Browse > Article

Reweighted L1-Minimization via Support Detection  

Lee, Hyuk (School of Information and Communication, Korea University)
Kwon, Seok-Beop (School of Information and Communication, Korea University)
Shim, Byong-Hyo (School of Information and Communication, Korea University)
Publication Information
Journal of the Institute of Electronics Engineers of Korea SP / v.48, no.2, 2011 , pp. 134-140 More about this Journal
Abstract
Recent work in compressed sensing theory shows that $M{\times}N$ independent and identically distributed sensing matrix whose entries are drawn independently from certain probability distributions guarantee exact recovery of a sparse signal with high probability even if $M{\ll}N$. In particular, it is well understood that the $L_1$-minimization algorithm is able to recover sparse signals from incomplete measurements. In this paper, we propose a novel sparse signal reconstruction method that is based on the reweighted $L_1$-minimization via support detection.
Keywords
compressed sensing (CS); L1-minimization; orthogonal matching pursuit (OMP);
Citations & Related Records
연도 인용수 순위
  • Reference
1 E. Candes and T. Tao, "Near optimal signal recovery from random projections: Universal encoding strategies," IEEE Trans. on Information Theory, 52(12), pp. 5406-5425, Dec. 2006.   DOI
2 K. Lange, "Optimization," Springer Texts in Statistics. Springer-Verlag, New York, 2004.
3 E. Candes and J. Romberg, "Sparsity and incoherence in compressive sampling," Inverse Problems, 23(3), pp. 969-985, 2007.   DOI   ScienceOn
4 D. L. Donoho and P. B. Stark, "Uncertainty prindiples and signal recovery," SIAM J. Appl. Math. 49, no. 3, pp. 906-931, 1989.   DOI   ScienceOn
5 D. L. Donoho and B. F. Logan, "Signal recovery and the large sieve," SIAM J. Appl. Math. 52, no. 2, pp. 557-591, 1992.
6 R. Tibshirani, "Regression shrinkage and selection via the lasso," J. Roy. Statist. Soc. Ser. B 58, no. 1, pp. 267-288, 1996.
7 S. S. Chen, D. L. Donoho, and M. A. Saunders, "Atomic decomposition by basis pursuit," SIAM J. Sci. Comput. 1, pp. 33-61, 1998.
8 M. S. O''Brien, A. N. Sinclair, and S. M. Kramer, "Recovery of sparse spike time series by 1 norm deconvolution," IEEE Trans. Signal Processing, vol. 42, pp. 3353-3365, 1994.   DOI   ScienceOn
9 E. J. Candes, M. B. Wakin, and S. Boyd, "Enhancing Sparsity by Reweighted L1-minimization," Journal of Fourier Analysis and Applications., 14(5), pp. 877-905, Dec. 2008.   DOI
10 R. Baraniuk, M. Davenport, R. DeVore, and M. Wakin, "A Simple Proof of the Restricted Isometry Property for Random Matrices," 2008.
11 J. A. Tropp and A. C. Gilbery, "Signal recovery from random measurements via orthogonal matching pursuit," 2006.
12 D. Needell and R. Vershynin, "Signal recovery from incomplete and inaccurate measurements via regularized orthogonal matching pursuit," 2007.
13 A. K. Fletcher, S. Rangan, and V. K. Goyal, "Necessary and Sufficient conditions on Sarsity Pattern recovery," arXiv:0804.1839v1[cs.IT]., Jan. 2009.   DOI
14 D. L. Donoho, Y. Tsaig, and Jean-Luc Starck, "Sparse solution of underdetermined linear equations by stagewise orthogonal matching pursuit," 2006.
15 W. Dai and O. Milenkovic, "Subspace Pusuit for Compressive Sensing: Closing the Gap Between Performance and Complexity," 2008.
16 W. Xu, M. A. Khajehnejad, A. S. Avestimehr, and B. Hassibi, "Breaking through the Thresholds: an Analysis for Iterative Reweighted 1-minimization via the Grassmann Angle Framework,"ICASSP 2010.
17 E. Candes, M. Rudelson, and T. Tao, "Error correction via linear programming," IEEE Computer Society, 2005.
18 D. Malioutov, M. Cetin, and A. Willsky, "A sparse signal reconstruction perspective for source localization with sensor arrays," IEEE Trans. Signal Process., 53(8), pp. 3010-3022, Aug.2005.   DOI
19 D. Model and M. Zibulevsky, "Signal reconstruction in sensor arrays using sparse representations," IEEE Trans. Signal Process., 86(3), pp. 624-638, Mar. 2006.   DOI   ScienceOn
20 D. Baron, M. B. Wakin, M. F. Duarte, S. Sarvotham, and R. G. Baraniuk, "Distributed compressed sensing," 2005.
21 E. Candes, J. Romberg, and T. Tao, "Robust uncertainty principles: Exact signal reconstruction from highly incomplete frequency information," IEEE Trans. on Information Theory, 52(2), pp. 489-509, Feb. 2006.   DOI
22 B. K. Natarajan, "Sparse approximate solutions to linear systems," SIAM J. Comput, 24(2), pp. 227-234, 1995.   DOI   ScienceOn
23 E. Candes and T. Tao, "Decoding by linear programming," IEEE Trans. on Information Theory, 51(12), pp. 4203-4215, Dec. 2005.   DOI   ScienceOn