Variational EM method for blur estimation using the spike-and-slab image prior

Juan G. Serra*, Javier Mateos, Rafael Molina, Aggelos K. Katsaggelos

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


Most state-of-the-art blind image deconvolution methods rely on the Bayesian paradigm to model the deblurring problem and estimate both the blur kernel and latent image. It is customary to model the image in the filter space, where it is supposed to be sparse, and utilize convenient priors to account for this sparsity. In this paper, we propose the use of the spike-and-slab prior together with an efficient variational Expectation Maximization (EM) inference scheme to estimate the blur in the image. The spike-and-slab prior, which constitutes the gold standard in sparse machine learning, selectively shrinks irrelevant variables while mildly regularizing the relevant ones. The proposed variational Expectation Maximization algorithm is more efficient than usual Markov Chain Monte Carlo (MCMC) inference and, also, proves to be more accurate than the standard mean-field variational approximation. Additionally, all the prior model parameters are estimated by the proposed scheme. After blur estimation, a non-blind restoration method is used to obtain the actual estimation of the sharp image. We investigate the behavior of the prior in the experimental section together with a series of experiments with synthetically generated and real blurred images that validate the method's performance in comparison with state-of-the-art blind deconvolution techniques.

Original languageEnglish (US)
Pages (from-to)116-129
Number of pages14
JournalDigital Signal Processing: A Review Journal
StatePublished - May 2019


  • Blind image deconvolution
  • Blur estimation
  • Spike and slab
  • Variational inference

ASJC Scopus subject areas

  • Signal Processing
  • Computer Vision and Pattern Recognition
  • Statistics, Probability and Uncertainty
  • Computational Theory and Mathematics
  • Electrical and Electronic Engineering
  • Artificial Intelligence
  • Applied Mathematics

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