Robust group sparse representation via half-quadratic optimization for face recognition

Sparse representation-based classifier (SRC), which represents a test sample with a linear combination of training samples, has shown promise in pattern classification. However, there are two shortcomings in SRC: (1) the ℓ₁-norm used to measure the reconstruction fidelity is noise-sensitive and (2) the ℓ₂-norm induced sparsity did not consider the correlation among the training samples. Furthermore, in real applications, face images with similar variations, such as illumination or expression, often have higher correlation than those from the same subject. Therefore, we propose to improve the performance of SRC from two aspects: (1) replace the noise-sensitive ℓ₂-norm with an M-estimator to enhance its robustness and (2) emphasize the sparsity of the number of classes instead of the number of training samples, which leads to the group sparsity. The proposed robust group sparse representation (RGSR) can be efficiently optimized via alternating minimization under the Half-Quadratic (HQ) framework. Extensive experiments on representative face data sets show that RGSR can achieve competitive performance in face recognition and outperforms several state-of-the-art methods in dealing with various types of noise such as corruption, occlusion and disguise.