Face recognition encounters significant challenges

particularly when images from different persons are similar to one another due to variations in illumination

expression

and occlusion.If we have sufficient training images of each person

which can span the facial variations of that person under testing conditions

then sparse representation-based classification (SRC) can achieve promising results.In many applications

however

the problems of small size of samples and lack of sufficient training images for each person are particularly significant.To solve these problems

this study presents a joint face recognition algorithm between a low-rank class dictionary and sparse error dictionary learning based on theory of sparse representation.The low-rank dictionary of each individual is a class-specific dictionary that captures the discriminative feature of an individual.The sparse error dictionary represents intra-class variations

such as illumination and expression changes. An initial low-rank decomposition dictionary and a sparse dictionary are obtained based on theory of low-rank decomposition.Then

combining theories of low-rank decomposition and structural irrelevance

the discriminative low-rank class dictionary and the sparse error dictionary are trained and subsequently merged as the dictionary that will be applied to the test part.Our method decomposes raw training data into a set of representative bases with corresponding sparse errors to efficiently model face images.We further promote structural incoherence among the bases learned from different classes.These bases are encouraged to be as independent as possible due to the regularization on structural incoherence.Additional discriminating capability is provided to the original low-rank models to improve performance.A sparse coefficient is acquired according to the L1 norm method (homotopy method).Test samples can be classified based on the reconstruction error. Experiments are conducted on the Extended Yale B and AR databases.A random matrix is used to reduce the dimensions of the training samples to shorten execution time.In the Extended Yale B database

which consists of samples with 504 dimensions

32 training samples are selected from each class.The result of the recognition rate that applies the proposed algorithm is 96.9%.Among the samples with 540 dimensions and without occlusion in the AR database

4 training samples are selected from each class.The result of the recognition rate is 83.3%.For the samples with 1 760 dimensions

the recognition rate is 87.6%.Among the samples with 540 dimensions and with occlusion

8 training samples are selected from each class.The recognition rate is 94.1%.The result of experiment on the training samples with 1 760 dimensions and with occlusion is 94.8%.The experiments show that the results of the proposed algorithm are better than the highest recognition rates of the SRC(Sparse representation-based classifier)

DKSVD(Discriminative K-SVD)

LRSI(Low rank matrix decomposition with structural incoherence) and LRSE+SC(Low rank and sparse error matrix+ sparse coding) algorithms

particularly in cases with insufficient training samples.The experiment in which all the occlusion images are used as the training samples and the unobstructed images are used as the test samples is first conducted to illustrate the importance of sparse error bases

and the recognition rate of the proposed algorithm is 43.6%.then we exchange training samples and test samples and the recognition rate of the proposed algorithm is 83.1%.The sparse coefficient in the test phase cannot remove interference because the sparse error dictionary lacks the composition of wearing scarves and sunglasses.Consequently

the recognition rate is significantly reduced.When occlusion images are used as training samples and unobstructed images are used as test samples

the interference is considerably smaller than the interference when wearing scarves and sunglasses although the sparse errors lack the composition of light and expression changes.Thus

the recognition rate is significantly higher than the former.In practical applications

only sparse error bases are sufficient

particularly in cases where images are disturbed to a high extent

and the recognition effect can be improved. The face recognition algorithm proposed in this study is robust and effective and can achieve an ideal recognition effect

particularly when training samples are insufficient or face recognition is disturbed considerably.The algorithm is suitable for practical applications.