메뉴 건너뛰기




Volumn 56, Issue 6, 2010, Pages 2967-2979

Information-theoretic limits on sparse signal recovery: Dense versus sparse measurement matrices

Author keywords

1 relaxation; Compressed sensing; Fano's method; High dimensional statistical inference; Information theoretic bounds; Sparse approximation; Sparse random matrices; Sparsity recovery; Subset selection; Support recovery

Indexed keywords

COMPRESSED SENSING; FANO'S METHOD; HIGH-DIMENSIONAL STATISTICAL INFERENCE; INFORMATION-THEORETIC BOUNDS; SPARSE APPROXIMATION; SPARSE RANDOM MATRICES; SPARSITY RECOVERY; SUBSET SELECTION;

EID: 77956932923     PISSN: 00189448     EISSN: None     Source Type: Journal    
DOI: 10.1109/TIT.2010.2046199     Document Type: Article
Times cited : (110)

References (35)
  • 1
    • 46749134451 scopus 로고    scopus 로고
    • Information-theoretic bounds to sensing capacity of sensor networks under fixed snr
    • presented at the, Sep.
    • S. Aeron, M. Zhao, and V. Saligrama, "Information-theoretic bounds to sensing capacity of sensor networks under fixed snr," presented at the Information Theory Workshop, Sep. 2007.
    • (2007) Information Theory Workshop
    • Aeron, S.1    Zhao, M.2    Saligrama, V.3
  • 5
    • 0042613398 scopus 로고    scopus 로고
    • An alternative point of view on Lepski's method
    • ser. IMS Lecture Notes. Beachwood, OH: Institute of Mathematical Statistics
    • L. Birgé, "An alternative point of view on Lepski's method," in State of the Art in Probability and Statistics, ser. IMS Lecture Notes. Beachwood, OH: Institute of Mathematical Statistics, 2001, pp. 113-133.
    • (2001) State of the Art in Probability and Statistics , pp. 113-133
    • Birgé, L.1
  • 6
    • 33745604236 scopus 로고    scopus 로고
    • Stable signal recovery from incomplete and inaccurate measurements
    • Aug.
    • E. Candes, J. Romberg, and T. Tao, "Stable signal recovery from incomplete and inaccurate measurements," Commun. Pure Appl. Math., vol.59, no.8, pp. 1207-1223, Aug. 2006.
    • (2006) Commun. Pure Appl. Math. , vol.59 , Issue.8 , pp. 1207-1223
    • Candes, E.1    Romberg, J.2    Tao, T.3
  • 7
    • 29144439194 scopus 로고    scopus 로고
    • Decoding by linear programming
    • Dec.
    • E. Candes and T. Tao, "Decoding by linear programming," IEEE Trans. Inf. Theory, vol.51, no.12, pp. 4203-4215, Dec. 2005.
    • (2005) IEEE Trans. Inf. Theory , vol.51 , Issue.12 , pp. 4203-4215
    • Candes, E.1    Tao, T.2
  • 8
    • 0032131292 scopus 로고    scopus 로고
    • Atomic decomposition by basis pursuit
    • S. Chen, D. L. Donoho, and M. A. Saunders, "Atomic decomposition by basis pursuit," SIAM J. Sci. Comput., vol.20, no.1, pp. 33-61, 1998.
    • (1998) SIAM J. Sci. Comput. , vol.20 , Issue.1 , pp. 33-61
    • Chen, S.1    Donoho, D.L.2    Saunders, M.A.3
  • 11
    • 33645712892 scopus 로고    scopus 로고
    • Compressed sensing
    • Apr.
    • D. Donoho, "Compressed sensing," IEEE Trans. Inf. Theory, vol.52, no.4, pp. 1289-1306, Apr. 2006.
    • (2006) IEEE Trans. Inf. Theory , vol.52 , Issue.4 , pp. 1289-1306
    • Donoho, D.1
  • 12
    • 33144483155 scopus 로고    scopus 로고
    • Stable recovery of sparse overcomplete representations in the presence of noise
    • Jan.
    • D. Donoho, M. Elad, and V. M. Temlyakov, "Stable recovery of sparse overcomplete representations in the presence of noise," IEEE Trans. Inf. Theory, vol.52, no.1, pp. 6-18, Jan. 2006.
    • (2006) IEEE Trans. Inf. Theory , vol.52 , Issue.1 , pp. 6-18
    • Donoho, D.1    Elad, M.2    Temlyakov, V.M.3
  • 14
    • 33846796161 scopus 로고    scopus 로고
    • Denoising by sparse approximation: Error bounds based on rate-distortion theory
    • A. K. Fletcher, S. Rangan, V. K. Goyal, and K. Ramchandran, "Denoising by sparse approximation: Error bounds based on rate-distortion theory," J. Appl. Signal Process., vol.10, pp. 1-19, 2006.
    • (2006) J. Appl. Signal Process. , vol.10 , pp. 1-19
    • Fletcher, A.K.1    Rangan, S.2    Goyal, V.K.3    Ramchandran, K.4
  • 16
    • 0009387419 scopus 로고
    • A lower bound on the risks of nonparametric estimates of densities in the uniform metric
    • R. Z. Has'minskii, "A lower bound on the risks of nonparametric estimates of densities in the uniform metric," Theory Prob. Appl., vol.23, pp. 794-798, 1978.
    • (1978) Theory Prob. Appl. , vol.23 , pp. 794-798
    • Has'minskii, R.Z.1
  • 18
    • 33747163541 scopus 로고    scopus 로고
    • High-dimensional graphs and variable selection with the lasso
    • N. Meinshausen and P. Buhlmann, "High-dimensional graphs and variable selection with the lasso," Ann. Statist., vol.34, no.3, pp. 1436-1462, 2006.
    • (2006) Ann. Statist. , vol.34 , Issue.3 , pp. 1436-1462
    • Meinshausen, N.1    Buhlmann, P.2
  • 20
    • 0029291966 scopus 로고
    • Sparse approximate solutions to linear systems
    • B. K. Natarajan, "Sparse approximate solutions to linear systems," SIAM J. Comput., vol.24, no.2, pp. 227-234, 1995.
    • (1995) SIAM J. Comput. , vol.24 , Issue.2 , pp. 227-234
    • Natarajan, B.K.1
  • 22
    • 52349112508 scopus 로고    scopus 로고
    • Sampling bounds for sparse support recovery in the presence of noise
    • Presented at The, Toronto, Canada
    • G. Reeves and M. Gastpar, "Sampling bounds for sparse support recovery in the presence of noise," presented at the Int. Symp. Information Theory, Toronto, Canada, 2008.
    • (2008) Int. Symp. Information Theory
    • Reeves, G.1    Gastpar, M.2
  • 23
    • 0004155375 scopus 로고
    • New York: Wiley, Wiley Series in Probability and Mathematical Statistics
    • J. Riordan, Combinatorial Identities. New York: Wiley, 1968, Wiley Series in Probability and Mathematical Statistics.
    • (1968) Combinatorial Identities
    • Riordan, J.1
  • 25
    • 39049110737 scopus 로고    scopus 로고
    • Sudocodes: Fast measurement and reconstruction of sparse signals
    • presented at the, Seattle, WA, Jul.
    • S. Sarvotham, D. Baron, and R. G. Baraniuk, "Sudocodes: Fast measurement and reconstruction of sparse signals," presented at the Int. Symp. Information Theory, Seattle, WA, Jul. 2006.
    • (2006) Int. Symp. Information Theory
    • Sarvotham, S.1    Baron, D.2    Baraniuk, R.G.3
  • 27
    • 0001287271 scopus 로고    scopus 로고
    • Regression shrinkage and selection via the lasso
    • R. Tibshirani, "Regression shrinkage and selection via the lasso," J. Roy. Statist. Soc. Ser. B, vol.58, no.1, pp. 267-288, 1996.
    • (1996) J. Roy. Statist. Soc. Ser. B , vol.58 , Issue.1 , pp. 267-288
    • Tibshirani, R.1
  • 28
    • 33645712308 scopus 로고    scopus 로고
    • Just relax: Convex programming methods for identifying sparse signals in noise
    • Mar.
    • J. Tropp, "Just relax: Convex programming methods for identifying sparse signals in noise," IEEE Trans. Inf. Theory, vol.52, no.3, pp. 1030-1051, Mar. 2006.
    • (2006) IEEE Trans. Inf. Theory , vol.52 , Issue.3 , pp. 1030-1051
    • Tropp, J.1
  • 29
    • 73849097267 scopus 로고    scopus 로고
    • Information-theoretic limits on sparsity recovery in the high-dimensional and noisy setting
    • Dec.
    • M. J.Wainwright, "Information-theoretic limits on sparsity recovery in the high-dimensional and noisy setting," IEEE Trans. Inf. Theory, vol.55, no.12, pp. 5728-5741, Dec. 2009.
    • (2009) IEEE Trans. Inf. Theory , vol.55 , Issue.12 , pp. 5728-5741
    • Wainwright, M.J.1
  • 30
    • 65749083666 scopus 로고    scopus 로고
    • Sharp thresholds for high-dimensional and noisy sparsity recovery using ℓ -constrained quadratic programming (Lasso)
    • May
    • M. J. Wainwright, "Sharp thresholds for high-dimensional and noisy sparsity recovery using ℓ -constrained quadratic programming (Lasso)," IEEE Trans. Inf. Theory, vol.55, no.5, pp. 2183-2202, May 2009.
    • (2009) IEEE Trans. Inf. Theory , vol.55 , Issue.5 , pp. 2183-2202
    • Wainwright, M.J.1
  • 33
    • 46749155099 scopus 로고    scopus 로고
    • Efficient compressed sensing with deterministic guarantees using expander graphs
    • presented at the, Sep.
    • W. Xu and B. Hassibi, "Efficient compressed sensing with deterministic guarantees using expander graphs," presented at the Information Theory Workshop (ITW), Sep. 2007.
    • (2007) Information Theory Workshop (ITW)
    • Xu, W.1    Hassibi, B.2
  • 34
    • 0033233737 scopus 로고    scopus 로고
    • Information-theoretic determination of minimax rates of convergence
    • Y. Yang and A. Barron, "Information-theoretic determination of minimax rates of convergence," Ann. Statist., vol.27, no.5, pp. 1564-1599, 1999.
    • (1999) Ann. Statist. , vol.27 , Issue.5 , pp. 1564-1599
    • Yang, Y.1    Barron, A.2
  • 35
    • 17644388356 scopus 로고    scopus 로고
    • Assouad, Fano and le Cam
    • Berlin, Germany: Springer-Verlag
    • B. Yu, "Assouad, Fano and Le Cam," in Festschrift for Lucien Le Cam. Berlin, Germany: Springer-Verlag, 1997, pp. 423-435.
    • (1997) Festschrift for Lucien le Cam , pp. 423-435
    • Yu, B.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.