Thresholded basis pursuit: LP algorithm for order-wise optimal support recovery for sparse and approximately sparse signals from noisy random measurements

IEEE Transactions on Information Theory

Volumn 57, Issue 3, 2011, Pages 1567-1586

  Saligrama, Venkatesh ^a   Zhao, Manqi ^a  

^a Boston University   (United States)

Author keywords

Approximate sparsity; compressed sensing; LASSO; linear programming; sign pattern recovery

Indexed keywords

APPROXIMATE SPARSITY; BASIS PURSUITS; COMPRESSED SENSING; CORRELATION TECHNIQUES; INPUT NOISE; LASSO; LP ALGORITHMS; NOISE LEVELS; NOISE MODELS; PERFORMANCE BOUNDS; POSITIVE CONSTANT; PROGRAMMING SOLUTIONS; RANDOM MEASUREMENT; RANDOM PROJECTIONS; SIGN PATTERNS; SIGN-PATTERN RECOVERY; SIGNAL SET; SPARSE SIGNALS;

LINEAR PROGRAMMING; MAXIMUM LIKELIHOOD ESTIMATION; OPTIMIZATION; SIGNAL RECONSTRUCTION;

RECOVERY;

EID: 79951872878     PISSN: 00189448     EISSN: None     Source Type: Journal    
DOI: 10.1109/TIT.2011.2104512     Document Type: Article

References (27)

1. M. Duarte, M. Davenport, D. Takhar, J. Laska, T. Sun, K. Kelly, and R. Baraniuk, "Single-pixel imaging via compressive sampling," IEEE Signal Process. Mag., vol. 25, no. 2, pp. 83-91, Mar. 2008.
2. E. Candès, J. Romberg, and T. Tao, "Robust uncertainity principles: Exact signal reconstruction from highly incomplete frequency information," IEEE Trans. Inf. Theory, vol. 52, no. 2, pp. 489-509, Feb. 2006. (Pubitemid 43174093)
3. E. Candès, J. Romberg, and T. Tao, "Stable signal recovery from incomplete and inaccuarte measurements," Commun. Pure Appl. Math., vol. 59, no. 8, pp. 1207-1223, Aug. 2006. (Pubitemid 43988295)
4. D. Donoho and J. Tanner, "Counting faces of randomly-projected polytopes when the projection radically lowers dimension," J. Amer. Math. Soc., vol. 22, no. 1, pp. 1-53, Jan. 2009.
5. E. 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. (Pubitemid 46445381)
6. E. Candès, J. Romberg, and T. Tao, "Decoding by linear programming," IEEE Trans. Inf. Theory, vol. 51, no. 12, pp. 4203-4215, Dec. 2005. (Pubitemid 41800353)
7. D. Donoho, "Compressed sensing," IEEE Trans. Inf. Theory, vol. 52, no. 4, pp. 1289-1306, Apr. 2006.
8. 1 -norm solution is also the sparsest solution," Commun. Pure Appl. Math., vol. 59, no. 6, pp. 797-829, Jun. 2006. (Pubitemid 43667226)
9. 1 minimization," IEEE Trans. Inf. Theory, vol. 51, no. 4, pp. 1568-1570, Apr. 2005. (Pubitemid 40555897)
10. W. Xu and B. Hassibi, Compressed Sensing Over the Grassmann Manifold: A Unified Analytical Framework, Jul. 2008, Preprint.
11. 1 minimization," Ann. Statist., vol. 37, no. 5A, pp. 2145-2177, 2009.
12. 1 -constrained quadratic programing (Lasso)," IEEE Trans. Inf. Theory, vol. 55, no. 5, pp. 2183-2202, May 2009.
13. A. K. Fletcher, S. Rangan, and V. K. Goyal, "Necessary and sufficient conditions on sparsity pattern recovery," IEEE Trans. Inf. Theory, vol. 55, no. 12, pp. 5758-5772, Dec. 2009.
14. S. Aeron, M. Zhao, and V. Saligrama, "Information theoretic bounds for compressed sensing," IEEE Trans. Inf. Theory, vol. 56, no. 10, pp. 5111-5130, Oct. 2010.
15. M.Wainwright, "Information-theoretic bounds on sparsity recovery in the high-dimensional and noisy setting," presented at the Int. Symp. Information Theory, Nice, France, Jun. 2007.
16. A. K. Fletcher, S. Rangan, V. K. Goyal, and K. Ramchandran, "Denoising by sparse approximation: Error bounds based on rate-distortion theory," EURASIP J. Appl. Signal Process., pp. 1-19, 2006.
17. M. Zhao, S. Aeron, and V. Saligrama, "Sensing capacity and compressed sensing: Bounds and algorithms," presented at the 45th Annu. Allerton Conf. Communication, Control and Computing, Monticello, IL, Sep. 2007.
18. R. Baraniuk, M. Davenport, R. Devore, and M.Wakin, "A simple proof of the restricted isometry property for random matrices," Constructive Approx., vol. 28, pp. 253-263, 2007.
19. E. Candès, "The restricted isometry property and its implications for compressed sensing.," Compte Rendus de l'Academie des Sciences, Paris Serie I vol. 346, pp. 589-592.
20. D. Bertsimas and J. N. Tsitsiklis, Introduction to Linear Optimization. Nashua, NH: Athena Scientific, 1997.
21. M. J. Todd, "Probabilistic models for linear programming," Math. Oper. Res., vol. 16, no. 4, pp. 671-693, Nov. 1991.
22. M. Rudelson and R.Vershynin, "Non-asymptotic theory of random matrices: Extreme singular values," presented at the Int. Congr. Mathematicians, Hyderabad, India, 2010.
23. M. Rudelson, "Lower estimates for the singular values of random matrices," C. R. Math. Acad. Sci. Paris, vol. 342, pp. 247-252, 2006. (Pubitemid 43137181)
24. R. A. Horn and C. R. Johnson, Matrix Analysis. Cambridge, U.K.: Cambridge Univ. Press, 1985.
25. A. M. Tulino and S. Verdú, Random Matrix Theory and Wireless Communications. Boston, MA: Now, 2004.
26. J. A. Tropp, "Just relax: Convex programming methods for identifying sparse signals," IEEE Trans. Inf. Theory, vol. 51, no. 3, pp. 1030-1051, Mar. 2006. (Pubitemid 46444890)
27. D. Needell and J. A. Tropp, "CoSaMP: Iterative signal recovery from incomplete and inaccurate samples," Appl. Comput. Harmon. Anal., no. 26, pp. 301-321, May 2009.