Sparse and low-rank matrix decompositions

2009 47th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2009

Volumn , Issue , 2009, Pages 962-967

  Chandrasekaran, Venkat ^a   Sanghavi, Sujay ^b   Parrilo, Pablo A ^a   Willsky, Alan S ^a  

^a USA   (United States)

^b The University of Texas at Austin   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

DECOMPOSITION METHODS; DECOMPOSITION PROBLEMS; FUNDAMENTAL PROBLEM; ILL POSED; LOW-RANK MATRICES; MATRIX; NP-HARD; SIMPLE METHOD; SPARSE MATRICES; TWO-COMPONENT; UNCERTAINTY PRINCIPLES;

COMPUTATIONAL COMPLEXITY; CONVEX OPTIMIZATION; DECOMPOSITION;

MATRIX ALGEBRA;

EID: 77949622781     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1109/ALLERTON.2009.5394889     Document Type: Conference Paper

References (18)

1. E. J. Candès and B. Recht. Exact matrix completion via convex optimization. Submitted for publication, 2008.
2. E. J. Candès, J. Romberg, and T. Tao. Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information. IEEE Transactions on Information Theory, 52(2), 2006.
3. V. Chandrasekaran, S. Sanghavi, P. A. Parrilo, and A. S. Willsky. Rank-sparsity incoherence for matrix decomposition. Technical report, 2009.
4. D. L. Donoho. Compressed sensing. IEEE Transactions on Information Theory, 52(4), 2006.
5. 1-norm solution is also the sparsest solution. Communications on Pure and Applied Mathematics, 59(6), 2006.
6. 1 minimization. Proceedings of the National Academy of Sciences, 100, 2003.
7. D. L. Donoho and X. Huo. Uncertainty principles and ideal atomic decomposition. IEEE Transactions on Information Theory, 47(7), 2001.
8. M. Fazel. Matrix Rank Minimization with Applications. PhD thesis, Stanford University, 2002.
9. M. Fazel and J. Goodman. Approximations for partially coherent optical imaging systems. Technical Report, Department of Electrical Engineering, Stanford University, 1998.
10. J. Harris. Algebraic Geometry: A First Course. Springer-Verlag, 1995.
11. S. L. Lauritzen. Graphical Models. Oxford University Press, 1996.
12. J. Lfberg. Yalmip : A toolbox for modeling and optimization in MATLAB. In Proceedings of the CACSD Conference, 2004.
13. S. Lokam. Spectral methods for matrix rigidity with applications to size-depth tradeoffs and communication complexity. In 36th IEEE Symposium on Foundations of Computer Science (FOCS), 1995.
14. B. Recht, M. Fazel, and P. A. Parrilo. Guaranteed minimum rank solutions to linear matrix equations via nuclear norm minimization. Submitted to SIAM Review, 2007.
15. R. T. Rockafellar. Convex Analysis. Princeton University Press, 1996.
16. K. C. Toh, M. J. Todd, and R. H. Tutuncu. Sdpt3 - a matlab software package for semidefinite-quadratic-linear programming. In Available from http://www.math.nus.edu.sg/ mat-tohkc/sdpt3.html.
17. L. G. Valiant. Graph-theoretic arguments in low-level complexity. In 6th Symposium on Mathematical Foundations of Computer Science, 1977.
18. L. Vandenberghe and S. Boyd. Semidefinite programming. SIAM Review, 38(1), 1996.