Recognition of low resolution face images is a challenging problem in many practical face recognition systems. Methods have been proposed in the face recognition literature for the problem which assume that the probe is low resolution, but a high resolution gallery is available for recognition. These attempts have been aimed at modifying the probe image such that the resultant image provides better discrimination. We formulate the problem differently by leveraging the information available in the high resolution gallery image and propose a dictionary learning approach for classifying the low-resolution probe image. An important feature of our algorithm is that it can handle resolution change along with illumination variations. Furthermore, we also kernelize the algorithm to handle non-linearity in data and present a joint dictionary learning technique for robust recognition at low resolutions. The effectiveness of the proposed method is demonstrated using standard datasets and a challenging outdoor face dataset. It is shown that our method is efficient and can perform significantly better than many competitive low resolution face recognition algorithms.