Signal recovery from incomplete and inaccurate measurements via regularized orthogonal matching pursuit

IEEE Journal on Selected Topics in Signal Processing

Volumn 4, Issue 2, 2010, Pages 310-316

  Needell, Deanna ^a   Vershynin, Roman ^b  

^a UNIVERSITY OF CALIFORNIA   (United States)

^b UNIVERSITY OF MICHIGAN   (United States)

Author keywords

Compressed sensing (CS); Orthogonal matching pursuit; Sparse approximation problem; Uncertainty principle

Indexed keywords

COMPRESSED SENSING; CONVEX PROGRAMMING; ERROR TERMS; ERROR VECTOR; GREEDY ALGORITHMS; GREEDY METHOD; LEAST SQUARES PROBLEMS; MEASUREMENT MATRIX; NOISE LEVELS; ORTHOGONAL MATCHING PURSUIT; SIGNAL RECOVERY; SPARSE APPROXIMATIONS; SPARSE RECOVERY; UNCERTAINTY PRINCIPLES;

ORTHOGONAL FUNCTIONS;

SIGNAL RECONSTRUCTION;

EID: 77949732443     PISSN: 19324553     EISSN: None     Source Type: Journal    
DOI: 10.1109/JSTSP.2010.2042412     Document Type: Article

References (24)

1. 3/ln n]l) operations," SIAM J. Opt., vol.9, no.4, pp. 803-812, 1999.
2. E. van den Berg and M. P. Friedlander, In Pursuit of a Root Dept.of Comput. Sci., Univ. of British Columbia, Vancouver, BC, Tech. Rep. TR-2007-2019, Jun. 2007.
3. T. Blumensath and M. E. Davies, Iterative Hard Thresholding for Compressed Sensing. Edinburgh, U.K.: Univ. of Edinburgh, 2009, Preprint.
4. E. Candès, "Compressive sampling," in Proc. Int. Congr. Math., Madrid, Spain, 2006, vol.3, pp. 1433-1452.
5. E. Candès, J. Romberg, and T. Tao, "Robust uncertainty principles: Exact signal reconstruction from highly incomplete Fourier information," IEEE Trans. Inf. Theory, vol.52, no.2, pp. 489-509, Feb. 2006.
6. E. Candès, J. Romberg, and T. Tao, "Stable signal recovery from incomplete and inaccurate measurements," Commun. Pure Appl. Math., vol.59, no.8, pp. 1207-1223, 2006.
7. E. Candès and T. Tao, "Decoding by linear programming," IEEE Trans. Inf. Theory, vol.51, no.12, pp. 4203-4215, Dec. 2005.
8. E. J. Candès, "The restricted isometry property and its implications for compressed sensing," C. R. Math. Acad. Sci. Paris, Ser. I, vol.346, pp. 589-592, 2008.
9. E. J. Candès and T. Tao, "Near optimal signal recovery from random projections: Universal encoding strategies?," IEEE Trans. Inf. Theory, vol.52, no.12, pp. 5406-5425, Dec. 2006.
10. W. Dai and O. Milenkovic, "Subspace pursuit for compressive sensing: Closing the gap between performance and complexity," IEEE Trans. Inf. Theory, vol.55, no.5, pp. 2230-2249, May 2009.
11. D. L. Donoho, "Compressed sensing," IEEE Trans. Inf. Theory, vol.52, no.4, pp. 1289-1306, Apr. 2006.
12. D. L. Donoho, "For most large underdetermined systems of linear equations the minimal- -norm solution is also the sparsest solution," Comm. Pure Appl. Math., vol.59, no.6, pp. 797-829, 2006.
13. D. L. Donoho, M. Elad, and V. N. Temlyakov, "Stable recovery of sparse overcomplete representations in the presence of noise," IEEE Trans. Inf. Theory, vol.52, no.1, pp. 6-18, Jan. 2006.
14. D. L. Donoho, "Neighborly polytopes and sparse solutions of underdetermined linear equations," 2005, Tech. Rep..
15. M. A. T. Figueiredo, R. D. Nowak, and S. J. Wright, "Gradient projection for sparse reconstruction: Application to compressed sensing and other inverse problems," IEEE J. Sel. Topics Signal Process., vol.1, no.4, pp. 586-598, Aug. 2007.
16. A. Gilbert, M. Strauss, J. Tropp, and R. Vershynin, "One sketch for all: Fast algorithms for compressed sensing," in Proc. 39th ACM Symp. Theory Comput., San Diego, CA, Jun. 2007.
17. Yu. Lyubarskii and R. Vershynin, "Uncertainty principles and vector quantization," 2008, submitted for publication.
18. D. Needell and J. A. Tropp, "CoSaMP: Iterative signal recovery from incomplete and inaccurate samples," California Inst. of Technol., Pasadena, ACM Tech. Rep. 2008-2101, Jul. 2008.
19. D. Needell and J. A. Tropp, "CoSaMP: Iterative signal recovery from noisy samples," Appl. Comput. Harmon. Anal., 2008, DOI: 10.1016/j. acha.2008.07.002.
20. D. Needell and R. Vershynin, "Uniform uncertainty principle and signal recovery via regularized orthogonal matching pursuit," Found. Comput. Math., 2007, DOI: 10.1007/s10208-008-9031-3.
21. H. Rauhut, "On the impossibility of uniform sparse reconstruction using greedy methods," Sampl. Theory Signal Image Process., vol.7, no.2, pp. 197-215, 2008.
22. J. A. Tropp, "Just relax: Convex programming methods for subset selection and sparse approximation," Univ. of Texas, Austin, ICES Rep. 04-04, 2004.
23. J. A. Tropp and A. C. Gilbert, "Signal recovery from random measurements via orthogonal matching pursuit," IEEE Trans. Inf. Theory, vol.53, no.12, pp. 4655-4666, Dec. 2007.
24. D. Goldfarb, W. Yin, S. Osher, and J. Darbon, "Bregman iterative algorithms for compressed sensing and related problems," SIAM Imag. Sci., vol.1, no.1, pp. 143-168, 2008.