On verifiable sufficient conditions for sparse signal recovery via ℓ 1 minimization

Mathematical Programming

Volumn 127, Issue 1, 2011, Pages 57-88

  Juditsky, Anatoli ^a   Nemirovski, Arkadi ^b  

^a UNIV GRENOBLE ALPES   (France)

^b GEORGIA INSTITUTE OF TECHNOLOGY   (United States)

Author keywords

1 recovery; Compressed sensing; Sparse recovery

Indexed keywords

BASIC CONCEPTS; COMPRESSED SENSING; EIGEN-VALUE; ERROR BOUND; MATRIX; MEASUREMENT NOISE; NEAR-OPTIMAL SOLUTIONS; NONZERO ENTRIES; OPTIMIZATION PROBLEMS; SPARSE RECOVERY; SPARSE SIGNALS; SUFFICIENT CONDITIONS; UPPER BOUND;

EIGENVALUES AND EIGENFUNCTIONS; ERROR ANALYSIS; OPTIMIZATION; SIGNAL RECONSTRUCTION; SPURIOUS SIGNAL NOISE;

RECOVERY;

EID: 79952741165     PISSN: 00255610     EISSN: 14364646     Source Type: Journal    
DOI: 10.1007/s10107-010-0417-z     Document Type: Article

References (23)

1. Andersen E.D., Andersen K.D.: The MOSEK optimization tools manual. Version 5.0 http://www.mosek.com/fileadmin/products/5-0/tools/doc/html/tools/ index.html
2. Ben-Tal A., Nemirovski A.: Lectures on Modern Convex Optimization. SIAM, Philadelphia (2001)
3. P.J. Bickel 2007 Discussion of The Dantzig selector: statistical estimation when p is much larger than n In: Candes, E.J., Tao, T. Annals of Stat. 35 2352 2357 2382645
4. Bickel, P.J., Ritov, Ya., Tsybakov, A.: Simultaneous analysis of Lasso and Dantzig selector. Ann. Stat. (to appear 2008)
5. E. J. Candès T. Tao 2007 The Dantzig selector: statistical estimation when p is much larger than n Ann. Stat. 35 2313 2351 1139.62019 10.1214/009053606000001523
6. E. J. Candès T. Tao 2006 Decoding by linear programming IEEE Trans. Inform. Theory 51 4203 4215 10.1109/TIT.2005.858979 (Pubitemid 41800353)
7. E. J. Candès T. Tao 2006 Near-optimal signal recovery from random projections and universal encoding strategies IEEE Trans. Inform. Theory 52 5406 5425 10.1109/TIT.2006.885507 2300700 (Pubitemid 46445381)
8. E. J. Candès J. Romberg T. Tao 2005 Signal recovery from incomplete and inaccurate measurements Comm. Pure Appl. Math. 59 8 1207 1223 10.1002/cpa.20124
9. Candès, E. J.: Compressive sampling. Sanz-Solé M. In: Javier, S., Juan, L. V., Joan, V. (eds). International Congress of Mathematicians, Madrid 2006, vol. III, pp. 1437-1452. European Mathematical Society Publishing House (2006)
10. E. J. Candès 2008 The restricted isometry property and its implications for compressed sensing Comptes Rendus de l'Acad. des Sci. Ser. I 346 589 592 1153.94002
11. Cohen, A., Dahmen, W., DeVore, R.: Compressed Sensing and Best k-term Approximation. Preprint, http://www.math.sc.edu/~devore/publications/CDDSensing- 6.pdf (2006)
12. d'Aspremont, A., El Ghaoui, L.: Testing the Nullspace Property using Semidefinite Programming. Preprint. http://arxiv.org/abs/0807.3520 (2008)
13. DeVore, R.: Deterministic Constructions of Compressed Sensing Matrices. Preprint, Department of Mathematics, University of South Carolina (2007)
14. D. Donoho X. Huo 2001 Uncertainty principles and ideal atomic decomposition IEEE Trans. Inf. Theory 47 7 2845 2862 1019.94503 10.1109/18.959265 1872845 (Pubitemid 33053488)
15. Donoho, D.: High-dimensional centrally-symmetric polytopes with neighborliness proportional to dimension. Technical report, Department of Statistics, Stanford University (2004)
16. Donoho, D.: Neighborly polytopes and sparse solutions of underdetermined linear equations. Technical report, Department of Statistics, Stanford University (2004)
17. D. Donoho M. Elad V. N. Temlyakov 2006 Stable recovery of sparse overcomplete representations in the presence of noise IEEE Trans. Inf. Theory 52 6 18 10.1109/TIT.2005.860430 2237332 (Pubitemid 43263116)
18. J.-J. Fuchs 2004 On sparse representations in arbitrary redundant bases IEEE Trans. Inf. Theory 50 1341 1344 10.1109/TIT.2004.828141
19. J.-J. Fuchs 2005 Recovery of exact sparse representations in the presence of bounded noise IEEE Trans. Inf. Theory 51 3601 3608 10.1109/TIT.2005.855614 (Pubitemid 41448600)
20. A. Nemirovski 2004 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 J. Optim. 15 229 251 1106.90059 10.1137/S1052623403425629 2112984 (Pubitemid 40360669)
21. R. Tibshirani 1996 Regression shrinkage and selection via the Lasso J. R. Stat. Soc. Ser. B 58 267 288 0850.62538 1379242
22. J.A. Tropp 2006 Just relax: convex programming methods for identifying sparse signals IEEE Trans. Info. Theory 51 3 1030 1051 10.1109/TIT.2005.864420 2238069 (Pubitemid 46444890)
23. Zhang, Y.: A simple proof for recoverability of ell-1-minimization: go over or under? Rice CAAM Department Technical Report TR05-09 (2005)