Sensing matrix optimization for block-sparse decoding

IEEE Transactions on Signal Processing

Volumn 59, Issue 9, 2011, Pages 4300-4312

  Zelnik Manor, Lihi ^a   Rosenblum, Kevin ^a   Eldar, Yonina C ^a  

^a TECHNION ISRAEL INSTITUTE OF TECHNOLOGY   (Israel)

Author keywords

Block sparsity; compressed sensing; sensing matrix design

Indexed keywords

APPROXIMATION TECHNIQUES; BLOCK STRUCTURES; BLOCK-SPARSITY; CLASSIFICATION ABILITY; COMPRESSED SENSING; MATRIX; MATRIX DESIGN; MATRIX OPTIMIZATION; MOTION SEGMENTATION; RECONSTRUCTION ERROR; SENSING MATRIX DESIGN; SIGNAL RECOVERY; SIGNALS OF INTERESTS; SUB-BLOCKS; WEIGHTED SUM;

ALGORITHMS; OPTIMIZATION; SIGNAL RECONSTRUCTION;

FACE RECOGNITION;

EID: 80051751662     PISSN: 1053587X     EISSN: None     Source Type: Journal    
DOI: 10.1109/TSP.2011.2159211     Document Type: Article

References (27)

1. E. Candes, 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. (Pubitemid 43174093)
2. D. Donoho, "Compressed sensing," IEEE Trans. Inf. Theory, vol. 52, no. 4, pp. 1289-1306, Apr. 2006.
3. 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. (Pubitemid 128689501)
4. J. Tropp, "Greed is good: Algorithmic results for sparse approximation," IEEE Trans. Inf. Theory, vol. 50, no. 10, pp. 2231-2242, Oct. 2004.
5. S. G. Mallat and Z. Zhang, "Matching pursuits and time-frequency dictionaries," IEEE Trans. Signal Process., vol. 41, no. 12, pp. 3397-3415, Dec. 1993.
6. Y. Weiss, H. S. Chang, and W. T. Freeman, "Learning compressed sensing," in Proc. Allerton Conf., Sep. 2007.
7. M. Elad, "Optimized projections for compressed sensing," IEEE Trans. Signal Process., vol. 55, no. 12, pp. 5695-5702, Dec. 2007. (Pubitemid 350201203)
8. J. M. Duarte-Carvajalino and G. Sapiro, "Learning to sense sparse signals: Simultaneous sensing matrix and sparsifying dictionary optimization," IMA Preprint Ser., no. 2211, May 2008.
9. Y. M. Lu and M. N. Do, "A theory for sampling signals from a union of subspaces," IEEE Trans. Signal Process., vol. 56, no. 6, pp. 2334-2345, Jun. 2008. (Pubitemid 351795887)
10. K. Gedalyahu and Y. C. Eldar, "Time delay estimation from low rate samples:Aunion of subspaces approach," IEEE Trans. Signal Process., vol. 58, no. 6, pp. 3017-3031, Jun. 2010.
11. Y. C. Eldar and M. Mishali, "Robust recovery of signals from a structured union of subspaces," IEEE Trans. Inf. Theory, vol. 55, no. 11, pp. 5302-5316, Nov. 2009.
12. R. Basri and D. Jacobs, "Lambertian refelectances and linear subspaces," IEEE Trans. Pattern Anal. Machine Intell., vol. 25, no. 2, pp. 383-390, Feb. 2003.
13. A. Y. Yang, J. Wright, Y. Ma, and S. Sastry, "Feature Selection in Face Recognition: A Sparse Representation Perspective," Univ. of California Berkeley, Berkeley, CA, Tech. Rep., 2007.
14. R. Vidal and Y. Ma, "A unified algebraic approach to 2-D and 3-D motion segmentation and estimation," J. Math. Imag. Vision, vol. 25, no. 3, pp. 403-421, Oct. 2006. (Pubitemid 44728465)
15. M. Mishali and Y. C. Eldar, "Blind multiband signal reconstruction: Compressed sensing for analog signals," IEEE Trans. Signal Process., vol. 57, no. 3, pp. 993-1009, Mar. 2009.
16. M. Mishali and Y. C. Eldar, "From theory to practice: Sub-Nyquist sampling of sparse wideband analog signals," IEEE J. Sel. Topics Signal Process., vol. 4, no. 2, pp. 375-391, Apr. 2010.
17. H. J. Landau, "Necessary density conditions for sampling and interpolation of certain entire functions," Acta Math., vol. 117, no. 1, pp. 37-52, 1967.
18. F. Parvaresh, H. Vikalo, S. Misra, and B. Hassibi, "Recovering sparse signals using sparse measurement matrices in compressed DNA microarrays," IEEE J. Sel. Topics Signal Process., vol. 2, no. 3, pp. 275-285, Jun. 2008.
19. M. Stojnic, F. Parvaresh, and B. Hassibi, "On the reconstruction of block-sparse signals with an optimal number of measurements," IEEE Trans. Signal Process., vol. 57, no. 8, pp. 3075-3085, Aug. 2009.
20. Y. Eldar and H. Rauhut, "Average case analysis of multichannel sparse recovery using convex relaxation," IEEE Trans. Inf. Theory, vol. 56, no. 1, pp. 505-519, Jan. 2010.
21. F. Bach, "Consistency of the group lasso and multiple kernel learning," J. Mach. Learn. Res., vol. 9, pp. 1179-1225, 2008.
22. M.Yuan and Y. Lin, "Model selection and estimation in regression with grouped variables," J. Royal Statist. Soc.: Ser. B (Statist. Methodol.), vol. 68, no. 1, pp. 49-67, 2006. (Pubitemid 43415335)
23. J. Huang and T. Zhang, "The benefit of group sparsity," Ann. Statist., vol. 38, no. 4, pp. 1978-2004, 2010.
24. Y. C. Eldar, P. Kuppinger, and H. Bölcskei, "Block-sparse signals: Uncertainty relations and efficient recovery," IEEE Trans. Signal Process., vol. 58, no. 6, pp. 3042-3054, Apr. 2010.
25. Y. C. Eldar and H. Bölcskei, "Block-sparsity: Coherence and efficient recovery," in Proc. IEEE Int. Conf. Acoust., Speech, Signal Process., 2009, pp. 2885-2888.
26. M. Figueiredo, J. Bioucas-Dias, and R. Nowak, "Majorization- minimization algorithms for wavelet-based image restoration," IEEE Trans. Image Process., vol. 16, no. 12, pp. 2980-2991, Dec. 2007. (Pubitemid 350201231)
27. K. Rosenblum, L. Zelnik-Manor, and Y. C. Eldar, "Dictionary optimization for block-sparse representations," IEEE Trans. Signal Process., 2010, submitted for publication.