Half-Quadratic-Based Iterative Minimization for Robust Sparse Representation

• Published in: IEEE transactions on pattern analysis and machine intelligence Vol. 36; no. 2; pp. 261 - 275
• Main Authors: RAN HE, ZHENG, Wei-Shi, TIENIU TAN, ZHENAN SUN
• Format: Journal Article
• Language: English
• Published: Los Alamitos, CA IEEE 01-02-2014; IEEE Computer Society
• Subjects: (\ell_1)-minimization; Additives; Algorithm design and analysis; Algorithms; Applied sciences; Artificial Intelligence; Biometry - methods; Computer science; control theory; systems; Computer systems and distributed systems. User interface; correntropy; Data Interpretation, Statistical; Detection, estimation, filtering, equalization, prediction; Error correction; Exact sciences and technology; Face - anatomy & histology; half-quadratic optimization; Humans; Image Enhancement - methods; Image Interpretation, Computer-Assisted - methods; Information, signal and communications theory; M-estimator; Minimization; Noise; Optimization; Pattern Recognition, Automated - methods; Pattern recognition. Digital image processing. Computational geometry; Reproducibility of Results; Robustness; Sensitivity and Specificity; Signal and communications theory; Signal, noise; Software; sparse representation; Telecommunications and information theory; Biometrics; Occlusion; Image processing; Threshold detection; M-estimator; Iterative method; Entropy; Potential function; Modeling; Outlier; ℓ; Facies; half-quadratic optimization; Sparse representation; Threshold; Computer vision; Face recognition; Statistical moment; Minimization; Video cameras; Quadratic programming; correntropy; Surveillance; Problem solving; Error detection; Error correction; Occultation; M estimation; Quadratic function
• ISSN: 0162-8828; 1939-3539; 2160-9292
• DOI: 10.1109/TPAMI.2013.102

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 ℓ 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 ℓ 1 -regularized error detection method by learning from uncorrupted data iteratively. We also show that the ℓ 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.