters (hyperparameters) of the priors and the image formation noise. We show how the gamma distributions on the unknown hyperparameters can be used to prevent the proposed blind deconvolution method from converging to undesirable image and blur estimates and also how these distributions can be inferred in realistic situations. We apply variational methods to approximate the posterior probability of the unknown image, blur, and hyperparameters and propose two different approximations of the posterior distribution. One of these approximations coincides with a classical blind deconvolution method. The proposed algorithms are tested experimentally and compared with existing blind deconvolution methods.

Original languageEnglish (US)
Pages (from-to)3715-3727
Number of pages13
JournalIEEE Transactions on Image Processing
Issue number12
StatePublished - Dec 2006


  • Bayesian framework
  • Blind deconvolution
  • Parameter estimation
  • Variational methods

ASJC Scopus subject areas

  • Software
  • Computer Graphics and Computer-Aided Design


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