Relaxed conditions for sparse signal recovery with general concave priors

IEEE Transactions on Signal Processing

Volumn 57, Issue 11, 2009, Pages 4347-4354

  Trzasko, Joshua ^a   Manduca, Armando ^a  

^a MAYO CLINIC   (United States)

Author keywords

Compressed sensing; Compressive sensing; Restricted isometry property; Signal recovery; Weak recoverability

Indexed keywords

COMPRESSED SENSING; COMPRESSIVE SENSING; RESTRICTED ISOMETRY PROPERTY; SIGNAL RECOVERY; WEAK RECOVERABILITY;

DIGITAL SIGNAL PROCESSING; REPAIR; SIGNAL ANALYSIS; SIGNAL PROCESSING;

SIGNAL RECONSTRUCTION;

EID: 70350503590     PISSN: 1053587X     EISSN: None     Source Type: Journal    
DOI: 10.1109/TSP.2009.2025979     Document Type: Article

References (26)

1. E. Candès and J. Romberg, "Sparsity and incoherence in compressive sampling," Inverse Problems, vol. 23, no. 3, pp. 969-985, 2007.
2. E. 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. 489-509, 2006.
3. M. Lustig, D. Donoho, and J. Pauly, "Sparse MRI: The application of compressed sensing for rapid MR imaging," Magn. Reson. Med., vol. 58, no. 6, pp. 1182-1195, 2007.
4. D -minimization," IEEE Trans. Med. Imag., vol. 28, no. 1, pp. 106-121, 2009.
5. M. Duarte, M. Davenport, D. Tahkar, J. Laska, S. Ting, K. Kelly, and R. Baraniuk, "Single-pixel imaging via compressive sampling," IEEE Signal Process. Mag., vol. 25, no. 2, pp. 83-91, 2008.
6. B. Natarajan, "Sparse approximate solutions to linear systems," SIAM J. Scientif. Comput., vol. 24, no. 2, pp. 227-234, 1995.
7. D. Donoho, "Compressed sensing," IEEE Trans. Inf. Theory, vol. 52, no. 4, pp. 1289-1306, 2006.
8. R. Chartrand, "Exact reconstruction of sparse signal via nonconvex minimization," IEEE Signal Process. Lett., vol. 14, no. 10, pp. 707-710, 2007.
9. 1 minimization," J. Fourier Anal. Appl., vol. 14, no. 5-6, pp. 877-905, 2008.
10. D. Geman and G. Reynolds, "Nonlinear image recovery with half-quadratic regularization," IEEE Trans. Image Process., vol. 4, no. 7, pp. 932-946, 1995.
11. R. Gribonval and M. Nielsen, "Highly sparse representations from dictionaries are unique and independent of the sparseness measure," Appl. Computat. Harmon. Anal., vol. 22, no. 3, pp. 335-355, 2007.
12. E. Candès, "The restricted isometry property and its implications for compressed sensing," Comptes Rendus de l'Académie des Sciences, Série I, vol. 346, pp. 589-592, 2008.
13. E. Candès and T. Tao, "Decoding by linear programming," IEEE Trans. Inf. Theory, vol. 51, no. 12, pp. 4203-4215, 2005.
14. R. Baraniuk, M. Davenport, R. DeVore, and M.Wakin, "A simple proof of the restricted isometry property for random matrices," Construct. Approx., vol. 28, no. 3, pp. 253-263, 2008.
15. M. Rudelson and R. Vershynin, "Sparse reconstruction by convex relaxation: Fourier and Gaussian measurements," in Proc. 40th Ann. Conf. Inf. Sci. Syst., 2006.
16. J. Bobin, J. Starck, and R. Ottensamer, "Compressed sensing in astronomy," IEEE J. Sel. Topics Signal Process., vol. 2, no. 5, pp. 718-726, 2008.
17. R. DeVore, "Deterministic constructions of compressed sensing matrices," J. Complex., vol. 23, no. 4-6, pp. 918-925, 2007.
18. W. Bajwa, J. Haupt, A. Sayeed, and R. Nowak, "Toeplitz-structured compressed sensing matrices," in Proc. IEEE Workshop on Statist. Signal Process., 2007.
19. H. Rauhut, K. Schnass, and P. Vandergheynst, "Compressed sensing and redundant dictionaries," IEEE Trans. Inf. Theory, vol. 54, no. 5, pp. 2210-2219, 2008.
20. W. Press, S. Teukolsky, W. Vetterling, and B. Flannery, Numerical Recipes in C, 2nd ed. Cambridge, U.K.: Cambridge Univ. Press, 1992.
21. L. Wasserman, All of Statistics: A Concise Course in Statistical Inference. New York: Springer, 2004.
22. M. Heath, Scientific Computing: An Introductory Survey. New York: McGraw-Hill, 2002.
23. H. Edmundson, "Bounds on the expectation of a convex function of a random variable," RAND Corp. Paper, no. 982, 1956.
24. A. Madansky, "Bounds on the expectation of a convex function of a multivariate random variable," Ann. Math. Stat., vol. 30, no. 3, pp. 743-746, 1959.
25. H. Chernoff, "A measure of asymptotic efficiency for tests of a hypothesis based on the sum of observations," Ann. Math. Stat., vol. 23, no. 4, pp. 493-507, 1952.
26. W. Hoeffding, "Probability inequalities for sums of bounded random variables," J. Amer. Statist. Assoc., vol. 58, no. 301, pp. 13-30, 1963.