Spatial resolution of Diffusion Weighted (DW) images is currently limited by diverse considerations. This situation introduces a series of artifacts, such as the partial volume effect (PVE), that therefore affect the sensitivity of DW imaging analysis. In this paper, a new multiscale/sparse super-resolution method increases the spatial resolution of the DW images. Based on the redundancy presented in this kind of images, the proposed method uses local information and the multiscale shearlet transformation to closely approach the DW image acquisition process. A comparison of this proposal with a classical image interpolation method demonstrates an improvement of 2.27 dB in the PSNR measure and 1.67% in the SSIM metric.