The application of sparse representation (SR) theory to the fusion of multispectral (MS) and panchromatic images is giving a large impulse to this topic, which is recast as a signal reconstruction problem from a reduced number of measurements. This letter presents an effective implementation of this technique, in which the application of SR is limited to the estimation of missing details that are injected in the available MS image to enhance its spatial features. We propose an algorithm exploiting the details self-similarity through the scales and compare it with classical and recent pansharpening methods, both at reduced and full resolution. Two different data sets, acquired by the WorldView-2 and IKONOS sensors, are employed for validation, achieving remarkable results in terms of spectral and spatial quality of the fused product.