Partially occluded faces are common in many applications of face recognition. While algorithms based on sparse representation have demonstrated promising results, they achieve their best performance on occlusions that are not spatially correlated (i.e. random pixel corruption). We show that such sparsity-based algorithms can be significantly improved by harnessing prior knowledge about the pixel error distribution. We show how a Markov Random Field model for spatial continuity of the occlusion can be integrated into the computation of a sparse representation of the test image with respect to the training images. Our algorithm ef-ficiently and reliably identifies the corrupted regions and excludes them from the sparse representation. Extensive experiments on both laboratory and real-world datasets show that our algorithm tolerates much larger fractions and varieties of occlusion than current state-of-the-art algorithms.