中文摘要：

目的为了增强图像超分辨率重建的准确性，克服传统插值所产生的边缘模糊与边缘锯齿等负面效果，提出一种基于多方向模板变分模型的单幅图像超分辨率重建方法。方法首先构建体现28个方向的多方向模板对输入图像的轮廓方向进行计算，同时通过将TV模型引入到图像轮廓的估计中来确定边缘轮廓的最优方向；在此基础上通过进行基于所提出的多方向模板的图像插值来实现图像的超分辨率重建。结果对比基于活动轮廓的图像边缘插值方法重建的经典高分辨率测试图像，本文方法在平均峰值信噪比和平均结构相似度方面分别提高了1．578dB和0．03002dB。结论本文方法可以有效地克服传统插值方法所产生的边缘模糊和边缘锯齿化等负面效果，也避免了较少方向模板所带来的边缘和纹理丰富区域的纹理失真现象，可以取得较好的重建效果。

英文摘要：

Objective A single image super-resolution reconstruction method based on a variational calculus model for multi- direction stencils is proposed in this study to enhance the accuracy of image super-resolution reconstruction and avoid distor- tion on the edges and areas with a rich texture caused by few stencil directions in classical interpolation. Method First, multi-direction stencils are built to reflect 28 directions used to calculate the contour directions of an input image. Then, the TV model is used to estimate image contours and to determine the optimized direction of the edge contours. Finally, image super-resolution reconstruction is realized through image interpolation based on the aforementioned multi-direction stencils. Result Compared with those in the classical high-resolution test image reconstruction method of image interpolation with contour stencils, the average peak signal-to-noise ratio and the average structural similarity obtained using the method presented in the current work are increased by 1. 578 dB and O. 030 02 dB, respectively. Conclusion The method proposed in the current work can effectively overcome the negative effects of traditional interpolation methods, such as blurred and jagged edges of images. Furthermore, this method can avoid distortion on the edges and areas with a rich texture caused by a few stencil directions. The effectiveness of this method has been verified via a large number of simulations.