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Volumn 54, Issue 11, 2008, Pages 4789-4812

Fast solution of ℓ1-Norm minimization problems when the solution may be sparse

Author keywords

1 minimization; Basis pursuit; Homotopy methods; LASSO; Least Angle Regression (Lars); Orthogonal matching pursuit; Polytope faces pursuit; Sparse representations; Underdetermined systems of linear equations

Indexed keywords

ARTIFICIAL INTELLIGENCE; COMMUNICATION SYSTEMS; INFORMATION THEORY; OPTIMIZATION; SIGNAL PROCESSING;

EID: 55349134896     PISSN: 00189448     EISSN: None     Source Type: Journal    
DOI: 10.1109/TIT.2008.929958     Document Type: Article
Times cited : (643)

References (55)
  • 4
    • 0002649812 scopus 로고
    • Wavelab and reproducible research
    • A. Antoniadis and G. Oppenheim, Eds. New York: Springer-Verlag
    • J. Buckheit and D. L. Donoho, "Wavelab and reproducible research," in Wavelets and Statistics, A. Antoniadis and G. Oppenheim, Eds. New York: Springer-Verlag, 1995, pp. 55-81.
    • (1995) Wavelets and Statistics , pp. 55-81
    • Buckheit, J.1    Donoho, D.L.2
  • 5
    • 29144439194 scopus 로고    scopus 로고
    • Decoding by linear programming
    • Dec
    • E. Candès 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
    • Candès, E.1    Tao, T.2
  • 7
    • 31744440684 scopus 로고    scopus 로고
    • Robust uncertainty principles: Exact signal reconstruction from highly incomplete frequency information
    • Feb
    • E. J. 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.
    • (2006) IEEE Trans. Inf. Theory , vol.52 , Issue.2 , pp. 489-509
    • Candès, E.J.1    Romberg, J.2    Tao, T.3
  • 8
    • 33745604236 scopus 로고    scopus 로고
    • Stable signal recovery from incomplete and inaccurate observations
    • Aug
    • E. J. Candès and T. Tao, "Stable signal recovery from incomplete and inaccurate observations," 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
    • Candès, E.J.1    Tao, T.2
  • 9
    • 0032131292 scopus 로고    scopus 로고
    • Atomic decomposition by basis pursuit
    • 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, 1999.
    • (1999) SIAM J. Sci Comp , vol.20 , Issue.1 , pp. 33-61
    • Chen, S.S.1    Donoho, D.L.2    Saunders, M.A.3
  • 11
    • 7044231546 scopus 로고    scopus 로고
    • An iterative thresholding algorithm for linear inverse problems with a sparsity constraint
    • Aug
    • Daubechies, M. Defrise, and C. De Mol, "An iterative thresholding algorithm for linear inverse problems with a sparsity constraint," Commun. Pure Appl. Math., vol. 57, no. 11, pp. 1413-1541, Aug. 2004.
    • (2004) Commun. Pure Appl. Math , vol.57 , Issue.11 , pp. 1413-1541
    • Daubechies, M.D.1    De Mol, C.2
  • 13
    • 30844437386 scopus 로고    scopus 로고
    • Neighborly Polytopes and Sparse Solution of Underdetermined Linear Equations Dept. Statist., Stanford Uni., Stanford, CA
    • Tech. Rep
    • D. L. Donoho, Neighborly Polytopes and Sparse Solution of Underdetermined Linear Equations Dept. Statist., Stanford Uni., Stanford, CA, 2005, Tech. Rep..
    • (2005)
    • Donoho, D.L.1
  • 14
    • 33645712892 scopus 로고    scopus 로고
    • Compressed sensing
    • Apr
    • D. L. 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.L.1
  • 15
    • 33744552752 scopus 로고    scopus 로고
    • 1 solution is also the sparsest solution
    • Jul
    • 1 solution is also the sparsest solution," Commun. Pure Appl. Math., vol. 59, no. 7, pp. 907-934, Jul. 2006.
    • (2006) Commun. Pure Appl. Math , vol.59 , Issue.7 , pp. 907-934
    • Donoho, D.L.1
  • 16
    • 33646365077 scopus 로고    scopus 로고
    • 1-norm near-solution approximates the sparsest near-solution
    • Jun
    • 1-norm near-solution approximates the sparsest near-solution," Commun. Pure Appl. Math., vol. 59, no. 6, pp. 797-829, Jun. 2006.
    • (2006) Commun. Pure Appl. Math , vol.59 , Issue.6 , pp. 797-829
    • Donoho, D.L.1
  • 17
    • 33646479497 scopus 로고    scopus 로고
    • High-dimensional centrosymmetric polytopes with neighborliness proportional to dimension
    • May
    • D. L. Donoho, "High-dimensional centrosymmetric polytopes with neighborliness proportional to dimension," Discr. Comput. Geom., vol. 35, no. 4, pp. 617-652, May 2006.
    • (2006) Discr. Comput. Geom , vol.35 , Issue.4 , pp. 617-652
    • Donoho, D.L.1
  • 19
    • 33144483155 scopus 로고    scopus 로고
    • Stable recovery of sparse overcomplete representations in the presence of noise
    • Jan
    • D. L. Donoho, M. Elad, and V. N. 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.L.1    Elad, M.2    Temlyakov, V.N.3
  • 20
    • 0035504028 scopus 로고    scopus 로고
    • Uncertainty principles and ideal atontic decomposition
    • Nov
    • D. L. Donoho and X. Huo, "Uncertainty principles and ideal atontic decomposition," IEEE Trans. Inf. Theory, vol. 47, no. 7, pp. 2845-2862, Nov. 2001.
    • (2001) IEEE Trans. Inf. Theory , vol.47 , Issue.7 , pp. 2845-2862
    • Donoho, D.L.1    Huo, X.2
  • 21
    • 0026845575 scopus 로고
    • Signal recovery and the large sieve
    • 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.
    • (1992) SIAM J. Appl. Math , vol.52 , Issue.2 , pp. 577-591
    • Donoho, D.L.1    Logan, B.F.2
  • 22
    • 55349107071 scopus 로고    scopus 로고
    • Counting faces of randomly-projected polytopes when the projection radically lowers dimension
    • posted online July 10, to be published
    • D. L. Donoho and J. Tanner, "Counting faces of randomly-projected polytopes when the projection radically lowers dimension," J. Amer. Math. Soc., posted online July 10, 2008, to be published.
    • (2008) J. Amer. Math. Soc
    • Donoho, D.L.1    Tanner, J.2
  • 23
    • 55349104303 scopus 로고    scopus 로고
    • D. L. Donoho, Y. Tsaig, 1. Drori, and J.-L. Starck, Sparse Solution of Underdetermined Linear Equations by Stagewise Orthogonal Matching Pursuit, 2006, submitted for publication.
    • D. L. Donoho, Y. Tsaig, 1. Drori, and J.-L. Starck, "Sparse Solution of Underdetermined Linear Equations by Stagewise Orthogonal Matching Pursuit," 2006, submitted for publication.
  • 25
    • 55349122369 scopus 로고    scopus 로고
    • B. Efron and T. Hastie, LARS Softare Web Site Online. Available: http:// www-stat.stanford.edu/~hastie/Papers/LARS/
    • B. Efron and T. Hastie, LARS Softare Web Site Online. Available: http:// www-stat.stanford.edu/~hastie/Papers/LARS/
  • 27
    • 55349123812 scopus 로고    scopus 로고
    • Coordinate and subspace optimization methods for linear least squares with nonquadratic regularization
    • to be published
    • M. Elad, B. Matalon, and M. Zibulevsky, "Coordinate and subspace optimization methods for linear least squares with nonquadratic regularization," Appl. Comp. Harm. Anal., to be published.
    • Appl. Comp. Harm. Anal
    • Elad, M.1    Matalon, B.2    Zibulevsky, M.3
  • 28
    • 0036714214 scopus 로고    scopus 로고
    • A generalized uncertainty principle and sparse representations in pairs of bases
    • Sep
    • M. Elad and A. M. Bruckstein, "A generalized uncertainty principle and sparse representations in pairs of bases," IEEE Trans. Inf. Theory vol. 48, no. 9, pp. 2558-2567, Sep. 2002.
    • (2002) IEEE Trans. Inf. Theory , vol.48 , Issue.9 , pp. 2558-2567
    • Elad, M.1    Bruckstein, A.M.2
  • 29
    • 2942640138 scopus 로고    scopus 로고
    • On sparse representations in arbitrary redundant bases
    • Jun
    • J. J. Fuchs, "On sparse representations in arbitrary redundant bases," IEEE Trans. Inf. Theory, vol. 50, no. 6, pp. 1341-1344, Jun. 2004.
    • (2004) IEEE Trans. Inf. Theory , vol.50 , Issue.6 , pp. 1341-1344
    • Fuchs, J.J.1
  • 30
    • 3543141538 scopus 로고
    • On widths of the Euclidean ball
    • A. Y. Garnaev and E. D. Gluskin, "On widths of the Euclidean ball," in Sov. Math. - Dok.. :, 1984, vol. 30, pp. 200-203.
    • (1984) Sov. Math. - Dok , vol.30 , pp. 200-203
    • Garnaev, A.Y.1    Gluskin, E.D.2
  • 32
  • 33
    • 0347968052 scopus 로고    scopus 로고
    • Sparse representations in unions of bases
    • Dec
    • R. Gribonval and M. Nielsen, "Sparse representations in unions of bases," IEEE Trans. Inf. Theory, vol. 49, no. 12, pp. 1320-1325, Dec. 2003.
    • (2003) IEEE Trans. Inf. Theory , vol.49 , Issue.12 , pp. 1320-1325
    • Gribonval, R.1    Nielsen, M.2
  • 37
    • 0001387808 scopus 로고
    • Diameters of certain finite-dimensional sets in classes of smooth functions
    • B. S. Kashin, "Diameters of certain finite-dimensional sets in classes of smooth functions," Izv. Akad. Nauk SSSR, Ser. Mat., vol. 41, no. 2, pp. 334-351, 1977.
    • (1977) Izv. Akad. Nauk SSSR, Ser. Mat , vol.41 , Issue.2 , pp. 334-351
    • Kashin, B.S.1
  • 40
    • 33646796359 scopus 로고    scopus 로고
    • D. M. Malioutov, M. __ceCetin, and A. S. Willsky, Homotopy continuation for sparse signal representation, in Proc. IEEE Int. Conf. Acoustics, Speech and Signal Processing, Philadelphia, PA, Mar. 2005, 5, pp. 733-736.
    • D. M. Malioutov, M. __ceCetin, and A. S. Willsky, "Homotopy continuation for sparse signal representation," in Proc. IEEE Int. Conf. Acoustics, Speech and Signal Processing, Philadelphia, PA, Mar. 2005, vol. 5, pp. 733-736.
  • 41
    • 0034215549 scopus 로고    scopus 로고
    • A new approach to variable selection in least squares problems
    • M. R. Osborne, B. Presnell, and B. A. Turlach, "A new approach to variable selection in least squares problems," IMA J. Numer. Anal. vol. 20, pp. 389-403, 2000.
    • (2000) IMA J. Numer. Anal , vol.20 , pp. 389-403
    • Osborne, M.R.1    Presnell, B.2    Turlach, B.A.3
  • 47
    • 27744574209 scopus 로고    scopus 로고
    • Image decomposition via the combination of sparse representation and a variational approach
    • Oct
    • J.-L. Starck, M. Elad, and D. L. Donoho, "Image decomposition via the combination of sparse representation and a variational approach," IEEE Trans. Image Process., vol. 14, no. 10, pp. 1570-1582, Oct. 2005.
    • (2005) IEEE Trans. Image Process , vol.14 , Issue.10 , pp. 1570-1582
    • Starck, J.-L.1    Elad, M.2    Donoho, D.L.3
  • 48
    • 3142656055 scopus 로고    scopus 로고
    • Redundant multiscale transforms and their application for morphological component analysis
    • J.-L. Starck, M. Elad, and D. L. Donoho, "Redundant multiscale transforms and their application for morphological component analysis," Adv. Imag. Electron Phys., vol. 132, pp. 287-348, 2004.
    • (2004) Adv. Imag. Electron Phys , vol.132 , pp. 287-348
    • Starck, J.-L.1    Elad, M.2    Donoho, D.L.3
  • 49
    • 0242323185 scopus 로고    scopus 로고
    • Grassmannian frames with applications to coding and communcations
    • T. Strohmer and R. Heath, Jr, "Grassmannian frames with applications to coding and communcations," Appl. Comp. Harm. Anal., vol. 14, no. 3, pp.257-275, 2003.
    • (2003) Appl. Comp. Harm. Anal , vol.14 , Issue.3 , pp. 257-275
    • Strohmer, T.1    Heath Jr, R.2
  • 50
    • 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., vol. 58, no. 1, pp. 267-288, 1996.
    • (1996) J. Roy. Statist. Soc , vol.58 , Issue.1 , pp. 267-288
    • Tibshirani, R.1
  • 51
    • 5444237123 scopus 로고    scopus 로고
    • Greed is good: Algorithmic results for sparse approximation
    • Oct
    • J. A. Tropp, "Greed is good: Algorithmic results for sparse approximation," IEEE Trans. Inf. Theory, vol. 50, no. 10, pp. 2231-2242, Oct. 2004.
    • (2004) IEEE Trans. Inf. Theory , vol.50 , Issue.10 , pp. 2231-2242
    • Tropp, J.A.1
  • 52
    • 33645712308 scopus 로고    scopus 로고
    • Just relax: Convex programming methods for subset selection and sparse approximation
    • Mar
    • J. A. Tropp, "Just relax: Convex programming methods for subset selection and sparse approximation," IEEE Trans. Inf. Theory, vol. 51, no. 3, pp. 1030-1051, Mar. 2006.
    • (2006) IEEE Trans. Inf. Theory , vol.51 , Issue.3 , pp. 1030-1051
    • Tropp, J.A.1
  • 54
    • 30844458202 scopus 로고    scopus 로고
    • 1-norm solution and the sparsest solution
    • Mar
    • 1-norm solution and the sparsest solution," Signal Process., vol. 86, no. 3, pp. 533-548, Mar. 2006.
    • (2006) Signal Process , vol.86 , Issue.3 , pp. 533-548
    • Tsaig, Y.1    Donoho, D.L.2
  • 55
    • 30844433547 scopus 로고    scopus 로고
    • Extensions of compressed sensing
    • Mar
    • Y. Tsaig and D. L. Donoho, "Extensions of compressed sensing," Signal Process., vol. 86, no. 3, pp. 549-571, Mar. 2006.
    • (2006) Signal Process , vol.86 , Issue.3 , pp. 549-571
    • Tsaig, Y.1    Donoho, D.L.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.