A fast algorithm for recovery of jointly sparse vectors based on the alternating direction methods

Journal of Machine Learning Research

Volumn 15, Issue , 2011, Pages 461-469

  Lu, Hongtao ^a   Long, Xianzhong ^a   Lv, Jingyuan ^a  

^a SHANGHAI JIAO TONG UNIVERSITY   (China)

Author keywords

[No Author keywords available]

Indexed keywords

ALTERNATING DIRECTION METHODS; COMPRESSIVE SENSING; FAST ALGORITHMS; L1 NORM; LAGRANGIAN MULTIPLIERS; MINIMIZATION PROBLEMS; MULTIPLE MEASUREMENT VECTORS; RECOVERED SIGNALS; SIGNAL MEASUREMENT; SMV MODEL; SPARSE SIGNALS; SPARSE VECTORS; STATE-OF-THE-ART METHODS; VECTOR MULTIPLICATION;

ARTIFICIAL INTELLIGENCE; SIGNAL RECONSTRUCTION; VECTORS;

RECOVERY;

EID: 84862270751     PISSN: 15324435     EISSN: 15337928     Source Type: Journal    
DOI: None     Document Type: Conference Paper

References (26)

1. A. Beck and M. Teboulle (2009). A fast iterative shrinkage-thresholding algorithm for linear inverse problems. SIAM Journal on Imaging Sciences, 2(1):183-202.
2. E. J. Candes, J. Romberg, and T. Tao (2006). Robust uncertainty principles: Exact signal reconstruction from highly incomplete frequency information. IEEE Transactions on Information Theory, 52(2): 489-509.
3. J. Chen and X. Huo (2006). Theoretical results Figure 5: Relative errors of MMV-ADM versus iteration numbers for different κ. on sparse representations of multiple-measurement vectors. IEEE Transactions on Signal Processing, 54(12):4634-4643.
4. S. F. Cotter, B. D. Rao, Kjersti Engan, and K. Kreutz- Delgado (2005). Sparse solutions to linear inverse problems with multiple measurement vectors. IEEE Transactions on Signal Processing, 53(7):2477-2488.
5. D. L. Donoho (1995). De-noising by softthresholding. IEEE Transactions on Information Theory, 41(3):613-627.
6. D. L. Donoho (2006a). Compressed sensing. IEEE Transactions on Information Theory, 52(4):1289-1306.
7. D. L. Donoho (2006b). For most large underdetermined systems of linear equations, the minimal l1norm solution is also the sparsest solution. Commun. Pure Appl. Math., 59(7):907-934.
8. D. L. Donoho and Y. Tsaig (2006). Fast solution of l1-norm minimization problems when the solution may be sparse. preprint, http://www.stanford.edu/ tsaig/research.html, 2006.
9. Y. C. Eldar and M. Mishali (2009). Robust recovery of signals from a structured union of subspaces. IEEE Transactions on Information Theory,55(11):5302-5316.
10. E. Esser (2009). Applications of Lagrangian-Based Alternating Direction Methods and Connections to Split Bregman. CAM Report, TR09-31, UCLA.
11. S. Erickson and C. Sabatti (2008). Empirical Bayes estimation of a sparse vector of gene expression changes. Statistical Applications in Genetics and Molecular Biology, 4(1):22.
12. R. Glowinski, and P. Le Tallec (1989). Augmented Lagrangian and operator splitting methods in nonlinear mechanics. SIAM.
13. I. F. Gorodnitsky and B. D. Rao (1997). Sparse signal reconstruction from limited data using FOCUSS: A re-weighted minimum norm algorithm. IEEE Transactions Signal Processing, 45(3):600-616.
14. S. Kim, K. Koh, M. Lustig, S. Boyd, and D. Gorinevsky (2007). An interior point method for large-scale l1-regularized least squares. IEEE Journal of Selected Topics in Signal Processing, 1(4):606-617.
15. D. Malioutov, M. Cetin, and A. Willsky (2003). Source localization by enforcing sparsity through a laplacian. In IEEE Workshop on Statistical Signal Processing, 553-556.
16. A. Nemirovski (2005). Prox-method with rate of convergence O(1=t) for variational inequalities with Lipschitz continuous monotone operators and smooth convex-concave saddle point problems. SIAM Journal on Optimization, 15(1):229-251.
17. M. Osborne, B. Presnell, and B. Turlach (2000). A new approach to variable selection in least squares problems. IMA Journal of Numerical Analysis, 20:389-404.
18. M. Stojnic, F. Parvaresh and B. Hassibi (2009). On the reconstruction of block-sparse signals with an optimal number of measurements. IEEE Transactions Signal Processing, 57(8):3075-3085.
19. R. T. Rockafellar (1973). The multiplier method of Hestenes and Powell applied to convex programming. J. Optimiz. Theory App., 12(6):555-562.
20. P. Stoica and R. Moses (1997). Introduction to Spectral Analysis. Upper Saddle River, NJ: Prentice-Hall.
21. J. A. Tropp, A. C. Gilbert, and M. J. Strauss (2006a). Algorithms for simultaneous sparse approximation. Part I: Greedy pursuit. Signal Proces., 86(3):572-588.
22. J. A. Tropp (2006b). Algorithms for simultaneous sparse approximation. Part II: Convex relaxation. Signal Proces., 86(3):589-602.
23. L. Sun, J. Liu, J. Chen, J. Ye (2009). Efficient Recovery of Jointly Sparse Vectors. In Adv. NIPS.
24. S. Wright, R. Nowak, and M. Figueiredo (2009). Sparse reconstruction by separable approximation. IEEE Transactions Signal Processing, 57(7):2479-2493.
25. J. Yang and Y. Zhang (2010). Alternating direction algorithms for l1-problems in compressive sensing. SIAM Journal on Scienctific Computing.
26. A. Yang, A. Ganesh, S. Sastry and Y. Ma (2010). Fast L1-minimization algorithms and an application in robust face recognition: a review. Technical Report, http://www.eecs.berkeley.edu/Pubs/TechRpts/2010/EECS-2010-13.html.