A good superresolution (SR) algorithm obtains high-resolution (HR) images from the corresponding low-resolution (LR) ones and, moreover, makes the former look like they had been acquired with a sensor having the expected resolution or at least as “natural” as possible. In general, fast SR algorithms usually result in more ill artifacts in the enlarged image, while the well-performed ones usually have great complexity and take much more computing time. For this purpose, four efficient SR algorithms based on regression models are proposed. In the proposed SR algorithms, the difference of a natural HR image and an HR image obtained by fast interpolation is taken as the lost detail and is supposed to be composed of several different oriented details. By the self-similarity of the input LR image and its corresponding HR image, a regression model is established by the input LR image to decide the proper respective weights of these oriented details which is then used to reconstruct the lost detail of the natural HR image. As shown in the experimental results, the proposed SR algorithms not only perform well in both objective criteria and visual quality but also take less computing time than some well-performing algorithms.