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 resolution reconstruction

consisting in that image interpolation and super resolution 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.