偏微分方程(PDE)已成为图像处理与分析中的重要工具。而数字图像处理的一个基本内容是图像放大，即从低分辨率图像获得高分辨率图像的图像处理技术。通过两种泛函模型，利用变分的思想，提出了基于TV-norm (total variation norm)插值模型和四阶偏微分方程插值模型的图像放大算法。通过仿真实验结果及均方误差（MSE）和峰值信噪比（PSNR）两种评价准则说明了该算法的有效性和可行性。

Partial differential equation(PDE) has become an important tool in image processing and analysis. A basic content of digital image processing is image zooming, namely an image processing technology obtaining a high resolution image from a low resolution image. This article proposes an image zooming algorithm based on the TV-norm (Total Variation norm) interpolation model and fourth order partial differential equation interpolation model, which adopts the idea of total variation model and two kinds of functional models. The validity and feasibility of the algorithm is tested through a simulation experiment and two appraisal criterions—mean square error(MSE) and peak value signal to noise ratio(PSNR).