Compressed sensing with partial support information: Coherence-based performance guarantees and alternative direction method of multiplier reconstruction algorithm

IET Signal Processing

Volumn 8, Issue 7, 2014, Pages 749-758

  Liu, Haixiao ^a   Song, Bin ^a   Tian, Fang ^a   Qin, Hao ^a  

^a XIDIAN UNIVERSITY   (China)

Author keywords

[No Author keywords available]

Indexed keywords

COMPRESSED SENSING;

ADAPTIVE MEASUREMENTS; ALTERNATING DIRECTION METHOD OF MULTIPLIERS; COMPRESSIVE SENSING; CONVENTIONAL METHODS; METHOD OF MULTIPLIERS; PERFORMANCE GUARANTEES; RECONSTRUCTION ALGORITHMS; RECONSTRUCTION ERROR;

ITERATIVE METHODS;

EID: 84907159747     PISSN: 17519675     EISSN: 17519683     Source Type: Journal    
DOI: 10.1049/iet-spr.2013.0394     Document Type: Article

References (24)

1. Donoho, D.L.: 'Compressed sensing', IEEE Trans. Inf. Theory, 2006, 52, (4), pp. 1289-1306
2. Cande`s, E., Romberg, J., Tao, T.: 'Stable signal recovery from incomplete and inaccurate measurements', Commun. Pure Appl. Math., 2006, 59, pp. 1207-1223
3. Cande`s, E., Romberg, J., Tao, T.: ' Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information', IEEE Trans. Inf. Theory, 2006, 52, (2), pp. 489-509
4. Vaswani, N., Lu,W.: 'Modified-CS: modifying compressive sensing for problems with partially known support', IEEE Trans. Signal Process., 2010, 58, (9), pp. 4595-4607
5. Vaswani, N., Lu,W.: 'Modified-CS: modifying compressive sensing for problems with partially known support'. Proc. IEEE Int. Symp. Information Theory (ISIT), 2009, pp. 488-492
6. Lu, W., Vaswani, N.: 'Modified BPDN for noisy compressive sensing with partially known support'. Proc. IEEE Int. Conf. Acoustics, Speech, Signal Processing (ICASSP), 2010, pp. 3926-3929
7. Lu, W., Vaswani, N.: 'Exact reconstruction conditions for regularized modified basis pursuit', IEEE Trans. Signal Process., 2012, 60, (5), pp. 2634-2640
8. Jacques, L.: 'A short note on compressed sensing with partially known signal support', Signal Process., 2010, 90, pp. 3308-3312
9. Wang, Y., Yin, W.: 'Sparse signal reconstruction via iterative support detection', SIAM J. Imaging Sci., 3, (3), pp. 462-491
10. Friedlander, M.P., Mansour, H., Saab, R., Yilmaz, O.: 'Recovering compressively sampled signals using partial support information', IEEE Trans. Inf. Theory, 2012, 58, (2), pp. 1122-1134
11. Ben-Haim, Z., Eldar, Y.C., Elad, M.: 'Coherence-based performance guarantees for estimating a sparse vector under random noise', IEEE Trans. Signal Process., 2010, 58, (10), pp. 5030-5043
12. Donoho, D., Huo, X.: 'Uncertainty principles and ideal atomic decomposition', IEEE Trans. Inf. Theory, 2001, 47, (7), pp. 2845-2862
13. Glowinski, R., Marrocco, A.: 'Sur l'approximation, par elements finisd'ordre un, et la resolution, par penalisation-dualite´ d'une classe de problems de dirichlet non lineares', Rev. Fr. Autom. Inform. Rech. Ope´r., 1975, 9, pp. 41-76
14. Gabay, D., Mercier, B.: 'A dual algorithm for the solution of nonlinear variational problems via finite element approximations', Comput. Math. Appl., 1976, 2, pp. 17-40
15. Afonso, M., Bioucas-Dias, J., Figueiredo, M.: 'Fast image recovery using variable splitting and constrained optimization', IEEE Trans. Image Process., 2010, 19, (9), pp. 2345-2356
16. Wang, Y., Yang, J., Yin, W., Zhang, Y.: 'A new alternating minimization algorithm for total variation image reconstruction', SIAM J. Imaging Sci., 2008, 1, (3), pp. 248-272
17. Liu, H., Song, B., Qin, H., Qiu, Z.: 'An adaptive-ADMMalgorithm with support and signal value detection for compressed sensing', IEEE Signal Process. Lett., 2013, 20, (4), pp. 315-318
18. Cai, T.T., Wang, L., Xu, G.: 'Stable recovery of sparse signals and an oracle inequality', IEEE Trans. Inf. Theory, 56, (7), pp. 3516-3522
19. Cai, T.T., Xu, G., Zhang, J.: 'On recovery of sparse signals via l1 minimization', IEEE Trans. Inf. Theory, 2009, 55, (7), pp. 3388-3397
20. Tseng, P.: 'Further results on a stable recovery of sparse overcomplete representations in the presence of noise', IEEE Trans. Inf. Theory, 2009, 55, (2), pp. 888-899
21. Elad, M.: 'Sparse and redundant representation: from theory to applications in signal and image processing' (Springer Press, 2010), pp. 79-109
22. Boyd, S., Parikh, N., Chu, E., Peleato, B., Eckstein, J.: 'Distributed optimization and statistical learning via the alternating direction method of multipliers', Found. Trends Mach. Learn., 2011, 3, (1), pp. 1-122
23. YUV video sequences. Available at http://trace.eas.asu.edu/yuv/
24. Strohmer, T., Heath, R.W.Jr: 'Grassmannian frames with applications to coding and communication', Appl. Comput. Harmon. Anal., 2003, 14, (3), pp. 257-275