Analysis of sparse regularization based robust regression approaches

IEEE Transactions on Signal Processing

Volumn 61, Issue 5, 2013, Pages 1249-1257

  Mitra, Kaushik ^a   Veeraraghavan, Ashok ^a   Chellappa, Rama ^b  

^a Rice University   (United States)

^b UNIVERSITY OF MARYLAND   (United States)

Author keywords

Compressive sensing; robust regression; sparse representation

Indexed keywords

COMBINATORIAL OPTIMIZATION PROBLEMS; COMBINATORIAL PROBLEM; COMPRESSIVE SENSING; HIGH-DIMENSIONAL REGRESSION PROBLEMS; POLYNOMIAL-TIME ALGORITHMS; PRINCIPAL ANGLES; REGRESSION PARAMETERS; REGULARIZATION APPROACH; RESEARCH GROUPS; RESTRICTED ISOMETRY PROPERTIES; ROBUST REGRESSIONS; SPARSE REGULARIZATIONS; SPARSE REPRESENTATION; TRAINING DATASET;

ALGORITHMS; COMBINATORIAL OPTIMIZATION; MATRIX ALGEBRA; SIGNAL RECONSTRUCTION; STATISTICS;

REGRESSION ANALYSIS;

EID: 84873913036     PISSN: 1053587X     EISSN: None     Source Type: Journal    
DOI: 10.1109/TSP.2012.2229992     Document Type: Article

References (28)

1. E. Candes and P. Randall, "Highly robust error correction byconvex programming," IEEE Trans. Inf. Theory, vol. 54, no., pp. 2829-2840, 2008.
2. E. J. Candes, "The restricted isometry property and its implications for compressed sensing," Comptes Rendus Mathematique, 2008.
3. E. J. Candès, J. K. Romberg, and T. Tao, "Robust uncertainty principles: Exact signal reconstruction from highly incomplete frequency information," IEEE Trans. Inf. Theory, vol. 52, no. 2, pp. 489-509, 2006.
4. E. J. Candes and T. Tao, "Decoding by linear programming," IEEE Trans. Inf. Theory, vol. 51, no. 12, pp. 4203-4215, 2005.
5. R. E. Carrillo, K. E. Barner, and T. C. Aysal, "Robust sampling and reconstruction methods for sparse signals in the presence of impulsive noise," IEEE J. Sel. Topics Signal Process., vol. 4, no. 2, pp. 392-408, 2010.
6. S. S. Chen, D. L. Donoho, and M. A. Saunders, "Atomic decomposition by basis pursuit," SIAM J. Scientif. Comput., vol. 20, pp. 33-61, 1998.
7. D. L. Donoho, "Compressed sensing," IEEE Trans. Inf. Theory, vol. 52, no. 4, pp. 1289-1306, 2006.
8. D. L. Donoho, "High-dimensional centrally symmetric polytopes with neighborliness proportional to dimension," Discrete Comput. Geometry, 2006.
9. D. L. Donoho and J. Tanner, "Counting faces of randomly projected polytopes when the projection radically lowers dimension," J. Amer. Math. Soc., 2009.
10. M. Fischler and R. Bolles, "Random sample consensus: A paradigm for model fitting with applications to image analysis and automated cartography," Comm. Assoc. Mach., 1981.
11. G. H. Golub and C. F. V. Loan, Matrix Computations. Baltimore, MD, USA: Johns Hopkins Univ. Press, 1996.
12. P. Huber, Robust Statistics.: Wiley Series in Probability and Statistics, 1981.
13. Y. Jin and B. D. Rao, "Algorithms for robust linear regression by exploiting the connection to sparse signal recovery," in Proc. Int. Conf. Acoust., Speech, Signal Process. (ICASSP), 2010, pp. 3830-3833.
14. J. N. Laska, M. A. Davenport, and R. G. Baraniuk, "Exact signal recovery from sparsely corrupted measurements through the pursuit of justice," in Conf. Rec. Asilomar Conf. Signals, Syst., Comput., 2009, pp. 1556-1560.
15. M. S. Lobo, L. Vandenberghe, S. Boyd, and H. Lebret, "Applications of second-order cone programming," Linear Algebra Appl., 1998.
16. A. Maleki and D. L. Donoho, "Optimally tuned iterative reconstruction algorithms for compressed sensing," IEEE J. Sel. Topics Signal Process., vol. 4, no. 2, pp. 330-341, 2010.
17. R. A. Maronna, R. D. Martin, and V. J. Yohai, Robust Statistics, Theory and Methods, ser. Wiley Series in Probability and Statistics. New York, NY, USA: Wiley, 2006.
18. K. Mitra, A. Veeraraghavan, and R. Chellappa, "Robust regression using sparse learning for high dimensional parameter estimation problems," in Proc. Int. Conf. Acoust., Speech, Signal Process. (ICASSP), 2010, pp. 3846-3849.
19. P. J. Rousseeuw, "Least median of squares regression," J. Amer. Stat. Assoc., 1984.
20. P. J. Rousseeuw and A. M. Leroy, Robust Regression and Outlier Detection, ser. Wiley Series in Probability and Mathematical Statistics. New York, NY, USA: Wiley, 1986.
21. P. J. Rousseeuw and V. Yohai, "Robust regression by means of s-es-timators," in Robust and Nonlinear Time Series Analysis, ser. Lecture Notes in Statistics. New York, NY, USA: Springer-Verlag, 1984.
22. C. V. Stewart, "Robust parameter estimation in computer vision," SIAM Rev., 1999.
23. C. Studer and R. G. Baraniuk, "Stable restoration and separation of approximately sparse signals," Appl. Comput. Harmon. Anal., 2011, submitted for publication.
24. C. Studer, P. Kuppinger, G. Pope, and H. Bölcskei, "Recovery of sparsely corrupted signals," IEEE Trans. Inf. Theory, vol. 58, no. 5, pp. 3115-3130, 2012.
25. M. E. Tipping, "Sparse Bayesian learning and the relevance vector machine," J. Mach. Learn. Res., 2001.
26. P. H. S. Torr and A. Zisserman, "Mlesac: A new robust estimator with application to estimating image geometry," Comput. Vis. Image Understand., 2000.
27. D. P. Wipf and B. D. Rao, "Sparse Bayesian learning for basis selection," IEEE Trans. Signal Process., vol. 52, no. 8, pp. 2153-2164, 2004.
28. V. J. Yohai, "High breakdown-point and high efficiency robust estimates for regression," Ann. Statist., Jun. 1987.