logo

SCIENCE CHINA Information Sciences, Volume 59, Issue 5: 052107(2016) https://doi.org/10.1007/s11432-015-5419-2

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

More info
  • ReceivedMay 24, 2015
  • AcceptedJul 8, 2015
  • PublishedMar 7, 2016

Abstract

This paper proposes a general method for dealing with the problem of recovering the low-rank structure, in which the data can be deformed by some unknown transformations and corrupted by sparse or nonsparse noises. Nonconvex penalization method is used to remedy the drawbacks of existing convex penalization method and a quadratic penalty is further used to better tackle the nonsparse noises in the data. We exploits the local linear approximation (LLA) method for turning the resulting nonconvex penalization problem into a series of weighted convex penalization problems and these subproblems are efficiently solved via the augmented Lagrange multiplier (ALM). Besides comparing with the method of robust alignment by sparse and low-rank decomposition for linearly correlated images (RASL), we also propose a nonconvex penalized low-rank and sparse decomposition (NLSD) model as comparison. Numerical experiments are conducted on both controlled and uncontrolled data to demonstrate the outperformance of the proposed method over RASL and NLSD.


Funded by

national Natural Science Foundation of China(61303168)

national Natural Science Foundation of China(61333019)


Acknowledgment

Acknowledgments

This work was supported by national Natural Science Foundation of China (Grant Nos. 61303168, 61333019).


References

[1] Eckart C, Young G. Psychometrika, 1936, 1: 211-218 Google Scholar

[2] Jolliffe I. Principal Component Analysis. Berlin: Springer-Verlag, 1986. Google Scholar

[3] Cand{è}s E J, Li X D, Ma Y, et al. Robust principal component analysis? J ACM, 2011, 58: 1--37. Google Scholar

[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. Google Scholar

[5] Learned-Miller E G. IEEE Trans Patt Anal Mach Intell, 2006, 28: 236-250 Google Scholar

[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. Google Scholar

[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. Google Scholar

[8] Fan J Q, Li R Z. J Amer Stat Assoc, 2001, 96: 1348-1360 Google Scholar

[9] Zou H. J Amer Stat Assoc, 2006, 101: 1418-1429 Google Scholar

[10] Leng C L, Lin Y, Wahba G. Stat Sinica, 2006, 16: 1273-1284 Google Scholar

[11] Zhang C H. Ann Stat, 2010, 38: 894-942 Google Scholar

[12] Zhang C H, Zhang T. Stat Sci, 2012, 27: 576-593 Google Scholar

[13] Fan J Q, Xue L Z, Zou H. Ann Stat, 2014, 42: 819-849 Google Scholar

[14] Bunea F, She Y Y, Wegkamp M H. Ann Stat, 2011, 39: 1282-1309 Google Scholar

[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. Google Scholar

[16] Deng Y, Dai Q H, Liu R S, et al. IEEE Trans Neural Netw Learn Syst, 2013, 24: 383-396 Google Scholar

[17] Cao W F, Wang Y, Yang C, et al. Neurocoumputing, 2015, 152: 261-273 Google Scholar

[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. Google Scholar

[19] Peng Y G, Ganesh A, Wright J, et al. IEEE Trans Patt Anal Mach Intell, 2012, 34: 2233-2246 Google Scholar

[20] Basri R, Jacobs D W. IEEE Trans Patt Anal Mach Intell, 2003, 25: 218-233 Google Scholar

[21] Wang X G, Zhang Z D, Ma Y, et al. Neural Comput, 2014, 26: 611-635 Google Scholar

[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. Google Scholar

[23] Wright J, Yang A Y, Ganesh A, et al. IEEE Trans Patt Anal Mach Intell, 2009, 31: 210-227 Google Scholar

[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. Google Scholar

[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. Google Scholar

[26] Cai J F, Cand{è}s E J, Shen Z W. SIAM J Optim, 2010, 20: 1956-1982 Google Scholar

[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. Google Scholar

Copyright 2020 Science China Press Co., Ltd. 《中国科学》杂志社有限责任公司 版权所有

京ICP备18024590号-1