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

Abstract

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
Volume23
Issue number2
DOIs
StatePublished - Mar 2013

Keywords

  • 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

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