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We present a face recognition algorithm based on simultaneous sparse approximations under varying illumination and pose. A dictionary is learned for each class based on given training examples which minimizes the representation error with a sparseness constraint. A novel test image is projected onto the span of the atoms in each learned dictionary. The resulting residual vectors are then used for classification. To handle variations in lighting conditions and pose, an image relighting technique based on pose-robust albedo estimation is used to generate multiple frontal images of the same person with variable lighting. As a result, the proposed algorithm has the ability to recognize human faces with high accuracy even when only a single or a very few images per person are provided for training. The efficiency of the proposed method is demonstrated using publicly available databases available databases and it is shown that this method is efficient and can perform significantly better than many competitive face recognition algorithms.