Loose L_1/2 regularised sparse representation for face recognition

Sparse representation (or sparse coding) has been applied to deal with frontal face recognition. Two representative methods are the sparse representation-based classification (SRC) and the collaborative representation-based classification (CRC), in which the query face image is represented by a sparse linear combination of all the training samples. The difference between SRC and CRC is that the L1-norm constraint of coding is employed in the former to guarantee the sparse property, while the L₂-norm constraint is utilised in the latter. In this paper, we propose a novel loose L_1/2 regularised sparse representation (SR) for face recognition, named L_1/2 classification (LHC), which is inspired by L_1/2 regularisation. Additionally, an iterative Tikhonov regularisation (ITR) is proposed to solve LHC efficiently compared with the original algorithm. Using ITR, the balance between the collaborative representation (CR) and the SR can be tuned by the iterations. Attributed to the sparser L_1/2 regularisation and the iterative solution mechanism, a better performance can be achieved by LHC. Extensive experiments on three benchmark face databases demonstrated that LHC is more effective than the state-of-the-art SR-based methods in dealing with frontal face recognition.