Performance bounds for expander-based compressed sensing in poisson noise

IEEE Transactions on Signal Processing

Volumn 59, Issue 9, 2011, Pages 4139-4153

  Raginsky, Maxim ^a   Jafarpour, Sina ^b   Harmany, Zachary T ^a   Marcia, Roummel F ^c   Willett, Rebecca M ^a   Calderbank, Robert ^d  

^a Duke University   (United States)

^b Princeton University   (United States)

^c UNIVERSITY OF CALIFORNIA   (United States)

^d DUKE UNIVERSITY   (United States)

Author keywords

Compressive measurement; expander graphs; packet counters; photon limited imaging; RIP 1

Indexed keywords

COMPRESSIVE MEASUREMENT; EXPANDER GRAPHS; PACKET COUNTERS; PHOTON-LIMITED IMAGING; RIP-1;

ALGORITHMS; GRAPHIC METHODS; POISSON DISTRIBUTION;

SIGNAL RECONSTRUCTION;

EID: 80051771803     PISSN: 1053587X     EISSN: None     Source Type: Journal    
DOI: 10.1109/TSP.2011.2157913     Document Type: Article

References (38)

1. D. Donoho, "Compressed sensing," IEEE Trans. Inf. Theory, vol. 52, no. 4, pp. 1289-1306, Apr. 2006.
2. E. Candès, J. Romberg, and T. Tao, "Stable signal recovery from incomplete and inaccurate measurements," Commun. Pure Appl. Math., vol. 59, no. 8, pp. 1207-1223, 2006. (Pubitemid 43988295)
3. D. Snyder, A. Hammond, and R. White, "Image recovery from data acquired with a charge-coupled-device camera," J. Opt. Soc. Amer. A, vol. 10, pp. 1014-1023, 1993.
4. D. Bertsekas and R. Gallager, Data Networks. Englewood Cliffs, NJ: Prentice-Hall, 1992.
5. I. Rish and G. Grabarnik, "Sparse signal recovery with exponentialfamily noise," in Proc. Allerton Conf. Commun., Control, Comput., 2009, pp. 60-66.
6. L. Jacques, D. K. Hammond, and M. J. Fadili, "Dequantizing compressed sensing with non-Gaussian constraints," in Proc. ICIP, 2009, pp. 1465-1468.
7. R. E. Carrillo, K. E. Barner, and T. C. Aysal, "Robust sampling and reconstruction methods for sparse signals in the presence of impulsive noise," IEEE J. Sel. Topics Signal Process., vol. 4, no. 2, pp. 392-408, 2010.
8. J. N. Laska, M. A. Davenport, and R. G. Baraniuk, "Exact signal recovery from sparsely corrupted measurements through the pursuit of justice," in Proc. 43rd Asilomar Conf. Signals, Syst., Comput., 2009, pp. 1556-1560.
9. R. Willett and M. Raginsky, "Performance bounds on compressed sensing with Poisson noise," in Proc. IEEE Int. Symp. Inf. Theory, Seoul, Korea, Jun./Jul. 2009, pp. 174-178.
10. M. Raginsky, Z. Harmany, R. Marcia, and R. Willett, "Compressed sensing performance bounds under Poisson noise," IEEE Trans. Signal Process., vol. 58, pp. 3990-4002, Aug. 2010.
11. E. Candès and T. Tao, "Near optimal signal recovery from random projections: Universal encoding strategies," IEEE Trans. Inf. Theory, vol. 52, no. 12, pp. 5406-5425, Dec. 2006. (Pubitemid 46445381)
12. 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. (Pubitemid 43174093)
13. S. Hoory, N. Linial, and A.Wigderson, "Expander graphs and their applications," Bull. Amer. Math. Soc. (New Series), vol. 43, pp. 439-561, 2006. (Pubitemid 44448254)
14. R. Berinde and P. Indyk, "Sparse recovery using sparse random matrices," MIT, Cambridge, MA, Tech. Rep., 2008.
15. S. Jafarpour, W. Xu, B. Hassibi, and R. Calderbank, "Efficient and robust compressed sensing using optimized expander graphs," IEEE Trans. Inf. Theory, vol. 55, no. 9, pp. 4299-4308, Sep. 2009.
16. 1 norm," in Proc. 46th Annu. Allerton Conf. Commun., Control, Comput., 2008, pp. 198-205.
17. 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.
18. R. Berinde, A. Gilbert, P. Indyk, H. Karloff, and M. Strauss, "Combining geometry and combinatorics: A unified approach to sparse signal recovery," in Proc. 46th Annu. Allerton Conf. Commun., Control, Comput., Sep. 2008, pp. 798-805.
19. 1 norm," in Proc. 49th Annu. IEEE Symp. Found. Comput. Sci. (FOCS), 2008, pp. 199-207.
20. N. Alon and J. Spencer, The Probabilistic Method. New York:Wiley-Interscience, 2000.
21. M. Sipser and D. Spielman, "Expander codes," IEEE Trans. Inf. Theory, vol. 42, no. 6, pp. 1710-1722, 1996. (Pubitemid 126769170)
22. 1 via expander codes," in Proc. 19th Annu. ACM-SIAM Symp. Discrete Algorithms (SODA), Jan. 2008, pp. 353-362.
23. V. Guruswami, C. Umans, and S. Vadhan, "Unbalanced expanders and randomness extractors from Parvaresh-Vardy codes," in Proc. IEEE Conf. Comput. Complexity (CCC), 2007, pp. 96-108. (Pubitemid 47485128)
24. F. Parvaresh and A. Vardy, "Correcting errors beyond the Guruswami-Sudan radius in polynomial time," in Proc. 46th Annu. IEEE Symp. Found. Comput. Sci. (FOCS), 2005, pp. 285-294. (Pubitemid 44375740)
25. T. M. Cover and J. A. Thomas, Elements of Information Theory, 2nd ed. New York: Wiley, 2006.
26. P. McCullagh and J. Nelder, Generalized Linear Models, 2nd ed. London, U.K.: Chapman & Hall, 1989.
27. L. Wasserman, All of Statistics: A Concise Course in Statistical Inference. New York: Springer, 2003.
28. Z. Harmany, R. Marcia, and R. Willett, "Sparse Poisson intensity reconstruction algorithms," in Proc. IEEE Stat. Signal Process. Workshop, 2009, pp. 634-637.
29. C. Estan and G. Varghese, "New directions in traffic measurement and accounting: Focusing on the elephants, ignoring the mice," ACMTrans. Comput. Sys., vol. 21, no. 3, pp. 270-313, 2003.
30. Y. Lu, A. Montanari, B. Prabhakar, S. Dharmapurikar, and A. Kabbani, "Counter braids: A novel counter architecture for per-flow measurement," in Proc. ACM SIGMETRICS, 2008, pp. 121-132.
31. W. Fang and L. Peterson, "Inter-AS traffic patterns and their implications," in Proc. IEEE GLOBECOM, 1999, pp. 1859-1868.
32. A. Feldmann, A. Greenberg, C. Lund, N. Reingold, J. Rexford, and F. True, "Deriving traffic demands for operational IP networks: Methodology and experience," IEEE/ACM Trans. Networking, pp. 265-279, Jun. 2001. (Pubitemid 32650795)
33. R. Berinde, A. Gilbert, P. Indyk, H. Karloff, and M. Strauss, "Combining geometry and combinatorics: A unified approach to sparse signal recovery," in Proc. Allerton Conf., Sep. 2008, pp. 798-805.
34. M. A. Khajehnejad, A. G. Dimakis, W. Xu, and B. Hassibi, "Sparse Recovery of Nonnegative SignalsWith Minimal Expansion," IEEE Trans. Signal Process., vol. 59, no. 1, pp. 196-208, Jan. 2011.
35. 1-MAGIC: Recovery of sparse signals via convex programming, 2005 [Online]. Available: http://www.acm. caltech.edu/l1magic
36. R. Berinde and P. Indyk, "Sequential sparse matching pursuit," in Proc. 47th Annu. Allerton Conf. Commun., Control and Comput., 2009, pp. 36-43.
37. M. Grant and S. Boyd, CVX: Matlab Software for Disciplined Convex Programming. ver. 1.21, Jan. 2011 [Online]. Available: http://cvxr.com/cvx
38. M. Grant and S. Boyd, "Graph implementations for nonsmooth convex programs," in Recent Advances in Learning and Control, ser. Lecture Notes in Control and Information Sciences, V. Blondel, S. Boyd, and H. Kimura, Eds. New York: Springer-Verlag Ltd., 2008, pp. 95-110.