Objective

2

Face recognition has become one of the most popular biometric recognition methods because of rich facial information and wide application prospects. However

the quality of images taken by the equipment is often affected in the real environment. Various facial expressions

gestures

and illumination conditions will affect the quality of face images

resulting in occlusion

translation

and scale errors in normalized face images

thereby reducing the robustness and recognition accuracy of face recognition algorithms. Among many known algorithms

the sparse representation-based classification (SRC) algorithm has achieved good face recognition performance. The algorithm is robust to noise and partial occlusion. However

face recognition in cases of facial expression change

posture change

and small sample size remains a challenge. On the one hand

the SRC can be used successfully in face recognition when the training samples are sufficient

where a testing sample can be represented by a linear combination of the images of the same person in the database. On the other hand

the SRC will divide samples into the wrong classes due to misleading coefficients on the under-sampled database. Therefore

studying how to obtain better recognition results under polluted and small samples remains important. On the basis of this situation

this work aims to study a face recognition algorithm with SRC on an uncontrolled and under-sampled database.

Method

2

This study proposes a superposition linear sparse representation face recognition algorithm based on discriminant non-convex low-rank matrix decomposition considering the sparsity of the SRC method and the low-rank matrix decomposition because the low-rank matrix decomposition has a good effect on removing sample noise. A dictionary that can eliminate interclass correlation is obtained by decomposing the training samples twice. This dictionary is used to classify and recognize by reconstructing the sparse residual model. The proposed algorithm efficiently eliminates the errors caused by occlusion and other unavoidable factors. We utilize non-convex rank approximation (norm) to replace nuclear norm due to two major limitations of robust principal component analysis (RPCA):the lack of structural incoherence and the tendency to shrink all the singular values equally. Non-convex rank approximation overcomes the problem of the singular value of the matrix being scaled to the same multiple when solving the kernel norm by using traditional RPCA method

which may lead to errors in the recognition results. We add to the theory of structural irrelevance in low-rank decomposition to minimize the Frobenius norm among all kinds of low-rank dictionaries and the between-class scatter. In addition

this method increases the incoherence among the low-rank dictionaries

thus improving the discrimination ability of low-rank matrices. After obtaining the low-rank matrix

the classification is completed by superposed linear sparse representation classification (SLRC). We divide the low-rank matrix into the prototype dictionary and the variation dictionary according to SLRC. Then

the two dictionaries are combined into a training dictionary in SRC. The homotopy method is used to obtain the sparse coefficients of

$$l_{1}$$

norm. Furthermore

the dictionary is classified by reconstructing the sparse-minimizing residual model. This study eliminates the interference of intraclass/interclass correlation and even on the under-sampled database.

Result

2

This study selects the AR and CMU PIE databases for experiments. In the AR database

the recognition rate of our algorithm is 98.67 ±0.57% in 10 experiments

which is better than that of SRC

extended SRC

RPCA+SRC

low-rank matrix decomposition with structural incoherence (LRSI)

and superposed linear representation-based classification (SLRC-

$$l_{1}$$

)

among others. We choose different proportions from 0 to 3/7 of occluded pictures of people wearing a scarf or sunglasses. This condition means that the number of sunglasses or scarf increased from zero to three

and the total number of training images per class is seven. Our algorithm has better robustness to occluded images and has a higher recognition rate than other algorithms. The difference in the recognition rate of the algorithms decreases gradually as the number of occlusion training samples increases because the low-rank matrix decomposed by RPCA lacks discriminant information

even though the recognition rate of RPCA + SRC is better than that of SRC in all test samples. The proposed algorithm will not be affected by the presence of structural irrelevant terms. In addition

when the proportion of occluded pictures is increased in the training samples

the recognition performance of each algorithm is gradually improved

because the SRC part of the algorithm is more sensitive to the information of occluded pictures. For the CMU PIE database

we add salt-and-pepper noise from 0 to 40% in every image. The recognition rate of our algorithm reaches 90.1%

85.5%

77.8%

65.3%

and 46.1%

and is the highest among all the compared algorithms. In different methods

the recognition rate of the SRC-based method decreases significantly with the increase in the percentage of damaged pixels. The RPCA-based method performs better in noise elimination. Therefore

adding low-rank decomposition to the algorithm helps improve the recognition rate.

Conclusion

2

The proposed algorithm has a high recognition rate in different face databases

especially in the case of occlusion and noise pollution. In summary

discriminant non-convex low-rank matrix decomposition is introduced into superposed linear sparse representation

which improves the robustness and efficiency of recognition considerably because of improved recognition accuracy. Thus

the algorithm has good application value in practice. The proposed algorithm is only for static images; thus

how to combine static face recognition with dynamic video to effectively realize video-based face recognition needs further research.