We address the problem of image superresolution and present a novel approach to single-frame superresolution using fractal image coding. The proposed approach takes great advantage of the properties of fractals-resolution independence, similarity preservation, and nonlinear operation-which are suited for image superresolution, specifically for image restoration and magnification. The idea of our work is to estimate the fractal code of the original image from its degraded (blurred and noised) observation and decode it at a higher resolution, and all the strategies are performed in the fractal image coding framework. To achieve this, we employ an adaptive fractal coding scheme in the frequency domain, and further, we introduce an overlapping partition scheme to remove the blocky artifacts and improve the reconstruction quality. Experiments on simulated and real images show that the resulting fractal-based superresolution method yields superior performance to conventional single-frame superresolution methods.