Practical compressive sensing with toeplitz and circulant matrices

Proceedings of SPIE - The International Society for Optical Engineering

Volumn 7744, Issue , 2010, Pages

  Yin, Wotao ^a   Morgan, Simon ^b   Yang, Junfeng ^c   Zhang, Yin ^a  

^a Rice University   (United States)

^b NEW MEXICO CONSORTIUM   (United States)

^c NANJING UNIVERSITY   (China)

Author keywords

Circulant; Compressive sensing; Random matrix; Signal reconstruction; Toeplitz

Indexed keywords

CIRCULANT MATRIX; CIRCULANTS; COMPRESSIVE SENSING; COMPUTATIONAL RESULTS; FAST ALGORITHMS; HARDWARE REALIZATION; LINEAR MEASUREMENTS; RANDOM MATRICES; RANDOM MATRIX; RANDOM MEASUREMENT; TOEPLITZ;

COMMUNICATION; ENCODING (SYMBOLS); IMAGE COMMUNICATION SYSTEMS; IMAGING SYSTEMS; MOTION COMPENSATION; SIGNAL ANALYSIS; SIGNAL ENCODING; SIGNAL RECONSTRUCTION; VISUAL COMMUNICATION;

MATRIX ALGEBRA;

EID: 78649783376     PISSN: 0277786X     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1117/12.863527     Document Type: Conference Paper

References (29)

1. Donoho, D. L., "Compressed sensing," Information Theory, IEEE Transactions on 52(4), 1289-1306 (2006).
2. Candes, E. J., Romberg, J. K., and Tao, T., "Stable signal recovery from incomplete and inaccurate measurements," Communications on Pure and Applied Mathematics 59(8), 1207-1223 (2006).
3. Candès, E. and Tao, T., "Near optimal signal recovery from random projections: universal encoding strategies," IEEE Transactions on Information Theory 52(1), 5406-5425 (2006).
4. Rudelson, M. and Vershynin, R., "Geometric approach to error correcting codes and reconstruction of signals," International Mathematical Research Notices 64, 4019-4041 (2005).
5. Tropp, J., Wakin, M., Duarte, M., Baron, D., and Baraniuk, R., "Random filters for compressive sampling and reconstruction," in [Proceedings of IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP)], (2006).
6. Haupt, J., Bajwa, W. U., Raz, G., and Nowak, R. D., "Toeplitz compressed sensing matrices with applications to sparse channel estimation," Submitted to IEEE Transactions on Information Theory (2008).
7. Baraniuk, R. and Steeghs, P., "Compressive radar imaging," IEEE Radar Conference, Waltham, Massachusetts, 128-133 (2007).
8. Herman, M. A. and Strohmer, T., "High-resolution radar via compressed sensing," IEEE transactions on signal processing 57, 2275-2284 (2009).
9. Marcia, R. and Willett, R., "Compressive coded aperture superresolution image reconstruction," ICASSP'08, 833-836 (2008).
10. Marcia, R., Harmany, Z., and Willett, R., "Compressive coded aperture imaging," SPIE Electronic Imaging'09 (2009).
11. Romberg, J., "Compressive sensing by random convolution," Submitted to SIAM Journal on Imaging Sciences (2009).
12. Liang, D., Xu, G., Wang, H., King, K. F., and Ying, L., "Toeplitz random encoding mr imaging using compressed sensing," IEEE ISBI 2009 (2009).
13. Bajwa, W. U., Haupt, J. D., Raz, G. M., Wright, S. J., and Nowak, R. D., "Toeplitz-structured compressed sensing matrices," SSP'07 (2007).
14. Rauhut, H., "Circulant and toeplitz matrices in compressed sensing," In Proc. SPARS'09, Saint Malo, 2009 (2009).
15. Wang, Y., Yang, J., Yin, W., and Zhang, Y., "A new alternating minimization algorithm for total variation image reconstruction," SIAM Journal on Imaging Sciences 1(3), 248-272 (2008).
16. Hestenes, M. R., "Multiplier and gradient methods," Journal of Optimization Theory and Applications 4, 303-320 (1969).
17. Powell, M. J. D., "A method for nonlinear constraints in minimization problems," in [Optimization], Fletcher, R., ed., 283-298, Academic Press, New York (1972).
18. Glowinski, R. and Marrocco, A., "Sur lapproximation par elements finis dordre un, et la resolution par penalisation-dualite dune classe de problemes de Dirichlet nonlineaires," Rev. Francaise dAut. Inf. Rech. Oper. 2, 41-76 (1975).
19. Gabay, D. and Mercier, B., "A dual algorithm for the solution of nonlinear variational problems via finite-element approximations," Computers and Mathematics with Applications 2, 17-40 (1976).
20. 1-problems in compressive sensing," Rice University CAAM Technical Report TR09-37 (2009).
21. Fortin, M. and Glowinski, R., [Augmented Lagrangian Methods], North-Holland, Ambsterdam, New York (1983).
22. Yang, J., Yin, W., Zhang, Y., and Wang, Y., "A fast algorithm for edge-preserving variational multichannel image restoration," SIAM Journal on Imaging Sciences 2(2), 569-592 (2008).
23. Yang, J., Zhang, Y., and Yin, W., "An efficient TVL1 algorithm for deblurring multichannel images corrupted by impulsive noise," SIAM Journal on Scientific Computing 31(4), 2842-2865 (2009).
24. Osher, S., Burger, M., Goldfarb, D., Xu, J., and Yin, W., "An iterative regularization method for total variation-based image restoration," SIAM Journal on Multiscale Modeling and Simulation 4(2), 460-489 (2005).
25. 1-minimization with applications to compressed sensing," SIAM Journal on Imaging Sciences 1(1), 143-168 (2008).
26. Chartrand, R. and Yin, W., "Iteratively reweighted algorithms for compressive sensing," International Conference on Acoustics, Speech, and Signal Processing (ICASSP), 3869-2872 (2008).
27. Chartrand, R., "Fast algorithms for nonconvex compressive sensing: MRI reconstruction from very few data," IEEE International Symposium on Biomedical Imaging (ISBI) (2009).
28. Wang, Y. and Yin, W., "Compressed sensing via iterative support detection," Rice University CAAM Technical Report TR09-30. Submitted SIAM Journal on Imaging Sciences. (2009).
29. Yang, J., Zhang, Y., and Yin, W., "A fast alternating direction method for TVL1-L2 signal reconstruction from partial fourier data," To appear in IEEE Journal of Selected Topics in Signal Processing Special Issue on Compressed Sensing. (2008).