Variance-component based sparse signal reconstruction and model selection

IEEE Transactions on Signal Processing

Volumn 58, Issue 6, 2010, Pages 2935-2952

  Qiu, Kun ^a   Dogandzic, Aleksandar ^a  

^a Iowa State University of Science and Technology   (United States)

Author keywords

Compressive sampling; Model selection; Sparse Bayesian learning; Sparse signal reconstruction

Indexed keywords

BAYESIAN; COMPONENT BASED; COMPONENT-BASED METHOD; COMPRESSIVE SAMPLING; DATA FITS; LARGE-SCALE PROBLEM; LINEAR MODEL; MEMORY EFFICIENT; MODEL SELECTION; NOISE COVARIANCE MATRIX; NOISE LEVELS; NUMERICAL SIMULATION; OBJECTIVE FUNCTIONS; PARAMETER SPACES; PRIOR KNOWLEDGE; PROBABILISTIC MODELS; REGRESSION VECTORS; SIGNAL REPRESENTATIONS; SPARSE BAYESIAN LEARNING; SPARSE SIGNAL RECONSTRUCTION; TWO-DIMENSIONAL SIGNALS; VARIANCE COMPONENTS;

BAYESIAN NETWORKS; COMPUTER SIMULATION; COVARIANCE MATRIX; LINEAR SYSTEMS; MAXIMUM LIKELIHOOD; NUMERICAL METHODS; OPTIMIZATION; REPAIR; SIGNAL ANALYSIS;

SIGNAL RECONSTRUCTION;

EID: 77952572987     PISSN: 1053587X     EISSN: None     Source Type: Journal    
DOI: 10.1109/TSP.2010.2044828     Document Type: Article

References (44)

1. I. F. Gorodnitsky and B. D. Rao, "Sparse signal reconstruction from limited data using FOCUSS: A re-weighted minimum norm algorithm, " IEEE Trans. Signal Process., vol. 45, no. 3, pp. 600-616, Mar. 1997.
2. E. Candès and J. Romberg, C. Bouman and E. Miller, Eds., "Signal recovery from random projections, " in Proc. SPIE-IS&T Electronic Imaging Computational Imaging III, San Jose, CA, Jan. 2005, vol. 5674, pp. 76-86.
3. E. J. Candès and T. Tao, "Decoding by linear programming, " IEEE Trans. Inf. Theory, vol. 51, pp. 4203-4215, Dec. 2005.
4. D. Malioutov, M. Çetin, and A. S. Willsky, "A sparse signal reconstruction perspective for source localization with sensor arrays, " IEEE Trans. Signal Process., vol. 53, no. 8, pp. 3010-3022, Aug. 2005.
5. E. J. Candès, J. Romberg, and T. Tao, "Stable signal recovery from incomplete and inaccurate information, " Commun. Pure Appl. Math., vol. 59, pp. 1207-1233, Aug. 2006.
6. IEEE Signal Process. Mag. (Special Issue on Sensing, Sampling, and Compression), Mar. 2008.
7. A. M. Bruckstein, D. L. Donoho, and M. Elad, "From sparse solutions of systems of equations to sparse modeling of signals and images, " in SIAMRev., Mar. 2009, vol. 51, pp. 34-81.
8. B. K. Natarajan, "Sparse approximate solutions to linear systems, " SIAMJ. Comput., vol. 24, pp. 227-234, Apr. 1995.
9. S. Chen, D. Donoho, and M. Saunders, "Atomic decomposition by basis pursuit, " SIAM J. Sci. Comput., vol. 20, no. 1, pp. 33-61, 1998.
10. E. Candès and T. Tao, "The Dantzig selector: Statistical estimation when p is much larger than n, " Ann. Stat., vol. 35, pp. 2313-2351, Dec. 2007.
11. R. Tibshirani, "Regression shrinkage and selection via the lasso, " J. R. Stat. Soc, Ser. B, vol. 58, pp. 267-288, 1996.
12. M. A. T. Figueiredo, R. D. Nowak, and S. J. Wright, "Gradient projection for sparse reconstruction: Application to compressed sensing and other inverse problems, " IEEE J. Sel. Topics Signal Process., vol. 1, no. 4, pp. 586-597, Dec. 2007.
13. S. Mallat and Z. Zhang, "Matching pursuits with time-frequency dictionaries, " IEEETrans. Signal Process., vol. 41, no. 12, pp. 3397-3415, 1993.
14. J. A. Tropp and A. C. Gilbert, "Signal recovery from random measurements via orthogonal matching pursuit, " IEEE Trans. Inf. Theory, vol. 53, pp. 4655-4666, Dec. 2007.
15. D. L. Donoho, Y. Tsaig, I. Drori, and J.-L. Starck, Sparse solution of underdetermined linear equations by Stagewise Orthogonal Matching Pursuit (StOMP), " http://www-stat.standford.edu/~donoho/reports/html.
16. D. Needell and J. A. Tropp, "CoSaMP: Iterative signal recovery from incomplete and inaccurate samples, " Appl. Comput. Harmon. Anal., vol. 26, pp. 301-321, May 2009.
17. W. Dai and O. Milenkovic, "Subspace pursuit for compressive sensing signal reconstruction, " IEEE Trans. Inf. Theory, vol. 55, pp. 2230-2249, May 2009.
18. D. P. Wipf and B. D. Rao, "Sparse Bayesian learning for basis selection, " IEEE Trans. Signal Process., vol. 52, pp. 2153-2164, Aug. 2004.
19. D. P. Wipf and B. D. Rao, "Comparing the effects of different weight distributions on finding sparse representations, " in Adv. Neural In. Process. Syst., Y. Weiss, B. Schölkopf, and J. Platt, Eds. Cambridge, MA: MIT Press, 2006, vol. 18, pp. 1521-1528.
20. S. Ji, Y. Xue, and L. Carin, "Bayesian compressive sensing, " IEEE Trans. Signal Process., vol. 56, no. 6, pp. 2346-2356, Jun. 2008.
21. M. E. Tipping, "Sparse Bayesian learning and the relevance vector machine, " J. Mach. Learn. Res., vol. 1, pp. 211-244, 2001.
22. K. K. Herrity, A. C. Gilbert, and J. A. Tropp, "Sparse approximation via iterative thresholding, " in Proc. Int. Conf. Acoust., Speech, Signal Processing, Toulouse, France, May 2006, pp. 624-627.
23. T. Blumensath and M. E. Davies, "Iterative thresholding for sparse approximations, " J. Fourier Anal. Appl., vol. 14, pp. 629-654, Dec. 2008.
24. T. Blumensath and M. E. Davies, "Iterative hard thresholding for compressed sensing, " Appl. Comput. Harmon. Anal., vol. 27, pp. 265-274, Nov. 2009.
25. T. Blumensath and M. E. Davies, "Normalized iterative hard thresholding: Guaranteed stability and performance, " IEEE J. Sel. Topics Signal Process., vol. 4, no. 2, pp. 298-309, 2010.
26. A. Maleki and D. L. Donoho, "Optimally tuned iterative thresholding algorithms for compressed sensing, " IEEE J. Sel. Topics Signal Process., vol. 4, no. 2, pp. 330-341, 2010.
27. A. Dogandzic and K. Qiu, "Automatic hard thresholding for sparse signal reconstruction from NDE measurements, " in Rev. Progress Quantitat. Nondestruct. Eval., AIP Conf. Proc., D. O. Thompson and D. Chimenti, Eds., Melville, NY, 2010, vol. 29, pp. 806-813.
28. K. Qiu and A. Dogandzic, "Double overrelaxation thresholding methods for sparse signal reconstruction, " presented at the 44th Annu. Conf. Inf. Sci. Syst., Princeton, NJ, Mar. 2010.
29. B. D. Rao and K. Kreutz-Delgado, "An affine scaling methodology for best basis selection, " IEEE Trans. Signal Process., vol. 47, no. 1, pp. 187-200, Jan. 1999.
30. 1 minimization, " J. Fourier Anal. Appl., vol. 14, pp. 877-905, Dec. 2008.
31. R. Chartrand and W. Yin, "Iteratively reweighted algorithms for compressive sensing, " in Proc. Int. Conf. Acoust., Speech, Signal Process., Las Vegas, NV, Apr. 2008, pp. 3869-3872.
32. S. M. Kay, Fundamentals of Statistical Signal Processing: Detection Theory. Englewood Cliffs, NJ: Prentice-Hall, 1998.
33. M. H. Hansen and B. Yu, "Model selection and the principle of minimum description length, " J. Amer. Stat. Assoc., vol. 96, pp. 746-774, Jun. 2001. (Pubitemid 33695629)
34. J. Rissanen, Information and Complexity in Statistical Modeling. New York: Springer-Verlag, 2007.
35. A. Dogandzic and K. Qiu, "ExCoV: Expansion-compression variance-component based sparse-signal reconstruction from noisy measurements, " in Proc. 43rd Annu. Conf. Inform. Sci. Syst., Baltimore, MD, Mar. 2009, pp. 186-191.
36. S. M. Kay, Fundamentals of Statistical Signal Processing: Estimation Theory. Englewood Cliffs, NJ: Prentice-Hall, 1993.
37. D. L. Donoho and J. Tanner, "Counting faces of randomly projected polytopes when the projection radically lowers dimension, " J. Amer. Math. Soc, vol. 22, pp. 1-53, Jan. 2009.
38. A. P. Dempster, N. M. Laird, and D. B. Rubin, "Maximum likelihood from incomplete data via the EM algorithm, " J. R. Stat. Soc, Ser. B, vol. 39, pp. 1-38, Jul. 1977.
39. G. J. Mclachlan and T. Krishnan, The EM Algorithm and Extensions, 2nd ed. New York: Wiley, 2008.
40. Å. Björck Numerical Methods for Least Squares Problems. Philadelphia, PA: SIAM, 1996.
41. 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, pp. 489-509, Feb. 2006.
42. 1-regularized least squares, " IEEE J. Sel. Topics Signal Process., vol. 1, no. 4, pp. 606-617, Dec. 2007. (Pubitemid 351266626)
43. D. A. Harville, Matrix Algebra From a Statistician's Perspective. New York: Springer-Verlag, 1997.
44. C. Luo, F. Wu, J. Sun, and C. W. Chen, "Compressive data gathering for large-scale wireless sensor networks, " in Proc. Int. Conf. Mobile Comput. Networking (MobiCom), Beijing, China, Sep. 2009, pp. 145-156.