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中文摘要：
利用图像非局部不连续性测度的概念,建立了面向图像超分辨的非局部正则化能量泛函和相应的变分框架.理论分析了该框架与目前关于双边滤波等一类广义邻域滤波器和经典的变分偏微分方程模型之间的联系.推导了该非局部泛函约束的变分模型最优解满足的积分形式欧拉-拉格朗日方程,并研究了其最速下降流满足的若干重要性质.基于图理论,设计了图像超分辨的自适应加权迭代算法.最后通过选择不同势函数的非局部正则化泛函进行图像去噪、去马赛克效应和图像超分辨处理,性能分析表明：相同势函数下,非局部正则化方法优于同类局部正则化方法,峰值信噪比提高0.5~1.0dB.
英文摘要：
A non-local regularization energy functional and variational framework for image super-resolution reconstruction is proposed using the conception of non-local discontinuity of imager.The fundamental relationships between a class of generalized neighborhood filter,such as bilateral filter,and the classical variational PDE models are theoretically analyzed in this framework.The Euler-Lagrange Equation with integral formulation is derived for nonlocal variational minimizations.Some important properties of the steepest descent flow in this framework are also proved.Based on the graph theory,the authors give a novel adaptive and weighted iterative algorithms for image super-resolution.In the end of paper,different examples of non-local regularization energy functional is used to image de-noising,image de-masaic,and image super-resolution.Experiments show that the non-local regularization functional has better performance than the classical regularization functional under the same potential function,and the Peak SNR values are averagely increased by about from 0.5 to 1.0 dB.
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