Abstract: The main difficulty in terms of face recognition lies in the occlusion as well as the changes in lightning and expre-
ssions, both of which may result in the similarity between the different face images. The classification algorithm based on sparse representation（SRC） is a classical face recognition algorithm. However, such method has the problem that the recognition rate decreases and the sparse representation has low efficiency when face training samples are insufficient. To eliminate these drawbacks, this paper proposes a face recognition algorithm based on discriminative Low Rank Recovery Fast Sparse Representation-based Classification（LRR_FSRC）. Firstly, low-rank decomposition theory is used to obtain a low-rank recovery dictionary and a sparse error dictionary. This is followed by the integrated utilization of the low-rank decomposition and structural incoherence theory, which are used to train discriminative low-rank dictionary and sparse error dictionary. The discriminative low-rank dictionary and sparse error dictionary are combined as dictionary for testing. Secondly, the method of coordinate descent is used to figure out the sparse coefficient to improve the computational efficiency. Finally, according to the reconstruction error, the classification of the test sample is achieved. Experimental results on the YALE and ORL databases show that the LRR_FSRC based face recognition method proposed in this paper has higher recognition rate and faster computational efficiency.

Key words: face recognition, sparse representation, low rank matrix recovery, coordinate descent method, Sparse Representation-based Classification（SRC） method

摘要： 人脸识别的主要难度在于，受到光照变化、表情变化以及遮挡的影响，会使得采集的不同人的人脸图像具有相似性。为有效解决基于稀疏表示的分类算法（Sparse Representation-based Classification，SRC）在人脸训练样本不足时会导致识别率降低和稀疏表示求解效率较低的问题，提出了基于判别性低秩分解与快速稀疏表示分类（Low Rank Recovery Fast Sparse Representation-based Classification，LRR_FSRC）的人脸识别算法。利用低秩分解理论得到低秩恢复字典以及稀疏误差字典，结合低秩分解和结构不相干理论，训练出判别性低秩类字典和稀疏误差字典，并把它们结合作为测试时所用的字典；用坐标下降法来求解稀疏系数以提高了计算效率；根据重构误差实现测试样本的分类。在YALE和ORL数据库上的实验结果表明，提出的基于LRR_FSRC的人脸识别方法具有较高的识别率和计算效率。

关键词: 人脸识别, 稀疏表示, 低秩矩阵恢复, 坐标下降法, 基于稀疏表示的分类（SRC）算法