A remark on compressed sensing

Mathematical Notes

Volumn 82, Issue 5-6, 2007, Pages 748-755

  Kashin, B S ^a   Temlyakov, V N ^b  

^a STEKLOV MATHEMATICAL INSTITUTE   (Russian Federation)

^b UNIVERSITY OF SOUTH CAROLINA   (United States)

Author keywords

Combinatorial optimization problem; Compressed sensing; Gelfand width; Kolmogorov width; Restricted isometry property; Signal processing; Sparsity

Indexed keywords

EID: 38349077426     PISSN: 00014346     EISSN: None     Source Type: Journal    
DOI: 10.1134/S0001434607110193     Document Type: Article

References (11)

1. S. S. Chen, D. L. Donoho, and M. A. Saunders, "Atomic decomposition by basis pursuit," SIAM Rev. 43(1), 129-159 (2001).
2. D. L. Donoho, M. Elad, and V. N. Temlyakov, "Stable recovery of sparse overcomplete representations in the presence of noise," IEEE Trans. Inform. Theory 52(1), 6-18 (2006).
3. E. J. Candes, "Compressive sampling," in International Congress of Mathematicians, Madrid, Spain, August 22-30, 2006 (Eur. Math. Soc., Zürich, 2006), Vol. 3, pp. 1433-1452.
4. R. DeVore, "Optimal computation," in International Congress of Mathematicians, Madrid, Spain, August 22-30, 2006 (Eur. Math. Soc., Zürich, 2006), Vol. 1, pp. 187-215.
5. D. L. Donoho, "Compressed sensing," IEEE Trans. Inform. Theory 52(4), 1289-1306 (2006).
6. A. Cohen, W. Dahmen, and R. DeVore, Compressed Sensing and k-Term Approximation (Manuscript, 2007).
7. R. S. Ismagilov, "Diameters of sets in normed linear spaces, and the approximation of functions by trigonometric polynomials," Uspekhi Mat. Nauk 3(177), 161-178 (1974) [Russian Math. Surveys 29 (3), 169-186 (1974)].
8. B. S. Kashin, "Diameters of some finite-dimensional sets and classes of smooth functions," Izv. Akad. Nauk SSSR Ser. Mat. 41, 334-351 (1977) [Math. USSR-Izv. 11, 317-333 (1978)].
9. A. Yu. Garnaev and E. D. Gluskin, "On widths of the Euclidean ball," Dokl. Akad. Nauk SSSR 277, 1048-1053 (1984) [Soviet Math., Dokl. 30 (5), 200-204 (1984)].
10. E. J. Candes and T. Tao, "Decoding by linear programming," IEEE Trans. Inform. Theory 51(12), 4203-4215 (2005).
11. E. J. Candes, J. K. Romberg, and T. Tao, "Stable signal recovery from incomplete and inaccurate measurements," Comm. Pure Appl. Math. 59(8), 1207-1223 (2006).