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Volumn 7, Issue 1, 2001, Pages 63-78

On the problem of local adaptive estimation in tomography

Author keywords

Adaptive methods; Radon transform

Indexed keywords


EID: 0010915732     PISSN: 13507265     EISSN: None     Source Type: Journal    
DOI: 10.2307/3318602     Document Type: Article
Times cited : (12)

References (22)
  • 1
    • 0030327799 scopus 로고    scopus 로고
    • A constrained risk inequality with applications to nonparametric functional estimation
    • Brown, L.D. and Low, M.G. (1996) A constrained risk inequality with applications to nonparametric functional estimation. Ann. Statist., 24, 2524-2535.
    • (1996) Ann. Statist. , vol.24 , pp. 2524-2535
    • Brown, L.D.1    Low, M.G.2
  • 2
    • 0029288068 scopus 로고
    • Nonlinear solution of linear inverse problems by wavelet-vaguelette decomposition
    • Donoho, D.L. (1995) Nonlinear solution of linear inverse problems by wavelet-vaguelette decomposition. Appl. Comput. Harmon. Anal., 2, 101 -126.
    • (1995) Appl. Comput. Harmon. Anal. , vol.2 , pp. 101-126
    • Donoho, D.L.1
  • 3
    • 0041958932 scopus 로고
    • Ideal spatial adaptation by wavelet shrinkage
    • Donoho, D.L. and Johnstone, I.M. (1994) Ideal spatial adaptation by wavelet shrinkage. Biometrika, 81, 425-455.
    • (1994) Biometrika , vol.81 , pp. 425-455
    • Donoho, D.L.1    Johnstone, I.M.2
  • 4
    • 0001573354 scopus 로고
    • Renormalization exponents and optimal pointwise rates of convergence
    • Donoho, D.L. and Low, M.G. (1992) Renormalization exponents and optimal pointwise rates of convergence. Ann. Statist., 20, 944-970.
    • (1992) Ann. Statist. , vol.20 , pp. 944-970
    • Donoho, D.L.1    Low, M.G.2
  • 6
    • 84904776239 scopus 로고
    • Learning algorithm for nonparametric filtering
    • Efroimovich, S.Yu. and Pinsker, M.S. (1984) Learning algorithm for nonparametric filtering. Automat. Remote Control, 45, 1434-1440.
    • (1984) Automat. Remote Control , vol.45 , pp. 1434-1440
    • Efroimovich, S.Yu.1    Pinsker, M.S.2
  • 7
    • 0031188112 scopus 로고    scopus 로고
    • Robust and efficient recovery of a signal passed through a filter and then contaminated by non-Gaussian noise
    • Efromovich, S. (1997) Robust and efficient recovery of a signal passed through a filter and then contaminated by non-Gaussian noise. IEEE Trans. Inform. Tlieory, 43, 1184-1191.
    • (1997) IEEE Trans. Inform. Tlieory , vol.43 , pp. 1184-1191
    • Efromovich, S.1
  • 8
    • 0000937636 scopus 로고    scopus 로고
    • On pointwise adaptive nonparametric deconvolution
    • Goldenshluger, A. (1999) On pointwise adaptive nonparametric deconvolution. Bernoulli, 5, 907-925.
    • (1999) Bernoulli , vol.5 , pp. 907-925
    • Goldenshluger, A.1
  • 9
    • 0001208998 scopus 로고
    • Adaptive spline estimates for nonparametric regression models
    • Golubev, G.K. and Nussbaum, M. (1992) Adaptive spline estimates for nonparametric regression models. Theory Probab. Appl., 37, 521-529.
    • (1992) Theory Probab. Appl. , vol.37 , pp. 521-529
    • Golubev, G.K.1    Nussbaum, M.2
  • 11
    • 0033408849 scopus 로고    scopus 로고
    • Wavelet shrinkage for correlated data and inverse problems: Adaptivity results
    • Johnstone, I.M. (1999) Wavelet shrinkage for correlated data and inverse problems: adaptivity results. Statist. Sinica, 9, 51-83.
    • (1999) Statist. Sinica , vol.9 , pp. 51-83
    • Johnstone, I.M.1
  • 12
    • 0000319983 scopus 로고
    • Speed of estimation in positron emission tomography and related inverse problems
    • Johnstone, I.M. and Silverman, B.W. (1990) Speed of estimation in positron emission tomography and related inverse problems. Ann. Statist., 18, 251-280.
    • (1990) Ann. Statist. , vol.18 , pp. 251-280
    • Johnstone, I.M.1    Silverman, B.W.2
  • 13
    • 0026187782 scopus 로고
    • Optimal rates of convergence of estimators in a probabilistic setup of tomography problem
    • Korostelev, A.P. and Tsybakov, A.B. (1991) Optimal rates of convergence of estimators in a probabilistic setup of tomography problem. Problems Inform. Transmission, 27, 73-81.
    • (1991) Problems Inform. Transmission , vol.27 , pp. 73-81
    • Korostelev, A.P.1    Tsybakov, A.B.2
  • 15
    • 0031504935 scopus 로고    scopus 로고
    • Optimal spatial adaptation to inhomogeneous smoothness: An approach based on kernel estimates with variable bandwith selectors
    • Lepski, O.V., Mammen, E. and Spokoiny, V.G. (1997) Optimal spatial adaptation to inhomogeneous smoothness: an approach based on kernel estimates with variable bandwith selectors. Ann. Statist., 25, 929-947.
    • (1997) Ann. Statist. , vol.25 , pp. 929-947
    • Lepski, O.V.1    Mammen, E.2    Spokoiny, V.G.3
  • 16
    • 0040795080 scopus 로고
    • Local adaptation to inhomogeneous smoothness: Resolution level
    • Lepski, O.V and Spokoiny, VG. (1995) Local adaptation to inhomogeneous smoothness: Resolution level. Math. Methods Statist., 4, 239-258.
    • (1995) Math. Methods Statist. , vol.4 , pp. 239-258
    • Lepski, O.V.1    Spokoiny, V.G.2
  • 17
    • 0031327277 scopus 로고    scopus 로고
    • Optimal pointwise adaptive methods in nonparametric estimation
    • Lepski, O.V. and Spokoiny, V.O. (1997) Optimal pointwise adaptive methods in nonparametric estimation. Ann. Statist., 25, 2512-2546.
    • (1997) Ann. Statist. , vol.25 , pp. 2512-2546
    • Lepski, O.V.1    Spokoiny, V.O.2
  • 18
    • 0000012624 scopus 로고
    • On a problem of adaptive estimation in Gaussian white noise
    • Lepskii, O.V. (1990) On a problem of adaptive estimation in Gaussian white noise. Theory Probab. Appl., 35, 454-466.
    • (1990) Theory Probab. Appl. , vol.35 , pp. 454-466
    • Lepskii, O.V.1
  • 19
    • 0019243247 scopus 로고
    • A Sobolev space analysis of picture recognition
    • Natterer, F. (1980) A Sobolev space analysis of picture recognition. SIAM J. Appl. Math., 39, 402-411.
    • (1980) SIAM J. Appl. Math. , vol.39 , pp. 402-411
    • Natterer, F.1
  • 21
    • 84972545853 scopus 로고
    • A statistical perspective on ill-posed inverse problems
    • O'Sullivan, F. (1986) A statistical perspective on ill-posed inverse problems. Statist. Sci., 1, 502-527.
    • (1986) Statist. Sci. , vol.1 , pp. 502-527
    • O'Sullivan, F.1
  • 22
    • 0032243618 scopus 로고    scopus 로고
    • Pointwise and sup-norm sharp adaptive estimation of functions on the Sobolev classes
    • Tsybakov, A.B. (1998) Pointwise and sup-norm sharp adaptive estimation of functions on the Sobolev classes. Ann. Statist., 26, 2420-2469.
    • (1998) Ann. Statist. , vol.26 , pp. 2420-2469
    • Tsybakov, A.B.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.