Posterior-Mean Super-Resolution With a Causal Gaussian Markov Random Field Prior
Posterior-Mean Super-Resolution With a Causal Gaussian Markov Random Field Prior
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DOI：
10.1109/tip.2012.2189578
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发表时间：
2012-07-01
影响因子：
10.6
通讯作者：
Inoue, Masato
中科院分区：
文献类型：
--
作者：
Katsuki, Takayuki;Torii, Akira;Inoue, Masato
提出了一种具有因果高斯马尔可夫随机场先验的贝叶斯图像超分辨率（SR）方法。SR是一种从给定的多幅低分辨率图像中估计出空间高分辨率图像的技术。具有线处理的磁流变函数模型为具有边缘的自然图像提供了较好的先验。我们改进了现有的图像变换模型、复合MRF模型及其超参数先验模型。我们还从基于l2范数（均方误差）的峰值信噪比的目标函数中推导出最优估计量——不是联合最大后验（MAP）或边缘最大似然（ML），而是后验均值（PM）。由于过度拟合，MAP和ML等点估计在病态高维问题中通常不稳定，而PM是一个稳定的估计，因为模型中的所有参数都被评估为分布。用变分贝叶斯方法对估计量进行了数值确定。变分贝叶斯方法是一种被广泛应用的近似确定复杂后验分布的方法，但由于需要共轭先验，通常使用起来比较困难。我们用简单的泰勒近似来解决这个问题。实验结果表明，本文提出的方法与现有方法相比具有更高的精度和可比性。
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.