메뉴 건너뛰기




Volumn 14, Issue 5-6, 2008, Pages 877-905

Enhancing sparsity by reweightedℓ1 minimization

Author keywords

1 Minimization; Compressive sensing; Dantzig selector; FOCUSS; Iterative reweighting; Sparsity; Underdetermined systems of linear equations

Indexed keywords


EID: 57349174008     PISSN: 10695869     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00041-008-9045-x     Document Type: Article
Times cited : (4576)

References (62)
  • 3
    • 0000364765 scopus 로고
    • Robust modeling with erratic data
    • 5
    • J.F. Claerbout F. Muir 1973 Robust modeling with erratic data Geophysics 38 5 826 844
    • (1973) Geophysics , vol.38 , pp. 826-844
    • Claerbout, J.F.1    Muir, F.2
  • 4
    • 0008988926 scopus 로고
    • Linear inversion of band-limited reflection seismograms
    • 4
    • F. Santosa W.W. Symes 1986 Linear inversion of band-limited reflection seismograms SIAM J. Sci. Stat. Comput. 7 4 1307 1330
    • (1986) SIAM J. Sci. Stat. Comput. , vol.7 , pp. 1307-1330
    • Santosa, F.1    Symes, W.W.2
  • 5
    • 0001616908 scopus 로고
    • Uncertainty principles and signal recovery
    • 3
    • D.L. Donoho P.B. Stark 1989 Uncertainty principles and signal recovery SIAM J. Appl. Math. 49 3 906 931
    • (1989) SIAM J. Appl. Math. , vol.49 , pp. 906-931
    • Donoho, D.L.1    Stark, P.B.2
  • 6
    • 0026845575 scopus 로고
    • Signal recovery and the large sieve
    • 2
    • D.L. Donoho B.F. Logan 1992 Signal recovery and the large sieve SIAM J. Appl. Math. 52 2 577 591
    • (1992) SIAM J. Appl. Math. , vol.52 , pp. 577-591
    • Donoho, D.L.1    Logan, B.F.2
  • 7
    • 0001287271 scopus 로고    scopus 로고
    • Regression shrinkage and selection via the lasso
    • 1
    • R. Tibshirani 1996 Regression shrinkage and selection via the lasso J. R. Stat. Soc. B 58 1 267 288
    • (1996) J. R. Stat. Soc. B , vol.58 , pp. 267-288
    • Tibshirani, R.1
  • 9
    • 44049111982 scopus 로고
    • Nonlinear total variation based noise removal algorithms
    • 1-4
    • L.I. Rudin S. Osher E. Fatemi 1992 Nonlinear total variation based noise removal algorithms Physica D 60 1-4 259 268
    • (1992) Physica D , vol.60 , pp. 259-268
    • Rudin, L.I.1    Osher, S.2    Fatemi, E.3
  • 10
    • 0032026262 scopus 로고    scopus 로고
    • Color TV: Total variation methods for restoration of vector-valued images
    • P. Blomgren T.F. Chan 1998 Color TV: total variation methods for restoration of vector-valued images IEEE Trans. Image Process. 7 304 309
    • (1998) IEEE Trans. Image Process. , vol.7 , pp. 304-309
    • Blomgren, P.1    Chan, T.F.2
  • 13
    • 0033228328 scopus 로고    scopus 로고
    • Low-authority controller design via convex optimization
    • 6
    • A. Hassibi J. How S. Boyd 1999 Low-authority controller design via convex optimization AIAA J. Guid. Control Dyn. 22 6 862 872
    • (1999) AIAA J. Guid. Control Dyn. , vol.22 , pp. 862-872
    • Hassibi, A.1    How, J.2    Boyd, S.3
  • 15
    • 33847366224 scopus 로고    scopus 로고
    • Portfolio optimization with linear and fixed transaction costs
    • 1
    • M. Lobo M. Fazel S. Boyd 2006 Portfolio optimization with linear and fixed transaction costs Ann. Oper. Res. 152 1 341 365
    • (2006) Ann. Oper. Res. , vol.152 , pp. 341-365
    • Lobo, M.1    Fazel, M.2    Boyd, S.3
  • 17
    • 33746329499 scopus 로고    scopus 로고
    • The fastest mixing Markov process on a graph and a connection to a maximum variance unfolding problem
    • 4
    • J. Sun S. Boyd L. Xiao P. Diaconis 2006 The fastest mixing Markov process on a graph and a connection to a maximum variance unfolding problem SIAM Rev. 48 4 681 699
    • (2006) SIAM Rev. , vol.48 , pp. 681-699
    • Sun, J.1    Boyd, S.2    Xiao, L.3    Diaconis, P.4
  • 19
    • 0035504028 scopus 로고    scopus 로고
    • Uncertainty principles and ideal atomic decomposition
    • 7
    • D.L. Donoho X. Huo 2001 Uncertainty principles and ideal atomic decomposition IEEE Trans. Inf. Theory 47 7 2845 2862
    • (2001) IEEE Trans. Inf. Theory , vol.47 , pp. 2845-2862
    • Donoho, D.L.1    Huo, X.2
  • 20
    • 0036714214 scopus 로고    scopus 로고
    • A generalized uncertainty principle and sparse representation in pairs of bases
    • 9
    • M. Elad A.M. Bruckstein 2002 A generalized uncertainty principle and sparse representation in pairs of bases IEEE Trans. Inf. Theory 48 9 2558 2567
    • (2002) IEEE Trans. Inf. Theory , vol.48 , pp. 2558-2567
    • Elad, M.1    Bruckstein, A.M.2
  • 21
    • 0347968052 scopus 로고    scopus 로고
    • Sparse representations in unions of bases
    • 12
    • R. Gribonval M. Nielsen 2003 Sparse representations in unions of bases IEEE Trans. Inf. Theory 49 12 3320 3325
    • (2003) IEEE Trans. Inf. Theory , vol.49 , pp. 3320-3325
    • Gribonval, R.1    Nielsen, M.2
  • 22
    • 33645712308 scopus 로고    scopus 로고
    • Just relax: Convex programming methods for identifying sparse signals in noise
    • J.A. Tropp 2006 Just relax: convex programming methods for identifying sparse signals in noise IEEE Trans. Inf. Theory 52 1030 1051
    • (2006) IEEE Trans. Inf. Theory , vol.52 , pp. 1030-1051
    • Tropp, J.A.1
  • 23
    • 31744440684 scopus 로고    scopus 로고
    • Robust uncertainty principles: Exact signal reconstruction from highly incomplete frequency information
    • 2
    • E.J. Candès J. Romberg T. Tao 2006 Robust uncertainty principles: Exact signal reconstruction from highly incomplete frequency information IEEE Trans. Inf. Theory 52 2 489 509
    • (2006) IEEE Trans. Inf. Theory , vol.52 , pp. 489-509
    • Candès, E.J.1    Romberg, J.2    Tao, T.3
  • 24
    • 33947416035 scopus 로고    scopus 로고
    • Near optimal signal recovery from random projections: Universal encoding strategies?
    • 12
    • E.J. Candès T. Tao 2006 Near optimal signal recovery from random projections: Universal encoding strategies? IEEE Trans. Inf. Theory 52 12 5406 5425
    • (2006) IEEE Trans. Inf. Theory , vol.52 , pp. 5406-5425
    • Candès, E.J.1    Tao, T.2
  • 26
    • 57349138185 scopus 로고    scopus 로고
    • Counting faces of randomly-projected polytopes when the projection radically lowers dimension
    • D.L. Donoho J. Tanner 2009 Counting faces of randomly-projected polytopes when the projection radically lowers dimension J. Am. Math. Soc. 22 1 53
    • (2009) J. Am. Math. Soc. , vol.22 , pp. 1-53
    • Donoho, D.L.1    Tanner, J.2
  • 27
    • 33745604236 scopus 로고    scopus 로고
    • Stable signal recovery from incomplete and inaccurate measurements
    • 8
    • E.J. Candès J. Romberg T. Tao 2006 Stable signal recovery from incomplete and inaccurate measurements Commun. Pure Appl. Math. 59 8 1207 1223
    • (2006) Commun. Pure Appl. Math. , vol.59 , pp. 1207-1223
    • Candès, E.J.1    Romberg, J.2    Tao, T.3
  • 28
    • 30844433547 scopus 로고    scopus 로고
    • Extensions of compressed sensing
    • 3
    • D. Donoho Y. Tsaig 2006 Extensions of compressed sensing Signal Process. 86 3 533 548
    • (2006) Signal Process. , vol.86 , pp. 533-548
    • Donoho, D.1    Tsaig, Y.2
  • 31
  • 37
    • 0142257025 scopus 로고    scopus 로고
    • Ph.D. thesis, Electrical Engineering Department, Stanford University
    • Fazel, M.: Matrix rank minimization with applications. Ph.D. thesis, Electrical Engineering Department, Stanford University (2002)
    • (2002) Matrix Rank Minimization with Applications
    • Fazel, M.1
  • 38
    • 33847366224 scopus 로고    scopus 로고
    • Portfolio optimization with linear and fixed transaction costs
    • 1
    • M.S. Lobo M. Fazel S. Boyd 2007 Portfolio optimization with linear and fixed transaction costs Ann. Oper. Res. 152 1 341 365
    • (2007) Ann. Oper. Res. , vol.152 , pp. 341-365
    • Lobo, M.S.1    Fazel, M.2    Boyd, S.3
  • 39
    • 0142215333 scopus 로고    scopus 로고
    • Log-det heuristic for matrix rank minimization with applications to Hankel and Euclidean distance matrices
    • June 2003
    • Fazel, M., Hindi, H., Boyd, S.: Log-det heuristic for matrix rank minimization with applications to Hankel and Euclidean distance matrices. In: Proceedings of Am. Control Conf., June 2003
    • Proceedings of Am. Control Conf
    • Fazel, M.1    Hindi, H.2    Boyd, S.3
  • 41
    • 36749072615 scopus 로고    scopus 로고
    • Majorization-minimization algorithms for wavelet-based image restoration
    • 12
    • M. Figueiredo J.M. Bioucas-Dias R.D. Nowak 2007 Majorization-minimization algorithms for wavelet-based image restoration IEEE Trans. Image Process. 16 12 2980 2991
    • (2007) IEEE Trans. Image Process. , vol.16 , pp. 2980-2991
    • Figueiredo, M.1    Bioucas-Dias, J.M.2    Nowak, R.D.3
  • 43
    • 33846114377 scopus 로고    scopus 로고
    • The adaptive Lasso and its oracle properties
    • 476
    • H. Zou 2006 The adaptive Lasso and its oracle properties J. Am. Stat. Assoc. 101 476 1418 1429
    • (2006) J. Am. Stat. Assoc. , vol.101 , pp. 1418-1429
    • Zou, H.1
  • 44
    • 51049104549 scopus 로고    scopus 로고
    • One-step sparse estimates in nonconcave penalized likelihood models
    • 4
    • H. Zou R. Li 2008 One-step sparse estimates in nonconcave penalized likelihood models Ann. Stat. 36 4 1509 1533
    • (2008) Ann. Stat. , vol.36 , pp. 1509-1533
    • Zou, H.1    Li, R.2
  • 45
    • 84891815019 scopus 로고
    • An iterative technique for absolute deviations curve fitting
    • 344
    • E.J. Schlossmacher 1973 An iterative technique for absolute deviations curve fitting J. Am. Stat. Assoc. 68 344 857 859
    • (1973) J. Am. Stat. Assoc. , vol.68 , pp. 857-859
    • Schlossmacher, E.J.1
  • 46
    • 84946263679 scopus 로고
    • Robust regression using iteratively reweighted least-squares
    • P. Holland R. Welsch 1977 Robust regression using iteratively reweighted least-squares Commun. Stat. Theor. Methods A6 813 827
    • (1977) Commun. Stat. Theor. Methods , vol.6 , pp. 813-827
    • Holland, P.1    Welsch, R.2
  • 50
    • 34548275795 scopus 로고    scopus 로고
    • The Dantzig selector: Statistical estimation when p is much larger than n
    • 6
    • E.J. Candès T. Tao 2007 The Dantzig selector: Statistical estimation when p is much larger than n Ann. Stat. 35 6 2313 2351
    • (2007) Ann. Stat. , vol.35 , pp. 2313-2351
    • Candès, E.J.1    Tao, T.2
  • 51
    • 33645038355 scopus 로고    scopus 로고
    • Second-order cone programming methods for total variation-based image restoration
    • 2
    • D. Goldfarb W. Yin 2005 Second-order cone programming methods for total variation-based image restoration SIAM J. Sci. Comput. 27 2 622 645
    • (2005) SIAM J. Sci. Comput. , vol.27 , pp. 622-645
    • Goldfarb, D.1    Yin, W.2
  • 52
    • 34548724437 scopus 로고    scopus 로고
    • Exact reconstruction of sparse signals via nonconvex minimization
    • 10
    • R. Chartrand 2007 Exact reconstruction of sparse signals via nonconvex minimization Signal Process. Lett. 14 10 707 710
    • (2007) Signal Process. Lett. , vol.14 , pp. 707-710
    • Chartrand, R.1
  • 53
    • 3142656055 scopus 로고    scopus 로고
    • Redundant multiscale transforms and their application for morphological component analysis
    • J.-L. Starck M. Elad D.L. Donoho 2004 Redundant multiscale transforms and their application for morphological component analysis Adv. Imaging Electron. Phys. 132 288 348
    • (2004) Adv. Imaging Electron. Phys. , vol.132 , pp. 288-348
    • Starck, J.-L.1    Elad, M.2    Donoho, D.L.3
  • 54
    • 34249671661 scopus 로고    scopus 로고
    • Analysis versus synthesis in signal priors
    • 3
    • M. Elad P. Milanfar R. Rubinstein 2007 Analysis versus synthesis in signal priors Inverse Probl. 23 3 947 968
    • (2007) Inverse Probl. , vol.23 , pp. 947-968
    • Elad, M.1    Milanfar, P.2    Rubinstein, R.3
  • 55
    • 0031102203 scopus 로고    scopus 로고
    • Sparse signal reconstruction from limited data using FOCUSS: A re-weighted minimum norm algorithm
    • 3
    • I.F. Gorodnitsky B.D. Rao 1997 Sparse signal reconstruction from limited data using FOCUSS: A re-weighted minimum norm algorithm IEEE Trans. Signal Process. 45 3 600 616
    • (1997) IEEE Trans. Signal Process. , vol.45 , pp. 600-616
    • Gorodnitsky, I.F.1    Rao, B.D.2
  • 59
    • 0032002170 scopus 로고    scopus 로고
    • Globally convergent edge-preserving regularized reconstruction: An application to limited-angle tomography
    • 2
    • A.H. Delaney Y. Bresler 1998 Globally convergent edge-preserving regularized reconstruction: An application to limited-angle tomography IEEE Trans. Image Process. 7 2 204 221
    • (1998) IEEE Trans. Image Process. , vol.7 , pp. 204-221
    • Delaney, A.H.1    Bresler, Y.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.