메뉴 건너뛰기




Volumn 12, Issue 4, 2014, Pages 1800-1827

On the compressive spectral method

Author keywords

Compressed sensing; Multiscale methods; PDEs; Sparse representation; Spectral method

Indexed keywords

COMPRESSED SENSING; HOMOGENIZATION METHOD; MATHEMATICAL OPERATORS; NUMERICAL METHODS; SPECTROSCOPY;

EID: 84920054077     PISSN: 15403459     EISSN: 15403467     Source Type: Journal    
DOI: 10.1137/140965909     Document Type: Article
Times cited : (46)

References (28)
  • 2
    • 31744440684 scopus 로고    scopus 로고
    • Robust uncertainty principles: Exact signal reconstruction from highly incomplete frequency information
    • E. J. Candès, J. Romberg, and T. Tao, Robust uncertainty principles: Exact signal reconstruction from highly incomplete frequency information, IEEE Trans. Inform. Theory, 52 (2006), pp. 489-509.
    • (2006) IEEE Trans. Inform. Theory , vol.52 , pp. 489-509
    • Candès, E.J.1    Romberg, J.2    Tao, T.3
  • 4
    • 0000018252 scopus 로고
    • Generation of semi-groups of nonlinear transformations on general banach spaces
    • M. G. Crandall and T. M. Liggett, Generation of semi-groups of nonlinear transformations on general Banach spaces, Amer. J. Math., 93 (1971), pp. 265-298.
    • (1971) Amer. J. Math , vol.93 , pp. 265-298
    • Crandall, M.G.1    Liggett, T.M.2
  • 5
    • 51149113295 scopus 로고    scopus 로고
    • A sparse spectral method for homogenization multiscale problems
    • I. Daubechies, O. Runborg, and J. Zou, A sparse spectral method for homogenization multiscale problems, Multiscale Model. Simul., 6 (2007), pp. 711-740.
    • (2007) Multiscale Model. Simul , vol.6 , pp. 711-740
    • Daubechies, I.1    Runborg, O.2    Zou, J.3
  • 6
    • 0029307534 scopus 로고
    • De-noising by soft-thresholding
    • D. L. Donoho, De-noising by soft-thresholding, IEEE Trans. Inform. Theory, 41 (1995), pp. 613-627.
    • (1995) IEEE Trans. Inform. Theory , vol.41 , pp. 613-627
    • Donoho, D.L.1
  • 8
    • 0031161210 scopus 로고    scopus 로고
    • A multiscale finite element method for elliptic problems in composite materials and porous media
    • T. Y. Hou and X.-H.Wu, A multiscale finite element method for elliptic problems in composite materials and porous media, J. Comput. Phys., 134 (1997), pp. 169-189.
    • (1997) J. Comput. Phys , vol.134 , pp. 169-189
    • Hou, T.Y.1    Wu, X.-H.2
  • 9
    • 85128858890 scopus 로고    scopus 로고
    • Equation-free, coarse-grained multiscale computation: Enabling macroscopic simulators to perform system-level analysis
    • I. G. Kevrekidis, C. W. Gear, J. M. Hyman, P. G. Kevrekidis, O. Runborg, and C. Theodoropoulos, Equation-free, coarse-grained multiscale computation: Enabling macroscopic simulators to perform system-level analysis, Commun. Math. Sci., 1 (2003), pp. 715-762.
    • (2003) Commun. Math. Sci , vol.1 , pp. 715-762
    • Kevrekidis, I.G.1    Gear, C.W.2    Hyman, J.M.3    Kevrekidis, P.G.4    Runborg, O.5    Theodoropoulos, C.6
  • 10
    • 55249095137 scopus 로고    scopus 로고
    • A framework for adaptive multiscale methods for elliptic problems
    • J. Nolen, G. Papanicolaou, and O. Pironneau, A framework for adaptive multiscale methods for elliptic problems, Multiscale Model. Simul., 7 (2008), pp. 171-196.
    • (2008) Multiscale Model. Simul , vol.7 , pp. 171-196
    • Nolen, J.1    Papanicolaou, G.2    Pironneau, O.3
  • 12
    • 44049111982 scopus 로고
    • Nonlinear total variation based noise removal algorithms
    • L. I. Rudin, S. Osher, and E. Fatemi, Nonlinear total variation based noise removal algorithms, Phys. D, 60 (1992), pp. 259-268.
    • (1992) Phys. D , vol.60 , pp. 259-268
    • Rudin, L.I.1    Osher, S.2    Fatemi, E.3
  • 14
    • 85028362826 scopus 로고    scopus 로고
    • Heterogeneous multiscale method: A general methodology for multiscale modeling
    • W. Eu, B. Engquist, and Z. Huang, Heterogeneous multiscale method: A general methodology for multiscale modeling, Phys. Rev. B, 67 (2003), 092101.
    • (2003) Phys. Rev. B , vol.67
    • Eu, W.1    Engquist, B.2    Huang, Z.3
  • 17
    • 79960675858 scopus 로고    scopus 로고
    • Robust principal component analysis?
    • E. J. Candès, X. Li, Y. Ma, and J. Wright, Robust principal component analysis?, J. ACM, 58 (2011), 11.
    • (2011) J. ACM , vol.58 , pp. 11
    • Candès, E.J.1    Li, X.2    Ma, Y.3    Wright, J.4
  • 19
    • 84969334819 scopus 로고    scopus 로고
    • The split bregman method for l1-regularized problems
    • T. Goldstein and S. Osher, The split Bregman method for L1-regularized problems, SIAM J. Imaging Sci., 2 (2009), pp. 323-343.
    • (2009) SIAM J. Imaging Sci , vol.2 , pp. 323-343
    • Goldstein, T.1    Osher, S.2
  • 21
    • 84872979901 scopus 로고    scopus 로고
    • Compressive sensing as a paradigm for building physics models
    • L. J. Nelson, G. L. W. Hart, F. Zhou, and V. Ozoliņš, Compressive sensing as a paradigm for building physics models, Phys. Rev. B, 87 (2013), 035125.
    • (2013) Phys. Rev. B , vol.87
    • Nelson, L.J.1    Hart, G.L.W.2    Zhou, F.3    Ozoliņš, V.4
  • 22
    • 84887425211 scopus 로고    scopus 로고
    • Compressed modes for variational problems in mathematics and physics
    • V. Ozoliņš, R. Lai, R. Caflisch, and S. Osher, Compressed modes for variational problems in mathematics and physics, Proc. Natl. Acad. Sci. USA, 110 (2013), pp. 18368-18373.
    • (2013) Proc. Natl. Acad. Sci. USA , vol.110 , pp. 18368-18373
    • Ozoliņš, V.1    Lai, R.2    Caflisch, R.3    Osher, S.4
  • 23
    • 84893459372 scopus 로고    scopus 로고
    • Compressed plane waves yield a compactly supported multiresolution basis for the laplace operator
    • V. Ozolinš, R. Lai, R. Caflisch, and S. Osher, Compressed plane waves yield a compactly supported multiresolution basis for the Laplace operator, Proc. Natl. Acad. Sci. USA, 111 (2014), pp. 1691-1696.
    • (2014) Proc. Natl. Acad. Sci. USA , vol.111 , pp. 1691-1696
    • Ozolinš, V.1    Lai, R.2    Caflisch, R.3    Osher, S.4
  • 26
    • 0003282411 scopus 로고
    • Operateurs maximaux monotones et semi-groupes de contractions dans les espaces de hilbert
    • Elsevier, New York
    • H. Brezis, Operateurs maximaux monotones et semi-groupes de contractions dans les espaces de Hilbert, North-Holland Math. Stud. 5, Elsevier, New York, 1973.
    • (1973) North-Holland Math. Stud , vol.5
    • Brezis, H.1
  • 27
    • 79251479900 scopus 로고    scopus 로고
    • Multiscale finite element methods: Theory and applications
    • Springer, New York
    • Y. Efendiev and T. Y. Hou, Multiscale Finite Element Methods: Theory and Applications, Surv. Tutor. Appl. Math. Sci. 4, Springer, New York, 2009.
    • (2009) Surv. Tutor. Appl. Math. Sci , vol.4
    • Efendiev, Y.1    Hou, T.Y.2
  • 28
    • 84957143659 scopus 로고
    • Solutions with compact support of variational inequalities
    • H. Brezis, Solutions with compact support of variational inequalities, Russian Math. Surveys, 29 (1974), pp. 103-108.
    • (1974) Russian Math. Surveys , vol.29 , pp. 103-108
    • Brezis, H.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.