Posterior-mean super-resolution with a causal gaussian markov random field prior

Takayuki Katsuki*, Akira Torii, Masato Inoue

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

26 Citations (Scopus)


We propose a Bayesian image super-resolution (SR) method with a causal Gaussian Markov random field (MRF) prior. SR is a technique to estimate a spatially high-resolution image from given multiple low-resolution images. An MRF model with the line process supplies a preferable prior for natural images with edges. We improve the existing image transformation model, the compound MRF model, and its hyperparameter prior model. We also derive the optimal estimatornot the joint maximum a posteriori (MAP) or the marginalized maximum likelihood (ML) but the posterior mean (PM)from the objective function of the L2-norm-based (mean square error) peak signal-to-noise ratio. Point estimates such as MAP and ML are generally not stable in ill-posed high-dimensional problems because of overfitting, whereas PM is a stable estimator because all the parameters in the model are evaluated as distributions. The estimator is numerically determined by using the variational Bayesian method. The variational Bayesian method is a widely used method that approximately determines a complicated posterior distribution, but it is generally hard to use because it needs the conjugate prior. We solve this problem with simple Taylor approximations. Experimental results have shown that the proposed method is more accurate or comparable to existing methods.

Original languageEnglish
Article number6161646
Pages (from-to)3182-3193
Number of pages12
JournalIEEE Transactions on Image Processing
Issue number7
Publication statusPublished - 2012 Jul


  • Bayesian inference
  • Markov random field (MRF) prior
  • Taylor approximation
  • line process
  • posterior mean (PM)
  • super-resolution (SR)
  • variational Bayesian method

ASJC Scopus subject areas

  • Software
  • Computer Graphics and Computer-Aided Design


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