L1-penalized robust estimation for a class of inverse problems arising in multiview geometry

Advances in Neural Information Processing Systems 22 - Proceedings of the 2009 Conference

Volumn , Issue , 2009, Pages 441-449

  Dalalyan, Arnak S ^a   Keriven, Renaud ^a  

^a UNIVERSITÉ PARIS EST   (France)

Author keywords

[No Author keywords available]

Indexed keywords

LINEAR PROGRAMMING; STATISTICS;

BAYESIAN; LAPLACE PRIORS; MAXIMUM A POSTERIORI; MULTI-VIEW GEOMETRY; MULTIVARIATE LAPLACE; NEW APPROACHES; REGULARISATION; ROBUST ESTIMATION; SPARSE RECOVERY; ∞NORM;

INVERSE PROBLEMS;

EID: 84858721716     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: None     Document Type: Conference Paper

References (29)

1. F. Bach. Bolasso: model consistent Lasso estimation through the bootstrap. In Twenty-fifth International Conference on Machine Learning (ICML), 2008.
2. P. J. Bickel, Y. Ritov, and A. B. Tsybakov. Simultaneous analysis of lasso and Dantzig selector. Ann. Statist., 37(4):1705-1732, 2009.
3. E. Candès and T. Tao. The Dantzig selector: statistical estimation when p is much larger than n. Ann. Statist., 35(6):2313-2351, 2007.
4. E. J. Candès. The restricted isometry property and its implications for compressed sensing. C. R. Math. Acad. Sci. Paris, 346(9-10):589-592, 2008.
5. E. J. Candès and P. A. Randall. Highly robust error correction by convex programming. IEEE Trans. Inform. Theory, 54(7):2829-2840, 2008.
6. E. J. Candès, J. K. Romberg, and T. Tao. Stable signal recovery from incomplete and inaccurate measurements. Comm. Pure Appl. Math., 59(8):1207-1223, 2006.
7. C. Chesneau and M. Hebiri. Some theoretical results on the grouped variables Lasso. Math. Methods Statist., 17(4):317-326, 2008.
8. A. S. Dalalyan, A. Juditsky, and V. Spokoiny. A new algorithm for estimating the effective dimension-reduction subspace. Journal of Machine Learning Research, 9:1647-1678, Aug. 2008.
9. A. S. Dalalyan and A. B. Tsybakov. Aggregation by exponential weighting, sharp PAC-bayesian bounds and sparsity. Machine Learning, 72(1-2):39-61, 2008
10. D. Donoho, M. Elad, and V. Temlyakov. Stable recovery of sparse overcomplete representations in the presence of noise. IEEE Trans. Inform. Theory, 52(1):6-18, 2006.
11. D. L. Donoho and X. Huo. Uncertainty principles and ideal atomic decomposition. IEEE Trans. Inform. Theory, 47(7):2845-2862, 2001.
12. O. Enqvist and F. Kahl. Robust optimal pose estimation. In ECCV, pages I: 141-153, 2008.
13. R. Hartley and F. Kahl. Optimal algorithms in multiview geometry. In ACCV, volume 1, pages 13 - 34, Nov. 2007.
14. R. Hartley and F. Kahl. Global optimization through rotation space search. IJCV, 2009.
15. ∞ minimization in geometric reconstruction problems. In CVPR (1), pages 504-509, 2004.
16. R. I. Hartley and A. Zisserman. Multiple View Geometry in Computer Vision. Cambridge University Press, June 2004.
17. ∞-norm. In ICCV, pages 1002-1009. IEEE Computer Society, 2005.
18. ∞ norm. IEEE Trans. Pattern Analysis and Machine Intelligence, 30(9):1603-1617, sep 2008.
19. T. Kanade and Q. Ke. Quasiconvex optimization for robust geometric reconstruction. In ICCV, pages II: 986-993, 2005.
20. Q. Ke and T. Kanade. Uncertainty models in quasiconvex optimization for geometric reconstruction. In CVPR, pages I: 1199-1205, 2006.
21. ∞ triangulation with outliers. In CVPR, pages 1-8, 2007.
22. D. Martinec and T. Pajdla. Robust rotation and translation estimation in multiview reconstruction. In CVPR, pages 1-8, 2007.
23. D. Nistér. An efficient solution to the five-point relative pose problem. IEEE Trans. Pattern Anal. Mach. Intell, 26(6):756-777, 2004.
24. ∞ problems using pseudoconvexity. In ICCV, pages 1-8, 2007.
25. ∞ error norm for geometric vision problems. In ICCV, pages 1-8, 2007.
26. Y. D. Seo, H. J. Lee, and S. W. Lee. Sparse structures in L-infinity norm minimization for structure and motion reconstruction. In ECCV, pages I: 780-793, 2008.
27. ∞ norm. In CVPR, pages I: 485-494, 2006.
28. J. F. Sturm. Using SeDuMi 1.02, a MATLAB toolbox for optimization over symmetric cones. Optim. Methods Softw., 11/12(1-4):625-653, 1999.
29. P. Zhao and B. Yu. On model selection consistency of Lasso. J. Mach. Learn. Res., 7:2541-2563, 2006.