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Mathematical Problems in Engineering
Volume 2017, Article ID 1458412, 16 pages
Research Article

Reconstructed Error and Linear Representation Coefficients Restricted by -Minimization for Face Recognition under Different Illumination and Occlusion

1College of Communication Engineering, Chongqing University, Chongqing 400030, China
2College of Computer Engineering, Yangtze Normal University, Fuling 408100, Chongqing, China
3College of Computer Science, Chongqing University, Chongqing 400030, China
4Faculty of Science and Technology, University of Macau, Macau

Correspondence should be addressed to Xuegang Wu; nc.ude.uqc@uwgx

Received 25 November 2016; Accepted 23 April 2017; Published 22 May 2017

Academic Editor: Elisa Francomano

Copyright © 2017 Xuegang Wu et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The problem of recognizing human faces from frontal views with varying illumination, occlusion, and disguise is a great challenge to pattern recognition. A general knowledge is that face patterns from an objective set sit on a linear subspace. On the proof of the knowledge, some methods use the linear combination to represent a sample in face recognition. In this paper, in order to get the more discriminant information of reconstruction error, we constrain both the linear combination coefficients and the reconstruction error by -minimization which is not apt to be disturbed by outliners. Then, through an equivalent transformation of the model, it is convenient to compute the parameters in a new underdetermined linear system. Next, we use an optimization method to get the approximate solution. As a result, the minimum reconstruction error has contained much valuable discriminating information. The gradient of this variable is measured to decide the final recognition. The experiments show that the recognition protocol based on the reconstruction error achieves high performance on available databases (Extended Yale B and AR Face database).