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Volumn 86, Issue 1, 2003, Pages 72-96

Using wavelet methods to solve noisy Abel-type equations with discontinuous inputs

Author keywords

Abel transform; Convergence rate; Fourier inversion; Ill posed problem; Indirect curve estimation; Integral equation; Mean squared error; Piecewise continuous target; Wicksell's problem

Indexed keywords


EID: 0038454632     PISSN: 0047259X     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0047-259X(02)00043-X     Document Type: Article
Times cited : (11)

References (23)
  • 1
    • 0000521350 scopus 로고    scopus 로고
    • Wavelet decomposition approaches to statistical inverse problems
    • F. Abramovich, B.W. Silverman, Wavelet decomposition approaches to statistical inverse problems, Biometrika 85 (1998) 115-129.
    • (1998) Biometrika , vol.85 , pp. 115-129
    • Abramovich, F.1    Silverman, B.W.2
  • 2
    • 0037907127 scopus 로고
    • On the use of linear functionals for Abel-type integral equations in applications
    • R.S. Anderssen, F.R. de Hoog, M.A. Lukas (Eds.), Proceedings of a Seminar held at the Australian National University, Canberra, 1978; Monographs and Textbooks on Mechanics of Solids and Fluids: Mechanics and Analysis, Nijhoff, The Hague
    • R.S. Anderssen, On the use of linear functionals for Abel-type integral equations in applications, in: R.S. Anderssen, F.R. de Hoog, M.A. Lukas (Eds.), Application and Numerical Solution of Integral Equations, Proceedings of a Seminar held at the Australian National University, Canberra, 1978; Monographs and Textbooks on Mechanics of Solids and Fluids: Mechanics and Analysis, Vol. 6, Nijhoff, The Hague, 1980, pp. 195-221.
    • (1980) Application and Numerical Solution of Integral Equations , vol.6 , pp. 195-221
    • Anderssen, R.S.1
  • 3
    • 0013096937 scopus 로고
    • Abel integral equations
    • M.A. Goldberg (Ed.), Mathematical Concepts and Methods in Science and Engineering, Plenum, New York
    • R.S. Anderssen, F.R. De Hoog, Abel integral equations, in: M.A. Goldberg (Ed.), Numerical Solution of Integral Equations, Mathematical Concepts and Methods in Science and Engineering, Vol. 42, Plenum, New York, 1990, pp. 373-410.
    • (1990) Numerical Solution of Integral Equations , vol.42 , pp. 373-410
    • Anderssen, R.S.1    DeHoog, F.R.2
  • 4
    • 77957009494 scopus 로고
    • Linear inverse and ill-posed problems
    • M. Bertero, Linear inverse and ill-posed problems, Adv. Electron. Electron Phys. 75 (1989) 1-120.
    • (1989) Adv. Electron. Electron Phys. , vol.75 , pp. 1-120
    • Bertero, M.1
  • 7
    • 0029288068 scopus 로고
    • Nonlinear solutions of linear inverse problems by wavelet-vaguelette decomposition
    • D.L. Donoho, Nonlinear solutions of linear inverse problems by wavelet-vaguelette decomposition, Appl. Comput. Harmon. Anal. 2 (1995) 101-126.
    • (1995) Appl. Comput. Harmon. Anal. , vol.2 , pp. 101-126
    • Donoho, D.L.1
  • 8
    • 78751703099 scopus 로고
    • Kernel estimation in Wicksell's corpuscle problem
    • B. Van Es, A. Hoogendoorn, Kernel estimation in Wicksell's corpuscle problem, Biometrika 77 (1990) 139-145.
    • (1990) Biometrika , vol.77 , pp. 139-145
    • Van Es, B.1    Hoogendoorn, A.2
  • 9
    • 1542427456 scopus 로고    scopus 로고
    • Methods for density estimation in thick-slice versions of Wicksell's problem
    • A. Feuerverger, P. Hall, Methods for density estimation in thick-slice versions of Wicksell's problem, J. Amer. Statist. Assoc. 95 (2000) 535-546.
    • (2000) J. Amer. Statist. Assoc. , vol.95 , pp. 535-546
    • Feuerverger, A.1    Hall, P.2
  • 10
    • 0011103548 scopus 로고    scopus 로고
    • A new method of solving noisy Abel-type equations
    • J. Garza, P. Hall, F.H. Ruymgaart, A new method of solving noisy Abel-type equations, J. Math. Anal. Appl. 257 (2001) 403-419.
    • (2001) J. Math. Anal. Appl. , vol.257 , pp. 403-419
    • Garza, J.1    Hall, P.2    Ruymgaart, F.H.3
  • 12
    • 0037907126 scopus 로고    scopus 로고
    • Locally controllable regularization of Abel integral equations via operator complementation
    • R. Gorenflo, T. Medvedeva, B. Rubin, Locally controllable regularization of Abel integral equations via operator complementation, J. Inv. Ill-Posed Pr. 5 (1997) 427-436.
    • (1997) J. Inv. Ill-Posed Pr. , vol.5 , pp. 427-436
    • Gorenflo, R.1    Medvedeva, T.2    Rubin, B.3
  • 14
    • 0001249413 scopus 로고
    • Formulae for mean integrated squared error of nonlinear wavelet-based density estimators
    • P. Hall, P. Patil, Formulae for mean integrated squared error of nonlinear wavelet-based density estimators, Ann. Statist. 23 (1995) 905-928.
    • (1995) Ann. Statist. , vol.23 , pp. 905-928
    • Hall, P.1    Patil, P.2
  • 15
    • 0000761958 scopus 로고    scopus 로고
    • On the choice of smoothing parameter, threshold and truncation in nonparametric regression by non-linear wavelet methods
    • P. Hall, P. Patil, On the choice of smoothing parameter, threshold and truncation in nonparametric regression by non-linear wavelet methods, J. Roy. Statist. Soc. Ser. B 58 (1996) 361-377.
    • (1996) J. Roy. Statist. Soc. Ser. B , vol.58 , pp. 361-377
    • Hall, P.1    Patil, P.2
  • 16
    • 0001139608 scopus 로고
    • The kernel method for unfolding sphere size distributions
    • P. Hall, R.L. Smith, The kernel method for unfolding sphere size distributions, J. Comput. Phys. 74 (1988) 409-421.
    • (1988) J. Comput. Phys. , vol.74 , pp. 409-421
    • Hall, P.1    Smith, R.L.2
  • 17
    • 0041427275 scopus 로고    scopus 로고
    • Inverting noisy integral equations using wavelet expansions: A class of irregular convolutions
    • M.C.M. de Gunst, C.A.J. Klaassen, A.W. van der Vaart (Eds.), Festschrift in honour of W.R. van Zwet, IMS Lecture Notes-Monograph Series, Beachwood, California
    • P. Hall, F.H. Ruymgaart, O. Van Gaans, A.C.M. Van Rooij, Inverting noisy integral equations using wavelet expansions: a class of irregular convolutions, in: M.C.M. de Gunst, C.A.J. Klaassen, A.W. van der Vaart (Eds.), State of the Art in Probability and Statistics, Festschrift in honour of W.R. van Zwet, IMS Lecture Notes-Monograph Series, Vol. 36, Beachwood, California, 2001, pp. 533-546.
    • (2001) State of the Art in Probability and Statistics , vol.36 , pp. 533-546
    • Hall, P.1    Ruymgaart, F.H.2    Van Gaans, O.3    Van Rooij, A.C.M.4
  • 18
    • 0033408849 scopus 로고    scopus 로고
    • Wavelet shrinkage for correlated data and inverse problems
    • I.M. Johnstone, Wavelet shrinkage for correlated data and inverse problems, Statist. Sin. 9 (1999) 51-83.
    • (1999) Statist. Sin. , vol.9 , pp. 51-83
    • Johnstone, I.M.1
  • 23


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.