In this paper, we consider the problem of automatically recognizing human faces from partially occluded frontal views. We argue that new mathematical theory from sparse signal representation offers the key to address this difficult problem. The desired representation is sparse, since the test face image should only be represented in terms of training face images of the same object. The occlusion of the face is also sparse, typically affecting only a fraction of the image pixels. We propose a simple, novel algorithm which uses ` minimization to express the test image as a sparse linear combination of the training images plus a sparse error due to occlusion. This algorithm achieves state-of-the-art performance using raw imagery data, with no need for dimension reduction, feature selection, synthetic training examples or domain-specific information. We investigate the implications of this new mathematical framework for the engineering of recognition systems, showing how to predict how much occlusion the algorithm can handle and how to choose the training data to maximize robustness to occlusion. Extensive experiments on publicly available databases verify the efficacy of the proposed method.
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