Algorithms for simultaneous sparse approximation. Part II: Convex relaxation

Signal Processing

Volumn 86, Issue 3, 2006, Pages 589-602

  Tropp, Joel A ^a  

^a UNIVERSITY OF MICHIGAN   (United States)

Author keywords

Combinatorial optimization; Convex relaxation; Multiple measurement vectors; Simultaneous sparse approximation

Indexed keywords

APPROXIMATION THEORY; COMBINATORIAL MATHEMATICS; COMPUTER PROGRAMMING; COMPUTER SOFTWARE; PROBLEM SOLVING;

COMBINATORIAL OPTIMIZATION; CONVEX RELAXATION; ELEMENTARY SIGNALS; MULTIPLE MEASUREMENT VECTORS; SIMULTANEOUS SPARSE APPROXIMATION;

ALGORITHMS;

EID: 30844461481     PISSN: 01651684     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.sigpro.2005.05.031     Document Type: Article

References (21)

1. J.A. Tropp, A.C. Gilbert, M.J. Strauss, Algorithms for simultaneous sparse approximation, Part I: greedy pursuit, Signal Process. 86 (3) (2006) 572-588, this issue.
2. G. Davis, S. Mallat, and M. Avellaneda Greedy adaptive approximation J. Constr. Approx. 13 1997 57 98
3. S.S. Chen, D.L. Donoho, and M.A. Saunders Atomic decomposition by basis pursuit SIAM J. Sci. Comput. 20 1 1999 33 61
4. J.A. Tropp Greed is good: algorithmic results for sparse approximation IEEE Trans. Inform. Theory 50 10 October 2004
5. D.L. Donoho, and M. Elad Maximal sparsity representation via ℓ 1 minimization Proc. Natl. Acad. Sci. 100 March 2003 2197 2202
6. B.K. Natarajan Sparse approximate solutions to linear systems SIAM J. Comput. 24 1995 227 234
7. S. Boyd, and L. Vanderberghe Convex Optimization 2004 Cambridge University Press Cambridge
8. J.A. Tropp, Just relax: convex programming methods for identifying sparse signals, June 2004; revised Feb. 2005, submitted for publication.
9. D.L. Donoho, M. Elad, V.N. Temlyakov, Stable recovery of sparse overcomplete representations in the presence of noise, IEEE Trans. Inform. Theory, February 2004, submitted for publication.
10. J.A. Tropp, Topics in sparse approximation, Ph.D. Dissertation, Computational and Applied Mathematics, The University of Texas at Austin, August 2004.
11. J. Bergh, and J. Löfström Interpolation Spaces: An Introduction Grundlehren der mathematischen Wissenschaften vol. 223 1976 Springer Berlin
12. J.A. Tropp, Just relax: convex programming methods for subset selection and sparse approximation, ICES Report 04-04, The University of Texas at Austin, 2004.
13. R.T. Rockafellar Convex Analysis 1970 Princeton University Press Princeton, NJ
14. J.-J. Fuchs Recovery of exact sparse representations in the presence of noise Proceedings of the 2004 IEEE International Conference on Acoustics, Speech, and Signal Processing Montréal May 2004
15. J.-J. Fuchs, Recovery of exact sparse representations in the presence of bounded noise, IEEE Trans. Inform. Theory, April 2004, accepted for publication.
16. J.-J. Fuchs On sparse representations in arbitrary redundant bases IEEE Trans. Inform. Theory 50 6 June 2004 1341 1344
17. J. Chen, X. Huo, Theoretical results about finding the sparsest representations of multiple measurement vectors (MMV) in an overcomplete dictionary using ℓ 1 minimization and greedy algorithms, IEEE Trans. Signal Process., 2004, submitted for publication.
18. S. Cotter, B.D. Rao, K. Engan, K. Kreutz-Delgado, Sparse solutions of linear inverse problems with multiple measurement vectors, IEEE Trans. Signal Process. 53 (7) (July 2005) 2477-2488.
19. J. Chen, and X. Huo Sparse representations for multiple measurement vectors (MMV) in an overcomplete dictionary Proceedings of the 2005 IEEE International Conference on Acoustics, Speech, and Signal Processing Philadelphia March 2005
20. D. Malioutov, M. Çetin, A. Willsky, Source localization by enforcing sparsity through a Laplacian prior: an SVD-based approach, in: IEEE Statistical Signal Processing Workshop, October 2003, pp. 553-556.
21. D. Malioutov, A sparse signal reconstruction perspective for source localization with sensor arrays, MSc. Thesis, MIT, Cambridge, MA, July 2003.