The classical super-resolution (SR) setting starts with a set of low-resolution (LR) images related by subpixel shifts and tries to reconstruct a single high-resolution (HR) image. In some cases, partial observations about the HR image are also available. Trying to complete the missing HR data without any reference to LR ones is an inpainting (or completion) problem. In this paper, we consider the problem of recov- ering a single HR image from a pair consisting of a complete LR and incomplete HR image pair. This setting arises in par- ticular when one wants to fuse image data captured at two different resolutions. We propose an efficient algorithm that allows to take advantage of both image data by first learning nonlocal interactions from an interpolated version of the LR image using patches. Those interactions are then used by a convex energy function whose minimization yields a super- resolved complete image.