On the Stable Recovery of the Sparsest Overcomplete Representations in Presence of Noise

IEEE Transactions on Signal Processing

Volumn 58, Issue 10, 2010, Pages 5396-5400

  Babaie Zadeh, Massoud ^a   Jutten, Christian ^b  

^a SHARIF UNIVERSITY OF TECHNOLOGY   (Iran)

^b INSTITUT UNIVERSITAIRE DE FRANCE   (France)

Author keywords

Compressed sensing; overcomplete dictionaries; sparse component analysis (SCA); sparse recovery; sparse signal decomposition

Indexed keywords

EID: 79952669826     PISSN: 1053587X     EISSN: 19410476     Source Type: Journal    
DOI: 10.1109/TSP.2010.2052357     Document Type: Article

References (22)

1. D. L. Donoho, M. Elad, and V. 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.
2. E. J. Candes, 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, Feb. 2006.
3. D. L. Donoho, “Compressed sensing,” IEEE Trans. Inf. Theory, vol. 52, no. 4, pp. 1289–1306, Apr. 2006.
4. R. G. Baraniuk, “Compressive sensing,” IEEE Signal Process. Mag., vol. 24, no. 4, pp. 118–124, Jul. 2007.
5. R. Gribonval and S. Lesage, “A survey of sparse component analysis for blind source separation: Principles, perspectives, and new challenges,” in Proc. Eur. Symp. Artificial Neural Networks (ESANN), Bruges, Belgium, Apr. 26–28, 2006, pp. 323–330.
6. P. Bofill and M. Zibulevsky, “Underdetermined blind source separation using sparse representations,” Signal Process., vol. 81, no. 11, pp. 2353–2362, 2001.
7. P. G. Georgiev, F. J. Theis, and A. Cichocki, “Blind source separation and sparse component analysis for over-complete mixtures,” in Proc. Int. Conf. Acoustics, Speech and Signal Processing (ICASSP), Montreal, QC, Canada, May 17–21, 2004, pp. 493–496.
8. Y. Li, A. Cichocki, and S. Amari, “Sparse component analysis for blind source separation with less sensors than sources,” in Proc. 4th Int. Symp. Independent Component Analysis and Blind Signal Separation (ICA), Nara, Japan, Apr. 1–4, 2003, pp. 89–94, Most Important Comments section.
9. S. S. Chen, D. L. Donoho, and M. A. Saunders, “Atomic decomposition by basis pursuit,” SIAM J. Sci. Comput., vol. 20, no. 1, pp. 33–61, 1999.
10. E. J. Candes and T. Tao, “Decoding by linear programming,” IEEE Trans. Inf. Theory, vol. 15, no. 12, pp. 4203–4215, 2005.
11. M. A. T. Figueiredo and R. D. Nowak, “An EM algorithm for wavelet-based image restoration,” IEEE Trans. Image Process., vol. 12, no. 8, pp. 906–916, 2003.
12. M. A. T. Figueiredo and R. D. Nowak, “A bound optimization approach to wavelet-based image deconvolution,” in Proc. IEEE Int. Conf. Image Processing (ICIP), Genoa, Italy, Sep. 11–14, 2005, pp. II-782–II-785, Most Important Comments section.
13. M. Elad, “Why simple shrinkage is still relevant for redundant representations?,” IEEE Trans. Image Process., vol. 52, no. 12, pp. 5559–5569, 2006.
14. I. F. Gorodnitsky and B. D. 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.
15. S. Mallat and Z. Zhang, “Matching pursuits with time-frequency dictionaries,” IEEE Trans. Signal Process., vol. 41, no. 12, pp. 3397–3415, 1993.
16. R. Gribonval and M. Nielsen, “Sparse decompositions in unions of bases,” IEEE Trans. Inf. Theory, vol. 49, no. 12, pp. 3320–3325, Dec. 2003.
17. 1 minimization,” Proc. Nat. Acad. Sci., vol. 100, no. 5, pp. 2197–2202, Mar. 2003.
18. 0 norm,” IEEE Trans. Signal Process., vol. 57, no. 1, pp. 289–301, Jan. 2009.
19. B. Wohlberg, “Noise sensitivity of sparse signal representations: Reconstruction error bounds for the inverse problem,” IEEE Trans. Signal Process., vol. 51, no. 12, pp. 3053–3060, Dec. 2003.
20. A. Eftekhari, M. Babaie-Zadeh, Ch. Jutten, and H. Abrishami-Moghaddam, “Robust-SL0 for stable sparse representation in noisy settings,” in Proc. Int. Conf. Acoustics, Speech and Signal Processing (ICASSP), Taipei, Taiwan, Apr. 19–24, 2009, pp. 3433–3436.
21. R. A. Horn and C. R. Johnson, Matrix Analysis. Cambridge, U.K.: Cambridge Univ. Press, 1985.
22. M. Babaie-Zadeh, H. Mohimani, and Ch. Jutten, “An upper bound on the estimation error of the sparsest solution of underdetermined linear systems,” presented at the Workshop Signal Processing With Adaptive Sparse Structured Representations (SPARS), Saint-Malo, France, Apr. 6–9, 2009.