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

Takayuki Katsuki, Akira Torii, Masato Inoue

    Research output: Contribution to journalArticle

    22 Citations (Scopus)

    Abstract

    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
    Volume21
    Issue number7
    DOIs
    Publication statusPublished - 2012 Jul

    Fingerprint

    Image resolution
    Maximum likelihood
    Mean square error
    Signal to noise ratio

    Keywords

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

    ASJC Scopus subject areas

    • Computer Graphics and Computer-Aided Design
    • Software

    Cite this

    Posterior-mean super-resolution with a causal gaussian markov random field prior. / Katsuki, Takayuki; Torii, Akira; Inoue, Masato.

    In: IEEE Transactions on Image Processing, Vol. 21, No. 7, 6161646, 07.2012, p. 3182-3193.

    Research output: Contribution to journalArticle

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