In this paper we present a new algorithm for restoring an object from multiple undersampled low-resolution (LR) images that are degraded by optical blur and additive white Gaussian noise. We formulate the multiframe superresolution problem as maximum a posteriori estimation. The prior knowledge that the object is sparse in some domain is incorporated in two ways: first we use the popular l_(1) norm as the regularization operator. Second, we model wavelet coefficients of natural objects using generalized Gaussian densities. The model parameters are learned from a set of training objects, and the regularization operator is derived from these parameters. We compare the results from our algorithms with an expectation-maximization (EM) algorithm for l_(1) norm minimization and also with the linear minimum-mean-squared error (LMMSE) estimator. Using only eight 4 X 4 pixel downsampled LR images the reconstruction errors of object estimates obtained from our algorithm are 5.5percent smaller than by the EM method and 14.3percent smaller than by the LMMSE method.
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机译:在本文中,我们提出了一种新算法,可从多个欠采样的低分辨率(LR)图像中恢复对象,这些图像由于光学模糊和加性高斯白噪声而退化。我们将多帧超分辨率问题公式化为最大后验估计。关于对象在某些域中是稀疏的先验知识以两种方式被结合:首先,我们使用流行的l_(1)范数作为正则化运算符。其次,我们使用广义高斯密度对自然物体的小波系数建模。从一组训练对象中学习模型参数,并从这些参数中导出正则化运算符。我们将算法的结果与用于l_(1)范数最小化的期望最大化(EM)算法以及线性最小均方误差(LMMSE)估计器进行比较。仅使用八张4 X 4像素的降采样LR图像,从我们的算法获得的对象估计的重建误差比EM方法小5.5%,比LMMSE方法小14.3%。
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