Imaging via compressive sampling: Introduction to compressive sampling and recovery via convex programming

IEEE Signal Processing Magazine

Volumn 25, Issue 2, 2008, Pages 14-20

  Romberg, J ^a  

^a GEORGIA INSTITUTE OF TECHNOLOGY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

IMAGE CODING; IMAGE COMPRESSION; MATHEMATICAL PROGRAMMING;

COMPRESSIVE RECOVERY; COMPRESSIVE SAMPLING; CONVEX PROGRAMMING; EXPANSION COEFFICIENTS;

SAMPLING;

EID: 85032751389     PISSN: 10535888     EISSN: None     Source Type: Journal    
DOI: 10.1109/MSP.2007.914729     Document Type: Article

References (25)

1. S. Boyd and L. Vandenberghe, Convex Optimization. Cambridge, U.K.: Cambridge Univ. Press. 2004.
2. E. Candès and J. Romberg, "Sparsity and incoherence in compressive sampling," Inverse Prob., vol. 23, no. 3, pp. 969-986, June 2007.
3. E. Candès, J. Romberg, and T. Tao, "Robust uncertainty principles: Exact signal reconstruction from highly incomplete frequency information," IEEE Trans. Inform. Theory, vol. 52, no. 2, pp. 489-509, Feb. 2006.
4. E. Candès, J. Romberg, and T. Tao, "Stable signal recovery from incomplete and inaccurate measurements," Comm. Pure Appl. Math., 59, no. 8, pp. 1207-1223, 2006.
5. E. Canès and T. Tao, "Near-optimal signal recovery from random projections and universal encoding strategies?," IEEE Trans. Inform. Theory, vol. 52, no. 12, pp. 5406-5245, Dec. 2006.
6. L. Candès and T. Tao, "The Dantzig selector: Statistical estimation when p is much smaller than n," submitted for publication.
7. 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.
8. R. Coifman, F. Geshwind, and Y. Meyer, "Noiselets", Appl. comp. Harmon. Anal., vol. 10, no. 1, pp. 27-44, 2001.
9. I. Daubechies, Ten Lectures on Wavelets. Philadelphia, PA: SIAM, 1992.
10. R.A. DeVore, "Nonlinear approximation," in Acta Numerica, vol. 7, pp. 51-150, 1998.
11. D.L. Donono, "Compressed sensing," IEEE Trans. Inform. Theory, vol. 52, no. 4, pp. 1289-1306, Apr. 2006.
12. D.L. Donoho and X. Huo, "Uncertainty principles and ideal atomic decomposition," IEEE Trans. Inform. Theory, vol. 47, no. 7, pp. 2845-2862, 2001.
13. D.L. Donoho and J. Tanner, "Neighborliness of randomly-projected simplices in high dimensions," Proc. Natl. Acad. Sci. USA, vol. 102, no. 27, pp. 9452-9457, 2005.
14. D.L. Donoho, M. Vetterli, R.A. DeVore, and I. Daubechies, "Data compression and harmonic analysis," IEEE Trans. Inform. Theory, vol. 44, p. 2435-2476, Oct. 1998.
15. J. Lee. A. Bandyopadhyay, I.F. Baskava. R. Robucci, and P. Hasler. "Image processing system using a programmable transform imager," in Proc. IEEE ICASSP, vol. 5, Philadelphia, PA, Mar. 2005, pp. 101-104.
16. S. Mallat, A Wavelet Tour of Signal Processing, 2nd ed. San Diego, CA: Academic, 1999.
17. B.K. Natarajan, "Sparse approximate solutions to linear systems," SIAM J. Cumput., vol. 24, no. 2, pp. 227-234, 1995.
18. W. B. Pennbaker and J.L. Mitchell, JPEG Still Image Data Compression Standard. New York: Springer-Verlag, 1993.
19. R. Robucci, L.K. Chiu, J. Gray, J. Romberg, P. Hasler, and D. Anderson, "Compressive sensing on a CMOS separable transform image sensor," submitted for publication.
20. M. Rudelson and R. Vershynin, "On sparse reconstruction from Fourier and Gaussian measurements," submitted for publication.
21. J. Shapiro, "Embedded image coding using zerotrees ot wavelet coefficients," IEEE Trans. Signal Processing, vol. 41, no. 12, pp. 3445-3462. Dec. 1993.
22. A. Skodras, C. Christopoulos, and T. Ebrahimi, "The JPEG2000 still image compression standard," IEEE Sianal Processing Mag., vol. 18, pp. 36-58, Sept. 2001.
23. D. Takhar, J.N. Laska, M.B. Wakin, M.F. Duarte, D. Baron, S. Sarvotham, K.F. Kelly, and R.G. Baraniuk, "A new compressive imaging camera architecture using optical-domain compression," in Proc. SPIE Conf. Computational Imaging IV, San Jose, CA, Jan. 2006, pp. 43-52.
24. J. Tropp, "Just relax: Convex programming methods for identifying sparse signals in noise," IEEE Trans. Inform. Theory, vol. 52, no. 3, pp. 1030-1051, 2006.
25. M. Vetterli and J. Kovacevic, Wavelets and Subband Coding. Englewood Cliffs, NJ: Prentice-Hall, 1995.