基于RPCA的群稀疏表示人脸识别方法

针对训练样本图像和测试样本图像均存在光照、污染、遮挡等情况下的人脸识别问题，提出一种基于鲁棒主成分分析的群稀疏表示人脸识别方法(group sparse representation face recognition method based on robust principal component analysis, GSR-RPCA)。该方法将人脸图像由空域变换到对数域，增强人脸图像的对比度，并通过结构非相关鲁棒主成分分析算法从训练样本图像矩阵D中分解出干净的低秩部分人脸图像矩阵A和误差图像矩阵E，以增强恢复数据的鉴别力；学习A与D之间的低秩映射关系矩阵P，并用P将存在遮挡的测试样本映射到其潜在的子空间下，得到干净的测试样本y；计算y在A上的群稀疏表示系数，并利用类关联重构残差对测试人脸进行识别，获得测试人脸的所属类别。在CMU PIE，Extended Yale B和AR数据库上的实验结果显示，提出方法具有较高的识别率和较强的鲁棒性。

Group sparse representation face recognition method based on RPCA

Due to the face recognition problem of illumination, pollution and occlusion in the test images and training images, a study of group sparse representation face recognition method based on robust principal component analysis with(GSR-RPCA)is proposed. Firstly,transferring the face image from the spatial domain to the logarithmic domain to enhance the contrast of the face image, and decomposes the clean low-rank partial face image from the training sample image matrix D by the structural incoherence robust principal component analysis algorithm. The matrix A and the error image matrix E are used to enhance the discriminating ability of the recovered data. Then, the low rank mapping relationship matrix P between A and D is learned, and P is used to map the occlusion test samples to their potential subspaces to get a clean test sample y. Finally, the group sparse representation coefficient of y is calculated, and the test face is identified by using the class association reconstruction residual to obtain the category of the test face. Experimental results on CMU PIE, Extended Yale B and AR database verify the effectiveness and robustness of our method.