An improved smoothed ℓo approximation algorithm for sparse representation

IEEE Transactions on Signal Processing

Volumn 58, Issue 4, 2010, Pages 2194-2205

  Hyder, Md Mashud ^a   Mahata, Kaushik ^a  

^a UNIVERSITY OF NEWCASTLE   (Australia)

Author keywords

o norm minimization; Basis pursuit; Compressive sampling; Linear programming; Nonconvex optimization; Overcomplete representation; Sparse representation

Indexed keywords

BASIS PURSUIT; BASIS PURSUITS; COMPRESSIVE SAMPLING; NONCONVEX OPTIMIZATION; OVERCOMPLETE REPRESENTATIONS; SPARSE REPRESENTATION;

COMPUTATIONAL COMPLEXITY; DYNAMIC PROGRAMMING; LINEAR PROGRAMMING; LINEARIZATION; OPTIMIZATION;

APPROXIMATION ALGORITHMS;

EID: 77949415337     PISSN: 1053587X     EISSN: None     Source Type: Journal    
DOI: 10.1109/TSP.2009.2040018     Document Type: Article

References (30)

1. R. A. DeVore, B. Jawerth, and B. J. Lucier, "Image compression through wavelet transform coding," IEEE Trans. Inf. Theory, vol.38, pp. 719-746, Mar. 1992.
2. J. Shapiro, "Embedded image coding using zerotrees of wavelet coefficients," IEEE Trans. Signal Process., vol.41, no.12, pp. 3445-3462, Dec. 1993.
3. S. S. Chen, D. L. Donoho, and M. A. Saunders, "Atomic decomposition by basis pursuit," SIAM J. Sci. Comput., vol.20, pp. 33-61, 1999.
4. E. J. Candés, J. Romberg, and T. Tao, "Robust uncertainty principles: Exact signal reconstruction from highly incomplete frequency information," IEEE Trans. Inf. Theory, vol.52, pp. 489-509, Feb. 2006.
5. 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.
6. D. L. Donoho, M. Elad, and V. Temlyakvo, "Stable recovery of sparse overcomplete representations in the presence of noise," IEEE Trans. Inf. Theory, vol.52, pp. 6-18, Jan. 2006.
7. E. J. Candès and T. Tao, "Decoding by linear programming," IEEE Trans. Inf. Theory, vol.51, pp. 4203-4215, Dec. 2005.
8. E. J. Candés and J. Romberg, "-Magic: Recovery of Sparse Signals Via Convex Programming," [Online]. Available: http://www.acm. caltech.edu/l1magic/downloads/l1magic.pdf, 2005
9. S. Boyd and L. Vandenberghe, Convex Optimization. Cambridge, U.K.: Cambridge Univ. Press, 2004.
10. I. Daubechies, M. Defrise, and C. DeMol, "An iterative thresholding algorithm for linear inverse problems with a sparsity constraint," Commun. Pure Appl. Math., vol.57, no.11, pp. 1413-1457, 2004.
11. E. J. Candès and T. Tao, "The dantzig selector: Statistical estimation when p is much larger than n," Ann. Stat., vol.35, pp. 2313-2351, 2007.
12. E. J. Candés, J. Romberg, and T. Tao, "Stable signal recovery from incomplete and inaccurate measurements," Commun. Pure Appl. Math., vol.59, pp. 1207-1223, Mar. 2006.
13. M. Figueiredo, R. Nowak, and S. 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. 586-597, Dec. 2007.
14. S. Wright, R. Nowak, and M. Figueiredo, "Sparse reconstruction by separable approximation," IEEE Trans. Signal Process., vol.57, no.7, pp. 2479-2493, Jul. 2009.
15. S.-J. Kim, K. Koh, M. Lustig, S. Boyd, and D. Gorinevsky, "An interior- point method for large-scale l1-regularized least squares," IEEE J. Sel. Topics Signal Process., vol.1, no.4, pp. 606-617, Dec. 2007.
16. D. L. Donoho, "Compressed sensing," IEEE Trans. Inf. Theory, vol.52, pp. 1289-1306, Apr. 2006.
17. I. Gorodnitsky and B. Rao, "Sparse signal reconstruction from limited data using FOCUSS: A re-weighted minimum norm algorithm," IEEE Trans. Signal Process., vol.45, no.3, pp. 600-616, Mar. 1997.
18. R. Chartrand and W. Yin, "Iteratively reweighted algorithms for compressive sensing," in Proc. IEEE Int. Conf. Acoustics, Speech, Signal Processing (ICASSP), Mar. 2008, pp. 3869-3872.
19. L. Mancera and J. Portilla, "L0-norm-based sparse representation through alternate projections," in Proc. IEEE Int. Conf. Image Processing (ICIP), Oct. 2006, pp. 2089-2092.
20. C. R. Berger, J. Areta, K. Pattipati, and P. Willett, "Compressed sensing-A look beyond linear programming," in Proc. IEEE Int. Conf. Acoustics, Speech, Signal Processing (ICASSP), Mar. 2008, pp. 3857-3860.
21. G. H. Mohimani, M. Babaie-Zadeh, and C. Jutten, "Fast sparse representation based on smoothed l0 norm," in Proc. 7th Int. Conf. Independent Component Analysis Signal Separation (ICA), London, U.K., Sep. 2007, pp. 389-396.
22. H. Mohimani, M. Babaie-Zadeh, and C. Jutten, "A fast approach for overcomplete sparse decomposition based on smoothed norm," IEEE Trans. Signal Process., vol.57, no.1, pp. 289-301, Jan. 2009.
23. 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.
24. R. Baraniuk, "Compressive sensing [lecture notes]," IEEE Signal Process. Mag., vol.24, no.4, pp. 118-121, Jul. 2007.
25. D. Donoho and X. Huo, "Uncertainty principles and ideal atomic decomposition," IEEE Trans. Inf. Theory, vol.47, no.7, pp. 2845-2862, Nov. 2001.
26. A. Papoulis, Probability, Random Variables, and Stochastic Processes. New York: McGraw-Hill, 1991.
27. J. C. Allwright, "Conjugate gradient versus steepest descent," J. Optim. Theory Appl., vol.20, no.1, pp. 129-134, Sep. 1976.
28. A. L. Yuille and A. Rangarajan, "The concave-convex procedure," Neural Comput., vol.15, no.4, pp. 915-936, 2003.
29. S. Boyd, Sequential convex programming," Stanford Univ., Stanford, CA, 2008, Lecture Notes.
30. D. Donoho, V. Stodden, and Y. Tsaig, Sparselab 2.1. 2007 [Online]. Available: http://sparselab.stanford.edu/