The Gelfand widths of ℓp-balls for 0 (4) Foucart, Simon a Pajor, Alain b Rauhut, Holger c Ullrich, Tino c a SORBONNE UNIVERSITÉ (France) b UNIVERSITÉ GUSTAVE EIFFEL (France) c UNIVERSITY OF BONN (Germany)

Journal of Complexity

Volumn 26, Issue 6, 2010, Pages 629-640

Author keywords

Compressive sensing; Gelfand widths; Sparse recovery; 1 minimization

Indexed keywords

COMPUTATIONAL COMPLEXITY; NUMERICAL ANALYSIS;

COMPRESSIVE SENSING; GELFAND WIDTHS; LOWER AND UPPER BOUNDS; SPARSE RECOVERY;

COMPRESSED SENSING;

EID: 78049478723     PISSN: 0885064X     EISSN: 10902708     Source Type: Journal    
DOI: 10.1016/j.jco.2010.04.004     Document Type: Article

References (39)

1. R.G. Baraniuk, M. Davenport, R.A. DeVore, and M. Wakin A simple proof of the restricted isometry property for random matrices Constr. Approx. 28 3 2008 253 263
2. S. Boyd, and L. Vandenberghe Convex Optimization 2004 Cambridge Univ. Press
3. H. Buhrman, P. Miltersen, J. Radhakrishnan, and S. Venkatesh Are bitvectors optimal? STOC'00: Proceedings of the Thirty-Second Annual ACM Symposium on Theory of Computing 2000 ACM 449 458
4. E.J. Cands, Compressive sampling, in: Proceedings of the International Congress of Mathematicians, 2006.
5. E.J. Cands The restricted isometry property and its implications for compressed sensing C. R. Acad. Sci., Paris Sr. I Math. 346 2008 589 592
6. E.J. Cands, J. Romberg, and T. Tao Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information IEEE Trans. Inform. Theory 52 2 2006 489 509
7. E.J. Cands, J. Romberg, and T. Tao Stable signal recovery from incomplete and inaccurate measurements Comm. Pure Appl. Math. 59 8 2006 1207 1223
8. E.J. Cands, and T. Tao Near optimal signal recovery from random projections: universal encoding strategies? IEEE Trans. Inform. Theory 52 12 2006 5406 5425
9. B. Carl Entropy numbers, s-numbers, and eigenvalue problems J. Funct. Anal. 41 1981 290 306
10. B. Carl, and A. Pajor Gel'fand numbers of operators with values in a Hilbert space Invent. Math. 94 3 1988 479 504
11. B. Carl, and I. Stephani Entropy, Compactness and the Approximation of Operators 1990 Cambridge University Press
12. R. Chartrand, and V. Staneva Restricted isometry properties and nonconvex compressive sensing Inverse Problems 24 035020 2008 1 14
13. S.S. Chen, D.L. Donoho, and M.A. Saunders Atomic decomposition by basis pursuit SIAM J. Sci. Comput. 20 1 1999 33 61
14. A. Cohen, W. Dahmen, and R.A. DeVore Compressed sensing and best k-term approximation J. Amer. Math. Soc. 22 1 2009 211 231
15. K. Do Ba, P. Indyk, E. Price, D. Woodruff, Lower bounds for sparse recovery, in: Proc. SODA, 2010.
16. D.L. Donoho, Neighborly polytopes and sparse solutions of underdetermined linear equations, 2005, preprint.
17. D.L. Donoho Compressed sensing IEEE Trans. Inform. Theory 52 4 2006 1289 1306
18. S. Foucart, and M. Lai Sparsest solutions of underdetermined linear systems via ℓq -minimization for 0 < q ≤ 1 Appl. Comput. Harmon. Anal. 26 3 2009 395 407
19. A.Y. Garnaev, and E.D. Gluskin On widths of the Euclidean ball Soviet Math. Dokl. 30 1984 200 204
20. E.D. Gluskin On some finite-dimensional problems in the theory of widths Vestn. Leningr. Univ. Math. 14 1982 163 170
21. E.D. Gluskin Norms of random matrices and widths of finite-dimensional sets Math. USSR-Sb. 48 1984 173 182
22. R. Graham, and N. Sloane Lower bounds for constant weight codes IEEE Trans. Inform. Theory 26 1 1980 37 43
23. R. Gribonval, and M. Nielsen Sparse representations in unions of bases IEEE Trans. Inform. Theory 49 12 2003 3320 3325
24. R. Gribonval, and M. Nielsen Highly sparse representations from dictionaries are unique and independent of the sparseness measure Appl. Comput. Harmon. Anal. 22 3 2007 335 355
25. O. Gudon, and A.E. Litvak Euclidean projections of a p-convex body Geometric Aspects of Functional Analysis Lecture Notes in Math. vol. 1745 2000 Springer Berlin
26. B.S. Kashin Diameters of some finite-dimensional sets and classes of smooth functions Math. USSR. Izv. 11 1977 317 333
27. T. Khn A lower estimate for entropy numbers J. Approx. Theory 110 1 2001 120 124
28. N. Linial, and I. Novik How neighborly can a centrally symmetric polytope be? Discrete Comput. Geom. 36 2 2006 273 281
29. G. Lorentz, M. von Golitschek, and Y. Makovoz Constructive Approximation: Advanced Problems Grundlehren der Mathematischen Wissenschaften vol. 304 1996 Springer Berlin
30. S. Mendelson, A. Pajor, and M. Rudelson The geometry of random - 1, 1 -polytopes Discrete Comput. Geom. 34 3 2005 365 379
31. S. Mendelson, A. Pajor, and N. Tomczak-Jaegermann Uniform uncertainty principle for Bernoulli and subgaussian ensembles Constr. Approx. 28 3 2009 277 289
32. N. Noam, and W. Avi Hardness vs randomness J. Comput. System Sci. 49 2 1994 149 167
33. E. Novak Optimal recovery and n-widths for convex classes of functions J. Approx. Theory 80 3 1995 390 408
34. E. Novak, and H. Woniakowski Tractability of Multivariate Problems. Vol. I. Linear Information 2008 EMS Zrich
35. A. Pinkus N-Widths in Approximation Theory 1985 Springer-Verlag Berlin
36. A. Pinkus N-widths and Optimal Recovery Lect. Notes AMS Short Course ed. Proc. Symp. Appl. Math. vol. 36 1986 51 66
37. H. Rauhut, Compressive sensing and structured random matrices, in: M. Fornasier (Ed.), Theoretical Foundations and Numerical Methods for Sparse Recovery, Radon Series Comp. Appl. Math. 9, De Gruyter, 2010.
38. C. Schtt Entropy numbers of diagonal operators between symmetric Banach spaces J. Approx. Theory 40 2 1984 121 128
39. J. Vybral Widths of embeddings in function spaces J. Complexity 24 4 2008 545 570