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.