Orthonormal expansion ℓ1-minimization algorithms for compressed sensing

IEEE Transactions on Signal Processing

Volumn 59, Issue 12, 2011, Pages 6285-6290

  Yang, Zai ^a   Zhang, Cishen ^b   Deng, Jun ^a   Lu, Wenmiao ^a  

^a NANYANG TECHNOLOGICAL UNIVERSITY   (Singapore)

^b SWINBURNE UNIVERSITY OF TECHNOLOGY   (Australia)

Author keywords

[No Author keywords available]

Indexed keywords

BASIS PURSUITS; COMPRESSED SENSING; MINIMIZATION ALGORITHMS; NUMBER OF SAMPLES; ORTHONORMAL; SIGNALS OF INTERESTS; SOFT-THRESHOLDING ALGORITHM; SPARSE SIGNALS; STATE-OF-THE-ART ALGORITHMS;

CONVEX OPTIMIZATION; SIGNAL RECONSTRUCTION;

ALGORITHMS;

EID: 81455136619     PISSN: 1053587X     EISSN: None     Source Type: Journal    
DOI: 10.1109/TSP.2011.2168216     Document Type: Article

References (23)

1. E. Candès, J. Romberg, and T. Tao, "Robust uncertainty principles: Exact signal reconstruction from highly incomplete frequency information," IEEE Trans. Inf. Theory, vol. 52, no. 2, pp. 489-509, 2006. (Pubitemid 43174093)
2. E. Candès and J. Romberg, "Sparsity and incoherence in compressive sampling," Inverse Problems, vol. 23, pp. 969-985, 2007. (Pubitemid 46838836)
3. D. Donoho, "Compressed sensing," IEEE Trans. Inf. Theory, vol. 52, no. 4, pp. 1289-1306, 2006.
4. I. Daubechies, M. Defrise, and C. De Mol, "An iterative thresholding algorithm for linear inverse problems with a sparsity constraint," Commun. Pure Appl. Math., vol. 57, no. 11, pp. 1413-1457, 2004. (Pubitemid 39427442)
5. K. Bredies and D. Lorenz, "Linear convergence of iterative soft-thresholding," J. Fourier Anal. Appl., vol. 14, no. 5, pp. 813-837, 2008.
6. S. Kim, K. Koh, M. Lustig, S. Boyd, and D. Gorinevsky, "An interiorpoint method for large-scale -regularized least squares," IEEE J. Sel. Topics Signal Process., vol. 1, no. 4, pp. 606-617, 2008.
7. M. Lustig, D. Donoho, and J. Pauly, "Sparse MRI: The application of compressed sensing for rapid MR imaging," Magn. Resonance Med., vol. 58, no. 6, pp. 1182-1195, 2007. (Pubitemid 350234205)
8. E. Hale, W. Yin, and Y. Zhang, "A fixed-point continuation method for l1-regularized minimization with applications to compressed sensing," Comput. Appl. Math. Dept., Rice Univ., Houston, TX, Tech. Rep. TR07-07, 2007 [Online]. Available: http://www.caam.rice.edu/~zhang/reports/tr0707.pdf
9. E. Candès and J. Romberg, "-magic: Recovery of sparse signals via convex programming," [Online]. Available: http://users.ece.gatech. edu/~justin/l1magic/downloads/l1magic.pdf, 2005
10. S. Becker, J. Bobin, and E. Candes, "NESTA: A fast and accurate firstorder method for sparse recovery," SIAM J. Imag. Sci., vol. 4, no. 1, pp. 1-39, 2011.
11. Y. Nesterov, "Smooth minimization of non-smooth functions," Math. Programm., vol. 103, no. 1, pp. 127-152, 2005. (Pubitemid 40537674)
12. J. Tropp and A. Gilbert, "Signal recovery from random measurements via orthogonal matching pursuit," IEEE Trans. Inf. Theory, vol. 53, no. 12, pp. 4655-4666, 2007.
13. D. Donoho, Y. Tsaig, I. Drori, and J. Starck, "Sparse solution of underdetermined linear equations by stagewise orthogonal matching pursuit," IEEE Trans. Signal Process, 2006, submitted for publication.
14. D. Needell and J. Tropp, "CoSaMP: Iterative signal recovery from incomplete and inaccurate samples," Appl. Comput. Harmon. Anal., vol. 26, no. 3, pp. 301-321, 2009.
15. Z. Wen, W. Yin, D. Goldfarb, and Y. Zhang, "A fast algorithm for sparse reconstruction based on shrinkage, subspace optimization and continuation," SIAM J. Sci. Comput., vol. 32, no. 4, pp. 1832-1857, 2010.
16. A. Maleki and D. Donoho, "Optimally tuned iterative thresholding algorithms for compressed sensing," IEEE J. Sel. Areas Signal Process., vol. 4, pp. 330-341, 2010.
17. D. Donoho, A. Maleki, and A. Montanari, "Message-passing algorithms for compressed sensing," Proc. Nat. Acad. Sci., vol. 106, no. 45, pp. 18 914-18 919, 2009.
18. J. Nocedal and S. Wright, Numerical Optimization. New York: Springer-Verlag, 2006.
19. D. Bertsekas, Constrained Optimization and Lagrange Multiplier Methods. Boston, MA: Academic, 1982.
20. D. Donoho and J. Tanner, "Counting the faces of randomly-projected hypercubes and orthants, with applications," Discrete Comput. Geometry, vol. 43, no. 3, pp. 522-541, 2010.
21. M. Stojnic, "Various thresholds for l1-optimization in compressed sensing," 2009, http://arxiv.org/abs/0907.3666.
22. D. Donoho and J. Tanner, "Observed universality of phase transitions in high-dimensional geometry, with implications for modern data analysis and signal processing," Philos. Trans. Roy. Soc. A, vol. 367, no. 1906, pp. 4273-4293, 2009.
23. Z. Yang and C. Zhang, "Sparsity-undersampling tradeoff of compressed sensing in the complex domain," in Proc. Int. Conf. Acoust., Speech, Signal Process. (ICASSP), 2011.