中文摘要：

众所周知，图像插值是根据一幅低分辨率噪声图像重建相应高分辨率清晰图像的数字图像处理技术。虽然已有一些文献报道了多种图像插值算法，然而现有算法在插值视觉效果和计算复杂度两者间往往难以实现均衡，为此，提出了一种局部几何结构驱动的偏微分方程（PDE）图像插值算法。该算法通过耦合边缘、纹理和角形3种不同几何结构的扩散机制来进行插值，插值结果表明，该算法不仅具有抗噪声性能，而且能够同时增强边缘、纹理以及角形结构。考虑到图像的超分辨率复原与插值放大在数学本质上的一致性，特将上述PDE应用推广到图像的超分辨率复原，并且针对高强度噪声情形下，超分辨率图像中出现的伪纹理结构，提出了一种耦合全变差模型的改进的PDE。实验结果表明，不论是插值放大图像，还是超分辨率复原图像都具有较高的视觉质量和峰值信噪比。

英文摘要：

Image Interpolation aims at reconstructing a high-resolution image from a low resolution noisy image. Though many magnification algorithms have been proposed in literatures, it is much difficult to balance the tradeoff between the visual quality of the interpolated image and the computational complexity of the algorithm. In the paper, a novel interpolation PDE approach is proposed driven by local geometric structures. Coupled with different diffusion mechanisms corresponding to edges, textures, and corners, the novel algorithm is not only robust to noise, but also capable of enhancing the edges and textures, as well as preserving the corner structures. The novel PDE is subsequently applied to super-resolutlon reconstruction, consisting in that image interpolation and super-resolutlon are mathematically consistent. Besides, coupled with total variation modeling, a slightly improved version of the novel PDE is proposed to remove the false textures in the super-resolved image in the case of high-level noise. Numerous experiment results demonstrate the effectiveness of our approach, both in the visual effect and the PSNR value.