Modified-CS: Modifying compressive sensing for problems with partially known support

IEEE Transactions on Signal Processing

Volumn 58, Issue 9, 2010, Pages 4595-4607

  Vaswani, Namrata ^a   Lu, Wei ^a  

^a Iowa State University of Science and Technology   (United States)

Author keywords

Compressive sensing; modified CS; partially known support; prior knowledge; sparse reconstruction

Indexed keywords

COMPRESSIVE SENSING; MODIFIED-CS; PARTIALLY KNOWN SUPPORT; PRIOR KNOWLEDGE; SPARSE RECONSTRUCTION;

ERRORS; RELAXATION PROCESSES; REPAIR;

SIGNAL RECONSTRUCTION;

EID: 77954588549     PISSN: 1053587X     EISSN: None     Source Type: Journal    
DOI: 10.1109/TSP.2010.2051150     Document Type: Article

References (32)

1. N. Vaswani and W. Lu, "Modified-CS: Modifying compressive sensing for problems with partially known support," in Proc. IEEE Int. Symp. Inf. Theory (ISIT), 2009, pp. 488-492.
2. W. Lu and N. Vaswani, "Modified compressive sensing for real-time dynamic MR imaging," in Proc. IEEE Int. Conf. Image Proc. (ICIP), 2009, pp. 3045-3048.
3. I. Carron, Nuit Blanche [Online]. Available: http://nuit-blanche. blogspot.com/
4. Rice Compressive Sensing Resources [Online]. Available: http://www. dsp.rice.edu/cs
5. S. Chen, D. Donoho, and M. Saunders, "Atomic decomposition by basis pursuit," SIAM J. Sci. Comput., vol.20, pp. 33-61, 1998.
6. D. Wipf and B. Rao, "Sparse Bayesian learning for basis selection," IEEE Trans. Signal Process., vol.52, pp. 2153-2164, Aug. 2004.
7. E. 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.
8. D. Donoho, "Compressed sensing," IEEE Trans. Inf. Theory, vol.52, no.4, pp. 1289-1306, Apr. 2006.
9. E. Candes and T. Tao, "Decoding by linear programming," IEEE Trans. Inf. Theory, vol.51, no.12, pp. 4203-4215, Dec. 2005.
10. J. A. Tropp, "Just relax: Convex programming methods for identifying sparse signals," IEEE Trans. Inf. Theory, pp. 1030-1051, Mar. 2006.
11. E. Candes and T. Tao, "The Dantzig selector: Statistical estimation when p is much larger than n," Ann. Stat., vol.35, no.6, pp. 2313-2351, 2006.
12. N. Vaswani, "Kalman filtered compressed sensing," in Proc. IEEE Int. Conf. Image (ICIP), 2008, pp. 893-896.
13. N. Vaswani, "LS-CS-residual (LS-Cs): compressive sensing on the least squares residual," IEEE Trans. Signal Process., vol.58, no.8, pp. 4108-4120, 2010.
14. A. Khajehnejad, W. Xu, A. Avestimehr, and B. Hassibi, "Weighted l1 minimization for sparse recovery with prior information," in Proc. IEEE Int. Symp. Inf. Theory (ISIT), 2009, pp. 483-487.
15. C. J. Miosso, R. von Borries, C. Potes, M. Argez, L. Valazquez, C. Quintero, and C. Potes, "Compressed sensing reconstruction with prior information by iteratively reweighted least-squares," IEEE Trans. Signal Process., vol.57, no.6, Jun. 2007.
16. D. Angelosante and G. Giannakis, "RLS-weighted lasso for adaptive estimation of sparse signals," in Proc. IEEE Int. Conf. Acoustics, Speech, Signal Process. (ICASSP), 2009, pp. 3245-3248.
17. M. Asif and J. Romberg, "Dynamic updating for sparse time varying signals," in Proc. CISS, 2009, pp. 3-8.
18. V. Cevher, A. Sankaranarayanan, M. Duarte, D. Reddy, R. Baraniuk, and R. Chellappa, "Compressive sensing for background subtraction," in Proc. Eur. Conf. Comput. Vis. (ECCV), 2008, pp. 155-168.
19. J. Park and M. Wakin, "A multiscale framework for compressive sensing of video," in Proc. Picture Coding Symp. (PCS), May 2009, pp. 287-298.
20. B. K. Natarajan, "Sparse approximate solutions to linear systems," SIAM J. Comput., vol.24, pp. 227-234, 1995.
21. S. Boyd and L. Vandenberghe, Convex Optimization. Cambridge, U.K.: Cambridge Univ. Press, 2004.
22. E. Candes, "The restricted isometry property and its implications for compressed sensing," Compte Rendus de l'Academie des Sciences, Paris, Serie I, pp. 589-592, 2008.
23. S. Foucart and M. J. Lai, "Sparsest solutions of underdetermined linear systems via ell-q-minimization for 0 < = q < = 1," Appl. Comput. Harmon. Anal., vol.26, pp. 395-407, 2009.
24. D. Needell and J. Tropp, "Cosamp: Iterative signal recovery from incomplete and inaccurate samples," Appl. Comput. Harmon. Anal., vol.26, pp. 301-321, 2008.
25. R. Baraniuk, M. Davenport, R. DeVore, and M.Wakin, "A simple proof of the restricted isometry property for random matrices," Construct. Approxim., vol.28, no.3, pp. 253-263, Dec. 2008.
26. C. Dossal, G. Peyre, and J. Fadili, "A numerical exploration of compressed sampling recovery," in Signal Processing with Adaptive Sparse Structured Representations (SPARS), Saint-Malo, France, Apr. 6-9, 2009.
27. C. Dossal, "A necessary and sufficient condition for exact recovery by l1 minimization," 2007, preprint HAL: hal-00164738.
28. W. Lu and N. Vaswani, "Modified BPDN for noisy compressive sensing with partially known support," in Proc. IEEE Int. Conf. Acoustics, Speech, Signal Process. (ICASSP), 2010, pp. 3926-3929.
29. L. Jacques, "A short note on compressed sensing with partially known signal support," ArXiv Preprint 0908.0660, 2009.
30. E. Candes and J. Romberg, L1 Magic Users Guide. Oct. 2005 [Online]. Available: http://www.acm.caltech.edu/l1magic/downloads/ l1magic.pdf
31. W. Lu and N. Vaswani, "Regularized modified BPDN for compressive sensing with partially known support," ArXiv Preprint 1002.0019, 2010.
32. N. Vaswani, "Stability (over time) of Modified-CS and LS-CS for recursive causal sparse reconstruction," ArXiv Preprint 1006.4818, 2010 [Online]. Available: http://arxiv.org/abs/1006.4818