Sparse representation for face recognition by discriminative low-rank matrix recovery

• A clean dictionary with enhanced discrimination ability is recovered.
• The dictionary elements between classes are made as independent as possible.
• A low-rank projection matrix for data recovery is solved in a closed form solution.
• The corrupted samples can be corrected by projection onto the underlying subspace.
• A query sample is represented by more training samples from the corrected class.

This paper proposes a discriminative low-rank representation (DLRR) method for face recognition in which both the training and test samples are corrupted owing to variations in occlusion and disguise. The proposed method extends the sparse representation-based classification algorithm by incorporating the low-rank structure of data representation. The DLRR algorithm recovers a clean dictionary with enhanced discrimination ability from the corrupted training samples for sparse representation. Simultaneously, it learns a low-rank projection matrix to correct corrupted test samples by projecting them onto their corresponding underlying subspaces. The dictionary elements from different classes are encouraged to be as independent as possible by regularizing the structural incoherence of the original training samples. This leads to a compact representation of a corrected test sample by a linear combination of more dictionary elements from the corrected class. The experimental results on benchmark databases show the effectiveness and robustness of our face recognition technique.