IEEE Trans Image Process - Posterior-mean super-resolution with a causal Gaussian Markov random field prior.

Tópicos

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Resumo

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 estimator--not 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.

Resumo Limpo

propos bayesian imag superresolut sr method causal gaussian markov random field mrf prior sr techniqu estim spatial highresolut imag given multipl lowresolut imag mrf model line process suppli prefer prior natur imag edg improv exist imag transform model compound mrf model hyperparamet prior model also deriv optim estimatornot joint maximum posteriori map margin maximum likelihood ml posterior mean pmfrom object function lnormbas mean squar error peak signaltonois ratio point estim map ml general stabl illpos highdimension problem overfit wherea pm stabl estim paramet model evalu distribut estim numer determin use variat bayesian method variat bayesian method wide use method approxim determin complic posterior distribut general hard use need conjug prior solv problem simpl taylor approxim experiment result shown propos method accur compar exist method

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