Variational Dirichlet Blur Kernel Estimation

Xu Zhou, Javier Mateos, Fugen Zhou, Rafael Molina, Aggelos K. Katsaggelos

Research output: Contribution to journalArticlepeer-review

27 Scopus citations


Blind image deconvolution involves two key objectives: 1) latent image and 2) blur estimation. For latent image estimation, we propose a fast deconvolution algorithm, which uses an image prior of nondimensional Gaussianity measure to enforce sparsity and an undetermined boundary condition methodology to reduce boundary artifacts. For blur estimation, a linear inverse problem with normalization and nonnegative constraints must be solved. However, the normalization constraint is ignored in many blind image deblurring methods, mainly because it makes the problem less tractable. In this paper, we show that the normalization constraint can be very naturally incorporated into the estimation process by using a Dirichlet distribution to approximate the posterior distribution of the blur. Making use of variational Dirichlet approximation, we provide a blur posterior approximation that considers the uncertainty of the estimate and removes noise in the estimated kernel. Experiments with synthetic and real data demonstrate that the proposed method is very competitive to the state-of-the-art blind image restoration methods.

Original languageEnglish (US)
Article number7265038
Pages (from-to)5127-5139
Number of pages13
JournalIEEE Transactions on Image Processing
Issue number12
StatePublished - Dec 1 2015


  • Blind deconvolution
  • Dirichlet distribution
  • constrained optimization
  • image deblurring
  • inverse problem
  • point spread function
  • variational distribution approximations

ASJC Scopus subject areas

  • Software
  • Computer Graphics and Computer-Aided Design


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