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Volumn 42, Issue 4, 2004, Pages 1479-1501

Adaptive wavelet Galerkin methods for linear inverse problems

Author keywords

Besov spaces; Galerkin methods; Minimax estimation; Statistical inverse problems; Wavelets and nonlinear methods

Indexed keywords

ALGORITHMS; LINEAR SYSTEMS; PROBLEM SOLVING; STATISTICAL METHODS;

EID: 25444486950     PISSN: 00361429     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0036142902411793     Document Type: Article
Times cited : (78)

References (27)
  • 1
    • 0000521350 scopus 로고    scopus 로고
    • Wavelet decomposition approaches to statistical inverse problems
    • F. ABRAMOVICH AND B.W. SILVERMAN, Wavelet decomposition approaches to statistical inverse problems, Biometrika, 85 (1998), pp. 115-129.
    • (1998) Biometrika , vol.85 , pp. 115-129
    • Abramovich, F.1    Silverman, B.W.2
  • 2
  • 3
    • 0004219794 scopus 로고
    • Longman Scientific and Technical, Harlow, UK
    • J.H. BRAMBLE, Multigrid Methods, Longman Scientific and Technical, Harlow, UK, 1993.
    • (1993) Multigrid Methods
    • Bramble, J.H.1
  • 4
    • 0036048503 scopus 로고    scopus 로고
    • Asymptotic equivalence theory for nonparametric regression with random design
    • L. BROWN, T. CAI, M. LOW, AND C.H. ZHANG, Asymptotic equivalence theory for nonparametric regression with random design, Ann. Statist., 30 (2002), pp. 688-707.
    • (2002) Ann. Statist. , vol.30 , pp. 688-707
    • Brown, L.1    Cai, T.2    Low, M.3    Zhang, C.H.4
  • 5
    • 0036470052 scopus 로고    scopus 로고
    • A wavelet-vaguelet method for unfolding sphere size distributions
    • S. CHAMPIER AND L. GRAMMONT, A wavelet-vaguelet method for unfolding sphere size distributions, Inverse Problems, 18 (2002), pp. 79-94.
    • (2002) Inverse Problems , vol.18 , pp. 79-94
    • Champier, S.1    Grammont, L.2
  • 6
    • 0003204969 scopus 로고
    • The finite element method for elliptic problems
    • North-Holland, Amsterdam, New York, Oxford
    • P. CIARLET, The Finite Element Method for Elliptic Problems, Stud. Math. Appl. 4, North-Holland, Amsterdam, New York, Oxford, 1978.
    • (1978) Stud. Math. Appl. , vol.4
    • Ciarlet, P.1
  • 7
    • 33846966749 scopus 로고    scopus 로고
    • Wavelet methods in numerical analysis
    • P.G. Ciarlet and J.L. Lions, eds., Elsevier, Amsterdam
    • A. COHEN, Wavelet methods in numerical analysis, in Handbook of Numerical Analysis, Vol. VII, P.G. Ciarlet and J.L. Lions, eds., Elsevier, Amsterdam, 2000, pp. 417-711.
    • (2000) Handbook of Numerical Analysis , vol.7 , pp. 417-711
    • Cohen, A.1
  • 8
    • 0035606214 scopus 로고    scopus 로고
    • Adaptive wavelet methods for elliptic operator equations: Convergence rates
    • A. COHEN, W. DAHMEN, AND R. DEVORE, Adaptive wavelet methods for elliptic operator equations: Convergence rates, Math. Comp., 70 (2001), pp. 27-75.
    • (2001) Math. Comp. , vol.70 , pp. 27-75
    • Cohen, A.1    Dahmen, W.2    Devore, R.3
  • 9
    • 0034354926 scopus 로고    scopus 로고
    • Restricted nonlinear approximation
    • A. COHEN, R. DEVORE, AND R. HOCHMUTH, Restricted nonlinear approximation, Constr. Approx., 16 (2000), pp. 85-113.
    • (2000) Constr. Approx. , vol.16 , pp. 85-113
    • Cohen, A.1    Devore, R.2    Hochmuth, R.3
  • 10
    • 0035446697 scopus 로고    scopus 로고
    • Maximal spaces with given rate of convergence for thresholding algorithms
    • A. COHEN, R. DEVORE, G. KERKYACHARIAN, AND D. PICARD, Maximal spaces with given rate of convergence for thresholding algorithms, Appl. Comput. Harmon. Anal., 11 (2001), pp. 167-191.
    • (2001) Appl. Comput. Harmon. Anal. , vol.11 , pp. 167-191
    • Cohen, A.1    Devore, R.2    Kerkyacharian, G.3    Picard, D.4
  • 11
    • 0002001578 scopus 로고
    • Translation-invariant de-noising
    • A. Antoniadis and G. Oppenheim, eds., Springer, New York
    • R.R. COIFMAN AND D.L. DONOHO, Translation-invariant de-noising, in Wavelets and Statistics, Lecture Notes in Statist. 103, A. Antoniadis and G. Oppenheim, eds., Springer, New York, 1995, pp. 125-150.
    • (1995) Wavelets and Statistics, Lecture Notes in Statist. , vol.103 , pp. 125-150
    • Coifman, R.R.1    Donoho, D.L.2
  • 14
    • 85009724776 scopus 로고    scopus 로고
    • Nonlinear approximation
    • R. DEVORE, Nonlinear approximation, Acta Numerica, 7 (1998), pp. 51-150.
    • (1998) Acta Numerica , vol.7 , pp. 51-150
    • Devore, R.1
  • 15
    • 85016849323 scopus 로고    scopus 로고
    • Wavelet- Galerkin methods for ill-posed problems
    • V. DICKEN AND P. MAASS, Wavelet- Galerkin methods for ill-posed problems, J. Inverse Ill-Posed Probl., 4 (1996), pp. 203-221.
    • (1996) J. Inverse Ill-posed Probl. , vol.4 , pp. 203-221
    • Dicken, V.1    Maass, P.2
  • 16
    • 0029288068 scopus 로고
    • Nonlinear solution of linear inverse problems by wavelet-vaguelette decomposition
    • D. DONOHO, Nonlinear solution of linear inverse problems by wavelet-vaguelette decomposition, Appl. Comput. Harmon. Anal., 2 (1995), pp. 101-126.
    • (1995) Appl. Comput. Harmon. Anal. , vol.2 , pp. 101-126
    • Donoho, D.1
  • 17
    • 0041958932 scopus 로고
    • Ideal spatial adaptation by wavelet shrinkage
    • D.L. DONOHO AND I.M. JOHNSTONE, Ideal spatial adaptation by wavelet shrinkage, Biometrika, 81 (1994), pp. 425-455.
    • (1994) Biometrika , vol.81 , pp. 425-455
    • Donoho, D.L.1    Johnstone, I.M.2
  • 20
    • 0004052864 scopus 로고
    • Springer-Verlag, New York
    • T. HIDA, Brownian Motion, Springer-Verlag, New York, 1980.
    • (1980) Brownian Motion
    • Hida, T.1
  • 21
    • 0000319983 scopus 로고
    • Speed of estimation in positron emission tomography and related inverse problems
    • I.M. JOHNSTONE AND B.W. SILVERMAN, Speed of estimation in positron emission tomography and related inverse problems, Ann. Statist., 18 (1990), pp. 251-280.
    • (1990) Ann. Statist. , vol.18 , pp. 251-280
    • Johnstone, I.M.1    Silverman, B.W.2
  • 22
    • 0001855706 scopus 로고
    • Discretization effects in statistical inverse problems
    • I.M. JOHNSTONE AND B.W. SILVERMAN, Discretization effects in statistical inverse problems, J. Complexity, 7 (1991), pp. 1-34.
    • (1991) J. Complexity , vol.7 , pp. 1-34
    • Johnstone, I.M.1    Silverman, B.W.2
  • 23
    • 0003298461 scopus 로고
    • Minimax theory of image reconstruction
    • Springer-Verlag, New York
    • A. KOROSTELEV AND A. TSYBAKOV, Minimax Theory of Image Reconstruction, Lecture Notes in Statist. 82, Springer-Verlag, New York, 1993.
    • (1993) Lecture Notes in Statist. , vol.82
    • Korostelev, A.1    Tsybakov, A.2
  • 24
    • 0030269038 scopus 로고    scopus 로고
    • Statistical inverse estimation in Hilbert scales
    • B. MAIR AND F. RUYMGAART, Statistical inverse estimation in Hilbert scales, SIAM J. Appl. Math., 56 (1996), pp. 1424-1444.
    • (1996) SIAM J. Appl. Math. , vol.56 , pp. 1424-1444
    • Mair, B.1    Ruymgaart, F.2
  • 25
    • 6344283226 scopus 로고    scopus 로고
    • The mathematics of computerized tomography
    • SIAM, Philadelphia
    • F. NATTERER, The Mathematics of Computerized Tomography, Classics Appl. Math. 32, SIAM, Philadelphia, 2001.
    • (2001) Classics Appl. Math. , vol.32
    • Natterer, F.1
  • 27
    • 25444521451 scopus 로고    scopus 로고
    • Minimax rates for nonparametric drift estimation in affine stochastic delay differential equations
    • M. REIß, Minimax rates for nonparametric drift estimation in affine stochastic delay differential equations, Stat. Inference Stoch. Process., 5 (2002), pp. 131-152.
    • (2002) Stat. Inference Stoch. Process. , vol.5 , pp. 131-152
    • Reiß, M.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.