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中文摘要：
图像放大技术是医学图像处理中的重要领域．医学图像细节丰富处经常呈现出明显的几何结构特征或模式，如边缘．提出了一种基于学习的方法，将低分辨率图像块作为可用的邻域像素并提取其几何特征信息组成训练集与高分辨率图像块之间建立局部对应关系，这种对应关系即为局部几何相似性．将训练集信息有效传递至待重建高分辨率图像块周像放大的问题转化为重建系数的最优化问题，并且基于非局部平均思想，将其进而转化为加权最小二乘问题得到正则化解．实验结果表明，本方法不仅可以进行任意倍图像放大，且它可以摆脱一般方法对训练集合的依赖，具有较好的独立性，自适应性和边缘保持特性．
英文摘要：
Image magnification is an important technology in medical image processing. High detail areas in medical images most often have a definite geometric structure or pattern, such as in the case of edges. This paper proposes a learning-based method. Geometric features extracted from the available neighboring pixels in the Low-resolution （LR） image form the training set. Assuming the training set is locally corresponding to geometric features from the High-resolution （HR） image patch to be reconstructed. Local geometric similarity is described as the correspondence. The task of image magnification is formulated as an optimization problem, where the optimization coefficients can adaptively tune its value to effectively propagating the features from the training set to the target HR image patch. The advantages are the ability to produce a magnified image by any factor, and not require any outlier supporters. A Weighted Least Square （WLS） method is provided to offer a convenient way of finding the regularized optimal solution, where the weight function is determined by the non-local means. Simulation and comparison results show that the proposed method is independent, adaptive and can produce sharp edges with rare ringing or jaggy artifacts.
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