On projection matrix optimization for compressive sensing systems

IEEE Transactions on Signal Processing

Volumn 61, Issue 11, 2013, Pages 2887-2898

  Li, Gang ^a   Zhu, Zhihui ^a   Yang, Dehui ^b   Chang, Liping ^a   Bai, Huang ^a  

^a ZHEJIANG UNIVERSITY OF TECHNOLOGY   (China)

^b Department of Geology and Geological Engineering   (United States)

Author keywords

Averaged mutual coherence; compressed sensing; optimization techniques; sparse representation

Indexed keywords

COMPRESSIVE SENSING; IDENTITY MATRICES; MINIMIZATION PROBLEMS; MUTUAL COHERENCE; OPTIMIZATION TECHNIQUES; PROJECTION MATRIX; SIGNAL RECOVERY; SPARSE REPRESENTATION;

ALGORITHMS; COMPRESSED SENSING; OPTIMIZATION; SENSORS;

SIGNAL RECONSTRUCTION;

EID: 84877903708     PISSN: 1053587X     EISSN: None     Source Type: Journal    
DOI: 10.1109/TSP.2013.2253776     Document Type: Article

References (23)

1. E. J. Candès, 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, pp. 489-509, Feb. 2006. (Pubitemid 43174093)
2. D. L. Donoho, "Compressed sensing," IEEE Trans. Inf. Theory, vol. 52, no. 4, pp. 1289-1306, Sep. 2006.
3. E. J. Candès and T. Tao, "Near optimal signal recovery from random projection: Universal encoding strategies?," IEEE Trans. Inf. Theory, vol. 52, no. 12, pp. 5406-5425, Dec. 2006. (Pubitemid 46445381)
4. E. J. Candès and M. B. Wakin, "An intoduction to compressive sampling," IEEE Signal Process. Mag., vol. 25, no. 2, pp. 21-30, Mar. 2008.
5. M. F. Duarte and Y. C. Eldar, "Structured compressed sensing: from theory to applications," IEEE Trans. Signal Process., vol. 59, no. 9, pp. 4053-4085, Sep. 2011.
6. D. L. Donoho andM. Elad, "Optimally sparse representation in general (nonorthonormal) dictionaries via minimization," Proc. Nat. Acad. Sci., vol. 100, no. 5, pp. 2197-2202, Mar. 2003. (Pubitemid 36297476)
7. J. Tropp, "Greed is good: Algorithmic results for sparse approximation," IEEE Trans. Inf. Theory, vol. 50, no. 10, pp. 2231-2242, Oct. 2004.
8. M. Zibulevsky and M. Elad, " optimization in signal and image processing," IEEE Signal Process. Mag., pp. 76-88, May 2010.
9. R. Gribonval and M. Nielsen, "Sparse representations in unions of bases," IEEE Trans. Inf. Theory, vol. 49, no. 12, pp. 3320-3325, 2003.
10. M. Elad, "Optimized projections for compressed sensing," IEEE Trans. Signal Process., vol. 55, no. 12, pp. 5695-5702, 2007. (Pubitemid 350201203)
11. J. M. Duarte-Carvajalino and G. Sapiro, "Learning to sense sparse signals: simultaneous sensing matrix and sparsifying dictionary optimization," IEEE Trans. Image Process., vol. 18, no. 7, pp. 1395-1408, 2009.
12. V. Abolghasemi, S. Ferdowsi, B. Makkiabadi, and S. Sanei, "On optimization of the measurement matrix for compressive sensing," in Proc. Eur. Signal Process. Conf., Aalborg, Denmark, Aug. 2010.
13. L. Zelnik-Manor, K. Rosenblum, and Y. C. Eldar, "Sensing matrix optimization for block-sparse decoding," IEEE Trans. Signal Process., vol. 59, no. 9, pp. 4300-4312, 2011.
14. W. Chen, M. R. D. Rodrigues, and I. J.Wassell, "On the use of unitnorm tight frames to improve the average MSE performance in compressive sensing applications," IEEE Signal Process. Lett., vol. 19, no. 1, pp. 8-11, Jan. 2012.
15. T. Strohmer and R.W. Heath, "Grassmannian frames with applications to coding and communication," Appl. Comp. Harmon. Anal., vol. 14, no. 3, pp. 257-275, May 2003.
16. O. Christensen, An Introduction to Frames and Riesz Bases. Boston, MA, USA: Birkhäuser, 2003.
17. J. Tropp, I. S. Dhillon, R. W. Heath, Jr., and T. Strohmer, "Designing structured tight frame via alternating projection," IEEE Trans. Inf. Theory, vol. 51, no. 1, pp. 188-209, 2005. (Pubitemid 40145995)
18. M. Yaghoobi, L. Daudet, and M. E. Davies, "Parametric dictionary design for sparse coding," IEEE Trans. Signal Process., vol. 57, no. 12, pp. 4800-4810, 2009.
19. V. Abolghasemi, S. Ferdowsi, and S. Sanei, "A gradient-based alternatingminimization approach for optimization of the measurementmatrix in compressive sensing," Signal Process., vol. 92, pp. 999-1009, 2012.
20. M. Gevers and G. Li, Parametrizations in Control, Estimation and Filtering Problems: Accuracy Aspects, Communication and Control Engineering Series. London, U.K.: Springer-Verlag, 1993.
21. R. A. Horn and C. R. Johnson, Matrix Analysis. Cambridge, U.K.: Cambridge Univ. Press, 1985.
22. W. Chen, M. R. D. Rodrigues, and I. J. Wassell, "On the design of optimized projections for sensing sparse signals in overcomplete dictionaries," in Proc. IEEE Int. Conf. Acoust., Speech Signal Process., Mar. 2012, pp. 3457-3460.
23. W. Chen,M. R. D. Rodrigues, and I. J. Wassell, "Projection design for statistical compressive sensing: A tight frame based approach," IEEE Trans. Signal Process., vol. 61, no. 8, pp. 2016-2029, Apr. 2013.