Superresolution (SR) algorithms have recently become a hot research topic. The main purpose of image upscaling is to obtain high-resolution images from low-resolution ones, and these upscaled images should look like they had been taken with a camera having a resolution the same as the upscaled images, and at least present natural textures. In general, some SR algorithms preserve clear edges but blur the textures, while others preserve detailed textures but cause some obvious artifacts along edges. The proposed SR algorithm presents the detailed textures and, meanwhile, refines the strong edges and avoids causing obvious artifacts. The goal is achieved by using orthogonal fractal as the preliminary upscaling method in conjunction with the proper postprocessing where directional enhancement is adopted. In fact, the postprocessing part in the proposed SR algorithm can effectively reduce most jagged artifacts caused by SR algorithms. In the simulation results, it is shown that the proposed SR algorithm performs well in both objective and subjective measurements. Moreover, most detailed textures are properly enhanced and most jagged artifacts caused by SR algorithms can also be effectively reduced.