Asymptotic analysis of MAP estimation via the replica method and compressed sensing

Advances in Neural Information Processing Systems 22 - Proceedings of the 2009 Conference

Volumn , Issue , 2009, Pages 1545-1553

  Rangan, Sundeep ^a   Fletcher, Alyson K ^b   Goyal, Vivek K ^c  

^a Qualcomm Technologies   (United States)

^b UNIVERSITY OF CALIFORNIA   (United States)

^c MASSACHUSETTS INSTITUTE OF TECHNOLOGY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

COMPRESSED SENSING; ESTIMATION; GAUSSIAN NOISE (ELECTRONIC); MEAN SQUARE ERROR; REGRESSION ANALYSIS; STATISTICAL PHYSICS;

COMPRESSED-SENSING; GAUSSIANS; LINEAR MEASUREMENTS; MAXIMUM A POSTERIORI ESTIMATION; MAXIMUM-A-POSTERIORI ESTIMATIONS; NON-GAUSSIAN; NONLINEAR PROBLEMS; REPLICA METHOD; STATISTICAL PHYSICS; ZERO NORMS;

ASYMPTOTIC ANALYSIS;

EID: 84858722178     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: None     Document Type: Conference Paper

References (19)

1. S. Rangan, A. K. Fletcher, and V. K. Goyal. Asymptotic analysis of MAP estimation via the replica method and applications to compressed sensing. arXiv:0906.3234v1 [cs.IT]., June 2009.
2. S. F. Edwards and P. W. Anderson. Theory of spin glasses. J. Phys. F: Metal Physics, 5:965-974, 1975.
3. H. Nishimori. Statistical physics of spin glasses and information processing: An introduction. International Series of Monographs on Physics. Oxford Univ. Press, Oxford, UK, 2001.
4. T. Tanaka. A statistical-mechanics approach to large-system analysis of CDMA multiuser detectors. IEEE Trans. Inform. Theory, 48(11):2888-2910, November 2002.
5. R. R. Müller. Channel capacity and minimum probability of error in large dual antenna array systems with binary modulation. IEEE Trans. Signal Process., 51(11):2821-2828, November 2003.
6. D. Guo and S. Verdú. Randomly spread CDMA: Asymptotics via statistical physics. IEEE Trans. Inform. Theory, 51(6):1983-2010, June 2005.
7. M. Talagrand. Spin Glasses: A Challenge for Mathematicians. Springer, New York, 2003.
8. A. Montanari and D. Tse. Analysis of belief propagation for non-linear problems: The example of CDMA (or: How to prove Tanaka's formula). arXiv:cs/0602028v1 [cs.IT]., February 2006.
9. E. J. Candès, J. Romberg, and T. Tao. Robust uncertainty principles: Exact signal reconstruction from highly incomplete frequency information. IEEE Trans. Inform. Theory, 52(2):489-509, February 2006.
10. D. L. Donoho. Compressed sensing. IEEE Trans. Inform. Theory, 52(4):1289-1306, April 2006.
11. E. J. Candès and T. Tao. Near-optimal signal recovery from random projections: Universal encoding strategies? IEEE Trans. Inform. Theory, 52(12):5406-5425, December 2006.
12. B. K. Natarajan. Sparse approximate solutions to linear systems. SIAM J. Computing, 24(2):227-234, April 1995.
13. S. S. Chen, D. L. Donoho, and M. A. Saunders. Atomic decomposition by basis pursuit. SIAM J. Sci. Comp., 20(1):33-61, 1999.
14. R. Tibshirani. Regression shrinkage and selection via the lasso. J. Royal Stat. Soc., Ser. B, 58(1):267-288, 1996.
15. D. L. Donoho, M. Elad, and V. N. Temlyakov. Stable recovery of sparse overcomplete representations in the presence of noise. IEEE Trans. Inform. Theory, 52(1):6-18, January 2006.
16. J. A. Tropp. Greed is good: Algorithmic results for sparse approximation. IEEE Trans. Inform. Theory, 50(10):2231-2242, October 2004.
17. J. A. Tropp. Just relax: Convex programming methods for identifying sparse signals in noise. IEEE Trans. Inform. Theory, 52(3):1030-1051, March 2006.
18. 1-constrained quadratic programming (lasso). IEEE Trans. Inform. Theory, 55(5):2183-2202, May 2009.
19. D. L. Donoho and J. Tanner. Counting faces of randomly-projected polytopes when the projection radically lowers dimension. J. Amer. Math. Soc., 22(1):1-53, January 2009.