Performance analysis for sparse support recovery

IEEE Transactions on Information Theory

Volumn 56, Issue 3, 2010, Pages 1383-1399

  Tang, Gongguo ^a   Nehorai, Arye ^a  

^a WASHINGTON UNIVERSITY IN ST LOUIS   (United States)

Author keywords

Chernoff bound; Compressive sensing; Fanos inequality; Jointly sparse signals; Multiple hypothesis testing; Probability of error; Support recovery

Indexed keywords

CHERNOFF BOUNDS; JOINTLY SPARSE SIGNALS; MULTIPLE HYPOTHESIS TESTING; PROBABILITY OF ERRORS; SPARSE SIGNALS;

CLUTTER (INFORMATION THEORY); DIRECTION OF ARRIVAL; PROBABILITY; RADIO DIRECTION FINDING SYSTEMS; SIGNAL RECONSTRUCTION;

RECOVERY;

EID: 77949499138     PISSN: 00189448     EISSN: None     Source Type: Journal    
DOI: 10.1109/TIT.2009.2039039     Document Type: Article

References (64)

1. M. B. Wakin, S. Sarvotham, M. F. Duarte, D. Baron, and R. G. Baraniuk, "Recovery of jointly sparse signals from few random projections," in Proc. Neural Inf. Process. Syst., Vancouver, Canada, Dec. 2005, pp. 1435-1442.
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, Feb. 2006.
3. D. Donoho, "Compressed sensing," IEEE Trans. Inf. Theory, vol.52, no.4, pp. 1289-1306, Apr. 2006.
4. E. Candès and T. Tao, "Decoding by linear programming," IEEE Trans. Inf. Theory, vol.51, no.12, pp. 4203-4215, Dec. 2005.
5. E. Candès and M. Wakin, "An introduction to compressive sampling," IEEE Signal Process. Mag., vol.25, no.2, pp. 21-30, Mar. 2008.
6. R. Baraniuk, "Compressive sensing [lecture notes]," IEEE Signal Process. Mag., vol.24, no.4, pp. 118-121, Jul. 2007.
7. D. Malioutov, M. Cetin, and A. 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.
8. D. Model and M. Zibulevsky, "Signal reconstruction in sensor arrays using sparse representations," Signal Process., vol.86, no.3, pp. 624-638, Mar. 2006.
9. V. Cevher, M. Duarte, and R. G. Baraniuk, "Distributed target localization via spatial sparsity," in Eur. Signal Process. Conf. (EUSIPCO 2008), Lausanne, Switzerland, Aug. 2008.
10. V. Cevher, P. Indyk, C. Hegde, and R. G. Baraniuk, "Recovery of clustered sparse signals from compressive measurements," in Proc. Int. Conf. Sampling Theory Appl. (SAMPTA 2009), Marseille, France, May 2009, pp. 18-22.
11. S. S. Chen, D. L. Donoho, and M. A. Saunders, "Atomic decomposition by basis pursuit," SIAM J. Sci. Comp., vol.20, no.1, pp. 33-61, 1998.
12. S. Mallat, AWavelet Tour of Signal Processing. San Diego, CA: Academic, 1998.
13. I. Gorodnitsky and B. 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.
14. E. Candès and T. Tao, "The Dantzig selector: Statistical estimation when p is much larger than-," Ann. Statist., vol.35, pp. 2313-2351, 2007.
15. J. Tropp and A. Gilbert, "Signal recovery from random measurements via orthogonal matching pursuit," IEEE Trans. Inf. Theory, vol.53, no.12, pp. 4655-4666, Dec. 2007.
16. W. Dai and O. Milenkovic, "Subspace pursuit for compressive sensing signal reconstruction," IEEE Trans. Inf. Theory, vol.55, no.5, pp. 2230-2249, May 2009.
17. D. Needell and J. Tropp, "CoSaMP: Iterative signal recovery from incomplete and inaccurate samples," Appl. Comput. Harmon. Anal., vol.26, no.3, pp. 301-321, May 2009.
18. P. Borgnat and P. Flandrin, "Time-frequency localization from sparsity constraints," in Proc. IEEE Int. Conf. Acoust., Speech Signal Process. (ICASSP 2008), Las Vegas, NV, Apr. 2008, pp. 3785-3788.
19. Z. Tian and G. Giannakis, "Compressed sensing for wideband cognitive radios," in Proc. IEEE Int. Conf. Acoust., Speech Signal Process. (ICASSP 2007), Honolulu, HI, Apr. 2007, pp. IV-1357-IV-1360.
20. M. A. Sheikh, S. Sarvotham, O. Milenkovic, and R. G. Baraniuk, "DNA array decoding from nonlinear measurements by belief propagation," in Proc. IEEE Workshop Statist. Signal Process. (SSP 2007), Madison, WI, Aug. 2007, pp. 215-219.
21. H. Vikalo, F. Parvaresh, and B. Hassibi, "On recovery of sparse signals in compressed DNA microarrays," in Proc. Asilomar Conf. Signals, Syst. Comput. (ACSSC 2007), Pacific Grove, CA, Nov. 2007, pp. 693-697.
22. F. Parvaresh, H. Vikalo, S. Misra, and B. Hassibi, "Recovering sparse signals using sparse measurement matrices in compressed DNA microarrays," IEEE J. Sel. Topics Signal Process., vol.2, no.3, pp. 275-285, Jun. 2008.
23. H. Vikalo, F. Parvaresh, S. Misra, and B. Hassibi, "Sparse measurements, compressed sampling, and DNA microarrays," in Proc. IEEE Int. Conf. Acoust., Speech Signal Process. (ICASSP 2008), Las Vegas, NV, Apr. 2008, pp. 581-584.
24. R. Baraniuk and P. Steeghs, "Compressive radar imaging," in Proc. IEEE Radar Conf. , Apr. 2007, pp. 128-133.
25. M. Herman and T. Strohmer, "Compressed sensing radar," in Proc. IEEE Radar Conf., May 2008, pp. 1-6.
26. M. A. Herman and T. Strohmer, "High-resolution radar via compressed sensing," IEEE Trans. Signal Process., vol.57, no.6, pp. 2275-2284, Jun. 2009.
27. E. G. Larsson and Y. Selen, "Linear regression with a sparse parameter vector," IEEE Trans. Signal Process., vol.55, no.2, pp. 451-460, Feb. 2007.
28. D. H. Johnson and D. E. Dudgeon, Array Signal Processing: Concepts and Techniques. Englewood Cliffs, NJ: Prentice-Hall, 1993.
29. J. Capon, "High-resolution frequency-wavenumber spectrum analysis," Proc. IEEE, vol.57, pp. 1408-1418, Aug. 1969.
30. R. Schmidt, "Multiple emitter location and signal parameter estimation," IEEE Trans. Antennas Propag., vol.34, no.3, pp. 276-280, Mar. 1986.
31. G. Bienvenu and L. Kopp, "Adaptivity to background noise spatial coherence for high resolution passive methods," in Proc. IEEE Int. Conf. Acoust., Speech Signal Process. (ICASSP 1980), Denver, CO, Apr. 1980, vol.5, pp. 307-310.
32. P. Stoica and A. Nehorai, "MUSIC, maximum likelihood, and Cramér-Rao bound: Further results and comparisons," IEEE Trans. Acoust., Speech, Signal Process., vol.38, no.12, pp. 2140-2150, Dec. 1990.
33. M. Duarte, S. Sarvotham, D. Baron, M. Wakin, and R. Baraniuk, "Distributed compressed sensing of jointly sparse signals," in Proc. Asilomar Conf. Signals, Syst. Comput. (ACSSC 2005), Pacific Grove, CA, Nov. 2005, pp. 1537-1541.
34. M. Duarte, M. Wakin, D. Baron, and R. Baraniuk, "Universal distributed sensing via random projections," in Proc. Int. Conf. Inf. Process. Sens. Netw. (IPSN 2006), Nashville, TN, Apr. 2006, pp. 177-185.
35. M. Fornasier and H. Rauhut, "Recovery algorithms for vector-valued data with joint sparsity constraints," SIAM J. Numer. Anal., vol.46, no.2, pp. 577-613, 2008.
36. M. Mishali and Y. Eldar, "The continuous joint sparsity prior for sparse representations: Theory and applications," in Proc. IEEE Int. Workshop Computat. Adv. Multi-Sens. Adapt. Process. (CAMPSAP 2007), St. Thomas, U.S. Virgin Islands, Dec. 2007, pp. 125-128.
37. S. Cotter, B. Rao, K. Engan, and K. Kreutz-Delgado, "Sparse solutions to linear inverse problems with multiple measurement vectors," IEEE Trans. Signal Process., vol.53, no.7, pp. 2477-2488, Jul. 2005.
38. J. Chen and X. Huo, "Sparse representations for multiple measurement vectors (MMV) in an over-complete dictionary," in Proc. IEEE Int. Conf. Acoust., Speech Signal Process. (ICASSP 2005), Philadelphia, PA, Mar. 2005, pp. 257-260.
39. J. Chen and X. Huo, "Theoretical results on sparse representations of multiple-measurement vectors," IEEE Trans. Signal Process., vol.54, no.12, pp. 4634-4643, Dec. 2006.
40. J. A. Tropp, A. C. Gilbert, and M. J. Strauss, "Algorithms for simultaneous sparse approximation. Part I: Greedy pursuit," Signal Process., vol.86, no.3, pp. 572-588, 2006.
41. J. A. Tropp, "Algorithms for simultaneous sparse approximation. Part II: Convex relaxation," Signal Process., vol.86, no.3, pp. 589-602, 2006.
42. S. Aeron, M. Zhao, and V. Saligrama, Information Theoretic Bounds to Performance of Compressed Sensing and Sensor Networks 2008 [Online]. Available: http://arxiv.org/pdf/0804.3439v4, to be published
43. M.Wainwright, "Information-theoretic bounds on sparsity recovery in the high-dimensional and noisy setting," in Proc. IEEE Int. Symp. Inf. Theory (ISIT 2007), Nice, France, Jun. 2007, pp. 961-965.
44. H. L. Van Trees, Detection, Estimation, and Modulation Theory, Part I. New York: Wiley-Interscience, 2001.
45. A. K. Gupta and D. K. Nagar, Matrix Variate Distributions. Boca Raton, FL: Chapman and Hall/CRC, 1999.
46. Y. S. Chow and H. Teicher, Probability Theory: Independence, Interchangeability, Martingales. New York: Springer-Verlag, 1988.
47. R. Baraniuk, V. Cevher,M. Duarte, and C. Hegde, Model-Based Compressive Sensing, submitted for publication.
48. D. S. Bernstein, Matrix Mathematics: Theory, Facts, and Formulas with Application to Linear Systems Theory. Princeton, NJ: Princeton Univ. Press, 2005.
49. R. A. Horn and C. R. Johnson, Matrix Analysis. New York: Cambridge Univ. Press, 1990.
50. O. Milenkovic, H. Pham, and W. Dai, "Sublinear compressive sensing reconstruction via belief propagation decoding," in Proc. Int. Symp. Inf. Theory (ISIT 2009), Seoul, South Korea, Jul. 2009, pp. 674-678.
51. T. M. Cover and J. A. Thomas, Elements of Information Theory, 2nd ed. Hoboken, NJ: Wiley-Interscience, 2006.
52. S. Kullback, Information Theory and Statistics. New York: Dover , 1997.
53. Y. G. Yatracos, "A lower bound on the error in nonparametric regression type problems," Ann. Statist., vol.16, no.3, pp. 1180-1187, 1988.
54. L. Birge, "Approximation dans les espaces métriques et théorie de l'estimation," Probabil. Theory and Related Fields, vol.65, no.2, pp. 181-237, Jun. 1983.
55. A. Dogandzic and A. Nehorai, "Space-time fading channel estimation and symbol detection in unknown spatially correlated noise," IEEE Trans. Signal Process., vol.50, no.3, pp. 457-474, Mar. 2002.
56. H. L. Van Trees, Optimum Array Processing. New York: Wiley-Interscience, 2002.
57. G. Tang and A. Nehorai, "Support recovery for source localization based on overcomplete signal representation," in Proc. IEEE Int. Conf. Acoust., Speech Signal Process. (CASSP 2010).
58. D. L. Donoho and P. B. Stark, "Uncertainty principles and signal recovery," SIAM J. Appl. Math., vol.49, no.3, pp. 906-931, 1989.
59. D. L. Donoho and B. F. Logan, "Signal recovery and the large sieve," SIAM J. Appl. Math., vol.52, no.2, pp. 577-591, 1992.
60. T. W. Anderson, An Introduction to Multivariate Statistical Analysis, 3rd ed. Hoboken, NJ: Wiley-Interscience, 2003.
61. A. K. Fletcher, S. Rangan, V. K. Goyal, and K. Ramchandran, "Denoising by sparse approximation: Error bounds based on rate-distortion theory," EURASIP J. Appl. Signal Process., vol.2006, pp. 1-19, 2006.
62. R. A. DeVore, "Deterministic constructions of compressed sensing matrices," J. Complexity, vol.23, no.4-6, pp. 918-925, 2007.
63. I. Gohberg, P. Lancaster, and L. Rodman, Indefinite Linear Algebra and Applications. Basel, Switzerland: Birkhäuser, 2005.
64. G. H. Golub and C. F. V. Loan, Matrix Computations, 3rd ed. Baltimore, MD: Johns Hopkins Univ. Press, 1996.