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Volumn 57, Issue 2, 2011, Pages 764-785

The dynamics of message passing on dense graphs, with applications to compressed sensing

Author keywords

Compressed sensing; density evolution; message passing algorithms; random matrix theory; state evolution

Indexed keywords

COMPRESSED SENSING; DENSITY EVOLUTION; MESSAGE PASSING ALGORITHMS; RANDOM MATRIX THEORY; STATE EVOLUTIONS;

EID: 79251496987     PISSN: 00189448     EISSN: None     Source Type: Journal    
DOI: 10.1109/TIT.2010.2094817     Document Type: Article
Times cited : (1137)

References (34)
  • 1
    • 0035626635 scopus 로고    scopus 로고
    • The¢ (2) limit in the random assignment problem
    • D. Aldous, "The¢ (2) limit in the random assignment problem," Random Struct. Algorith., vol. 18, pp. 381-418, 2001.
    • (2001) Random Struct. Algorith. , vol.18 , pp. 381-418
    • Aldous, D.1
  • 2
    • 1842487285 scopus 로고    scopus 로고
    • The objective method: Probabilistic combinatorial optimization and local weak convergence
    • H. Kesten, Ed. New York: Springer-Verlag
    • D. Aldous and J. M. Steele, "The objective method: Probabilistic combinatorial optimization and local weak convergence," in Probability On Discrete Structures, H. Kesten, Ed. New York: Springer-Verlag, 2003, pp. 1-72.
    • (2003) Probability on Discrete Structures , pp. 1-72
    • Aldous, D.1    Steele, J.M.2
  • 6
    • 7044231546 scopus 로고    scopus 로고
    • An iterative thresholding algorithm for linear inverse problems with a sparsity constraint
    • I. Daubechies, M. Defrise, and C. De Mol, "An iterative thresholding algorithm for linear inverse problems with a sparsity constraint," Commun. Pure and Appl. Math., vol. 75, pp. 1412-1457, 2004.
    • (2004) Commun. Pure and Appl. Math. , vol.75 , pp. 1412-1457
    • Daubechies, I.1    Defrise, M.2    De Mol, C.3
  • 7
    • 0041958932 scopus 로고
    • Ideal spatial adaptation viawavelet shrinkage
    • D. L. Donoho and I. M. Johnstone, "Ideal spatial adaptation viawavelet shrinkage," Biometrika, vol. 81, pp. 425-455, 1994.
    • (1994) Biometrika , vol.81 , pp. 425-455
    • Donoho, D.L.1    Johnstone, I.M.2
  • 9
    • 79251510293 scopus 로고    scopus 로고
    • Optimally tuned iterative thresholding algorithm for compressed sensing
    • to be published
    • D. L. Donoho and A. Maleki, "Optimally tuned iterative thresholding algorithm for compressed sensing," IEEE J. Sel. Areas Signal Process. 2009 [Online]. Available: http://arxiv.org/abs/0909.0777, to be published
    • (2009) IEEE J. Sel. Areas Signal Process.
    • Donoho, D.L.1    Maleki, A.2
  • 10
    • 73149095169 scopus 로고    scopus 로고
    • Message passing algorithms for compressed sensing
    • D. L. Donoho, A. Maleki, and A. Montanari, "Message passing algorithms for compressed sensing," Proc. Nat. Acad. Sci., vol. 106, pp. 18914-18919, 2009.
    • (2009) Proc. Nat. Acad. Sci. , vol.106 , pp. 18914-18919
    • Donoho, D.L.1    Maleki, A.2    Montanari, A.3
  • 11
    • 77954825041 scopus 로고    scopus 로고
    • Message passing algorithms for compressed sensing: I. Motivation and construction
    • Cairo, Egypt
    • D. L. Donoho, A. Maleki, and A. Montanari, "Message passing algorithms for compressed sensing: I. Motivation and construction," in Proc. IEEE Inf. Theory Workshop, Cairo, Egypt, 2010.
    • (2010) Proc. IEEE Inf. Theory Workshop
    • Donoho, D.L.1    Maleki, A.2    Montanari, A.3
  • 14
    • 33744552752 scopus 로고    scopus 로고
    • 1 -norm near-solution approximates the sparsest near-solution
    • 1 -norm near-solution approximates the sparsest near-solution," Commun. Pure and Appl. Math., vol. 59, pp. 907-934, 2006.
    • (2006) Commun. Pure and Appl. Math. , vol.59 , pp. 907-934
    • Donoho, D.1
  • 15
    • 22144471532 scopus 로고    scopus 로고
    • Neighborliness of randomly-projected simplices in high dimensions
    • D. L. Donoho and J. Tanner, "Neighborliness of randomly-projected simplices in high dimensions," Proc. Nat. Acad. Sci., vol. 102, no. 27, pp. 9452-9457, 2005.
    • (2005) Proc. Nat. Acad. Sci. , vol.102 , Issue.27 , pp. 9452-9457
    • Donoho, D.L.1    Tanner, J.2
  • 16
    • 57349138185 scopus 로고    scopus 로고
    • Counting faces of randomly projected polytopes when the projection radically lowers dimension
    • 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, 2009.
    • (2009) J. Amer. Math. Soc. , vol.22 , pp. 1-53
    • Donoho, D.L.1    Tanner, J.2
  • 17
    • 77949635021 scopus 로고    scopus 로고
    • A single-letter characterization of optimal noisy compressed sensing
    • Monticello, IL, Sep.
    • D. Guo, D. Baron, and S. Shamai, "A single-letter characterization of optimal noisy compressed sensing," in Proc. 47th Ann. Allerton Conf., Monticello, IL, Sep. 2009.
    • (2009) Proc. 47th Ann. Allerton Conf.
    • Guo, D.1    Baron, D.2    Shamai, S.3
  • 18
    • 20544442268 scopus 로고    scopus 로고
    • Randomly spread CDMA: Asymptotics via statistical physics
    • D. Guo and S. Verdu, "Randomly spread CDMA: Asymptotics via statistical physics," IEEE Trans. Inf. Theory, vol. 51, pp. 1982-2010, 2005.
    • (2005) IEEE Trans. Inf. Theory , vol.51 , pp. 1982-2010
    • Guo, D.1    Verdu, S.2
  • 19
    • 0000794880 scopus 로고    scopus 로고
    • Strong law for arrays and for the bootstrap mean and variance
    • T. C. Hu and R. L. Taylor, "Strong law for arrays and for the bootstrap mean and variance," Int. J. Math. and Math. Sci., vol. 20, pp. 375-383, 1997.
    • (1997) Int. J. Math. and Math. Sci. , vol.20 , pp. 375-383
    • Hu, T.C.1    Taylor, R.L.2
  • 20
    • 0242678317 scopus 로고    scopus 로고
    • A CDMA multiuser detection algorithm on the basis of belief propagation
    • Y. Kabashima, "A CDMA multiuser detection algorithm on the basis of belief propagation," J. Phys. A, vol. 36, pp. 11111-11121, 2003.
    • (2003) J. Phys. A , vol.36 , pp. 11111-11121
    • Kabashima, Y.1
  • 21
    • 72449137292 scopus 로고    scopus 로고
    • A typical reconstruction limit for compressed sensing based on -norm minimization
    • Y. Kabashima, T.Wadayama, and T. Tanaka, "A typical reconstruction limit for compressed sensing based on -norm minimization," J. Stat. Mech., 2009.
    • (2009) J. Stat. Mech.
    • Kabashima, Y.1    Wadayama, T.2    Tanaka, T.3
  • 23
    • 0000263234 scopus 로고
    • Distribution of eignevalues for some sets of random matrices
    • V. A. Marcenko and L. A. Pastur, "Distribution of eignevalues for some sets of random matrices," Math. USSR-Sbornik, vol. 1, 1967.
    • (1967) Math. USSR-Sbornik , vol.1
    • Marcenko, V.A.1    Pastur, L.A.2
  • 24
    • 33751033441 scopus 로고    scopus 로고
    • Analysis of belief propagation for non-linear problems: The example of CDMA (or: How to prove Tanaka's formula)
    • Uruguay
    • A. Montanari and D. Tse, "Analysis of belief propagation for non-linear problems: The example of CDMA (or: how to prove Tanaka's formula)," in Proc. IEEE Inf. TheoryWorkshop, Punta de l'Este, Uruguay, 2006.
    • (2006) Proc. IEEE Inf. TheoryWorkshop, Punta de l'Este
    • Montanari, A.1    Tse, D.2
  • 25
    • 24344432073 scopus 로고    scopus 로고
    • Improved message passing for inference in densely connected systems
    • J. P. Neirotti and D. Saad, "Improved message passing for inference in densely connected systems," Europhys. Lett., vol. 71, pp. 866-872, 2005.
    • (2005) Europhys. Lett. , vol.71 , pp. 866-872
    • Neirotti, J.P.1    Saad, D.2
  • 26
  • 28
    • 67649975560 scopus 로고    scopus 로고
    • Belief propagation: Optimal algorithm for random assignment problem
    • J. Salez and D. Shah, "Belief propagation: Optimal algorithm for random assignment problem," Math. Operat. Res., vol. 32, pp. 468-480, 2009.
    • (2009) Math. Operat. Res. , vol.32 , pp. 468-480
    • Salez, J.1    Shah, D.2
  • 29
    • 0000457248 scopus 로고
    • A bound for the error in the normal approximation to the distribution of a sum of dependent random variables
    • C. Stein, "A bound for the error in the normal approximation to the distribution of a sum of dependent random variables," in Proc. 6th Berkeley Symp. Math. Statist. Probab., 1972.
    • (1972) Proc. 6th Berkeley Symp. Math. Statist. Probab.
    • Stein, C.1
  • 31
    • 0036846395 scopus 로고    scopus 로고
    • A statistical-mechanics approach to large-system analysis of CDMA multiuser detectors
    • T. Tanaka, "A statistical-mechanics approach to large-system analysis of CDMA multiuser detectors," IEEE Trans. Inf. Theory, vol. 48, pp. 2888-2910, 2002.
    • (2002) IEEE Trans. Inf. Theory , vol.48 , pp. 2888-2910
    • Tanaka, T.1
  • 32
    • 22144454279 scopus 로고    scopus 로고
    • Statistical physics of information processing in mobile communications
    • T. Tanaka, "Statistical physics of information processing in mobile communications," Progr. Theory Phys. Suppl., vol. 157, pp. 176-183, 2005.
    • (2005) Progr. Theory Phys. Suppl. , vol.157 , pp. 176-183
    • Tanaka, T.1
  • 33
    • 0033098947 scopus 로고    scopus 로고
    • Linear multiuser receivers: Effective interference, effective bandwidth and user capacity
    • D. N. C. Tse and S. V. Hanly, "Linear multiuser receivers: Effective interference, effective bandwidth and user capacity," IEEE Trans. Inf. Theory, vol. 45, pp. 641-657, 1999.
    • (1999) IEEE Trans. Inf. Theory , vol.45 , pp. 641-657
    • Tse, D.N.C.1    Hanly, S.V.2
  • 34
    • 0033097227 scopus 로고    scopus 로고
    • Spectral efficiency of CDMA with random spreading
    • S. Verdú and S. Shamai, "Spectral efficiency of CDMA with random spreading," IEEE Trans. Inf. Theory, vol. 45, pp. 622-640, 1999.
    • (1999) IEEE Trans. Inf. Theory , vol.45 , pp. 622-640
    • Verdú, S.1    Shamai, S.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.