This paper proposes a new approach for interpolating natural images. Unlike other conventional interpolation methods, we exploit the characteristics of an image and decompose it into a texture part and a non-texture (cartoon) part. In the non-texture part, we interpolate it with bicubic interpolation which performs well for smooth areas. We deal the texture part with peak transform based interpolation which resets the image pixels to capture the characters of the texture through peak transform. The experiment results demonstrate our new interpolation method has higher PSNR and better subjective quality of the interpolated image, especially in the texture part.