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Half-Quadratic-Based Iterative Minimization for Robust Sparse Representation
Feb. 2014 (vol. 36 no. 2)
pp. 261-275
Ran He, Institute of Automation, Chinese Academy of Sciences, Beijing
Wei-Shi Zheng, Sun Yat-sen University, Guangzhou
Tieniu Tan, Institute of Automation, Chinese Academy of Sciences, Beijing
Zhenan Sun, Institute of Automation, Chinese Academy of Sciences, Beijing
Robust sparse representation has shown significant potential in solving challenging problems in computer vision such as biometrics and visual surveillance. Although several robust sparse models have been proposed and promising results have been obtained, they are either for error correction or for error detection, and learning a general framework that systematically unifies these two aspects and explores their relation is still an open problem. In this paper, we develop a half-quadratic (HQ) framework to solve the robust sparse representation problem. By defining different kinds of half-quadratic functions, the proposed HQ framework is applicable to performing both error correction and error detection. More specifically, by using the additive form of HQ, we propose an $(\ell_1)$-regularized error correction method by iteratively recovering corrupted data from errors incurred by noises and outliers; by using the multiplicative form of HQ, we propose an $(\ell_1)$-regularized error detection method by learning from uncorrupted data iteratively. We also show that the $(\ell_1)$-regularization solved by soft-thresholding function has a dual relationship to Huber M-estimator, which theoretically guarantees the performance of robust sparse representation in terms of M-estimation. Experiments on robust face recognition under severe occlusion and corruption validate our framework and findings.
Index Terms:
correntropy,$(\ell_1)$-minimization,half-quadratic optimization,sparse representation,M-estimator
Ran He, Wei-Shi Zheng, Tieniu Tan, Zhenan Sun, "Half-Quadratic-Based Iterative Minimization for Robust Sparse Representation," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 36, no. 2, pp. 261-275, Feb. 2014, doi:10.1109/TPAMI.2013.102
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