Nonconvex plus quadratic penalized low-rank and sparse decomposition for noisy image alignment

Science China Information Sciences

Volumn 59, Issue 5, 2016, Pages

  Chen, Xiai ^a,b   Han, Zhi ^a,b   Wang, Yao ^c   Tang, Yandong ^a,b   Yu, Haibin ^a,b  

^a SHENYANG INSTITUTE OF AUTOMATION   (China)

^b UNIVERSITY OF CHINESE ACADEMY OF SCIENCES   (China)

^c XI'AN JIAOTONG UNIVERSITY   (China)

Author keywords

batch image alignment; low rank decomposition; nonconvex relaxation; quadratic penalized; sparse or nonsparse noise

Indexed keywords

ALIGNMENT; LAGRANGE MULTIPLIERS;

IMAGE ALIGNMENT; LOW-RANK DECOMPOSITION; NONCONVEX; QUADRATIC PENALIZED; SPARSE OR NONSPARSE NOISE;

NUMERICAL METHODS;

EID: 84960075180     PISSN: 1674733X     EISSN: None     Source Type: Journal    
DOI: 10.1007/s11432-015-5419-2     Document Type: Article

References (27)

1. Eckart C, Young G. The approximation of one matrix by another of lower rank. Psychometrika, 1936, 1: 211–218
2. Jolliffe I. Principal Component Analysis. Berlin: Springer-Verlag, 1986
3. Candès E J, Li X D, Ma Y, et al. Robust principal component analysis? J ACM, 2011, 58: 1–37
4. Huang G B, Jain V, Learned-Miller E G. Unsupervised joint alignment of complex images. In: Proceedings of IEEE International Conference on Computer Vision (ICCV), Rio de Janeiro, 2007. 1–8
5. Learned-Miller E G. Data driven image models through continuous joint alignment. IEEE Trans Patt Anal Mach Intell, 2006, 28: 236–250
6. Cox M, Sridharan S, Lucey S, et al. Least squares congealing for unsupervised alignment of images. In: Proceedings of IEEE International Conference on Computer Vision (ICCV), Kyoto, 2009. 1949–1956
7. Vedaldi A, Guidi G, Soatto S. Joint data alignment up to (lossy) transformations. In: Proceedings of IEEE International Conference on Computer Vision and Pattern Recognition (CVPR), Anchorage Alaska, 2008. 1–8
8. Fan J Q, Li R Z. Variable selection via nonconcave penalized likelihood and its oracle properties. J Amer Stat Assoc, 2001, 96: 1348–1360
9. Zou H. The adaptive lasso and its oracle properties. J Amer Stat Assoc, 2006, 101: 1418–1429
10. Leng C L, Lin Y, Wahba G. A note on the lasso and related procedures in model selection. Stat Sinica, 2006, 16: 1273–1284
11. Zhang C H. Nearly unbiased variable selection under minimax concave penalty. Ann Stat, 2010, 38: 894–942
12. Zhang C H, Zhang T. A general theory of concave regularization for high-dimensional sparse estimation problems. Stat Sci, 2012, 27: 576–593
13. Fan J Q, Xue L Z, Zou H. Strong oracle optimality of folded concave penalized estimation. Ann Stat, 2014, 42: 819–849
14. Bunea F, She Y Y, Wegkamp M H. Optimal selection of reduced rank estimators of high-dimensional matrices. Ann Stat, 2011, 39: 1282–1309
15. Wang S S, Liu D H, Zhang Z H. Nonconvex relaxation approaches to robust matrix recovery. In: Proceedings of 23rd International Joint Conference on Artificial Intelligence, Beijing, 2013. 1764–1770
16. Deng Y, Dai Q H, Liu R S, et al. Low-rank structure learning via log-sum heuristic recovery. IEEE Trans Neural Netw Learn Syst, 2013, 24: 383–396
17. Cao W F, Wang Y, Yang C, et al. Folded-concave penalization appoarches to tensor completion. Neurocoumputing, 2015, 152: 261–273
18. Zhou Z H, Li X D, Wright J, et al. Stable principal component pursuit. In: Proceedings of IEEE International Symposium on Information Theory (ISIT), Austin, 2010. 1518–1522
19. Peng Y G, Ganesh A, Wright J, et al. RASL: robust alignment by sparse and low-rank decomposition for linearly correalted images. IEEE Trans Patt Anal Mach Intell, 2012, 34: 2233–2246
20. Basri R, Jacobs D W. Lambertian reflectance and linear subspaces. IEEE Trans Patt Anal Mach Intell, 2003, 25: 218–233
21. Wang X G, Zhang Z D, Ma Y, et al. Robust subspace discovery via relaxed rank minimization. Neural Comput, 2014, 26: 611–635
22. Guo X H, Zhao R Z, An G Y, et al. An algorithm of face alignment and recognition by sparse and low rank decomposition. In: Proceedings of International Conference on Signal Processing (ICSP), HangZhou, 2014. 1036–1040
23. Wright J, Yang A Y, Ganesh A, et al. Robust face recognition via sparse representation. IEEE Trans Patt Anal Mach Intell, 2009, 31: 210–227
24. Huang Z W, Zhao X W, Shan S G, et al. Coupling alignments with recognition for still-to-video face recognition. In: Proceedings of IEEE International Conference on Computer Vision (ICCV), Sydney, 2013. 3296–3303
25. Zhang Z D, Liang X, Ganesh A, et al. TILT: transform invariant low-rank textures. In: Proceedings of the Asian Conference on Computer Vision (ACCV), Queenstown, 2011. 314–328
26. Cai J F, Candès E J, Shen Z W. A singular value thresholding algorithm for matrix completion. SIAM J Optim, 2010, 20: 1956–1982
27. Zhang X Q, Wang D, Zhou Z Y, et al. Simultaneous rectification and alignment via robust recovery of low-rank tensors. In: Proceedings of 27th Annual Conference on Neural Information Processing Systems, Lake Tahoe, 2013. 1637–1645