We propose a Bayesian image super-resolution (SR) method with a causalGaussian Markov random field (MRF) prior. SR is a technique to estimate aspatially high-resolution image from given multiple low-resolution images. AnMRF model with the line process supplies a preferable prior for natural imageswith edges. We improve the existing image transformation model, the compoundMRF model, and its hyperparameter prior model. We also derive the optimalestimator -- not the joint maximum a posteriori (MAP) or marginalized maximumlikelihood (ML), but the posterior mean (PM) -- from the objective function ofthe L2-norm (mean square error) -based peak signal-to-noise ratio (PSNR). Pointestimates such as MAP and ML are generally not stable in ill-posedhigh-dimensional problems because of overfitting, while PM is a stableestimator because all the parameters in the model are evaluated asdistributions. The estimator is numerically determined by using variationalBayes. Variational Bayes is a widely used method that approximately determinesa complicated posterior distribution, but it is generally hard to use becauseit needs the conjugate prior. We solve this problem with simple Taylorapproximations. Experimental results have shown that the proposed method ismore accurate or comparable to existing methods.
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