Bayesian combination of sparse and non-sparse priors in image super resolution

S. Villena*, M. Vega, S. D. Babacan, R. Molina, A. K. Katsaggelos

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

106 Scopus citations


In this paper the application of image prior combinations to the Bayesian Super Resolution (SR) image registration and reconstruction problem is studied. Two sparse image priors, a Total Variation (TV) prior and a prior based on the ℓ1 norm of horizontal and vertical first-order differences (f.o.d.), are combined with a non-sparse Simultaneous Auto Regressive (SAR) prior. Since, for a given observation model, each prior produces a different posterior distribution of the underlying High Resolution (HR) image, the use of variational approximation will produce as many posterior approximations as priors we want to combine. A unique approximation is obtained here by finding the distribution on the HR image given the observations that minimizes a linear convex combination of Kullback-Leibler (KL) divergences. We find this distribution in closed form. The estimated HR images are compared with the ones obtained by other SR reconstruction methods.

Original languageEnglish (US)
Pages (from-to)530-541
Number of pages12
JournalDigital Signal Processing: A Review Journal
Issue number2
StatePublished - Mar 2013


  • Bayesian methods
  • Parameter estimation
  • Super resolution
  • Total variation
  • Variational methods

ASJC Scopus subject areas

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


Dive into the research topics of 'Bayesian combination of sparse and non-sparse priors in image super resolution'. Together they form a unique fingerprint.

Cite this