메뉴 건너뛰기




Volumn 48, Issue 1, 2011, Pages 47-59

Comparison of parameter choices in regularization algorithms in case of different information about noise level

Author keywords

Extrapolated Tikhonov method; Ill posed problem; Landweber method; Noise level; Regularization; Regularization parameter choice; Tikhonov method

Indexed keywords

EXTRAPOLATION; PROBLEM SOLVING;

EID: 79952281304     PISSN: 00080624     EISSN: None     Source Type: Journal    
DOI: 10.1007/s10092-010-0027-4     Document Type: Article
Times cited : (31)

References (33)
  • 1
    • 0013178793 scopus 로고
    • Remarks on choosing a regularization parameter using the quasi-optimality and ratio criterion
    • Bakushinskii, A. B.: Remarks on choosing a regularization parameter using the quasi-optimality and ratio criterion. Comp. Math. Math. Phys. 24(4), 181-182 (1984).
    • (1984) Comp. Math. Math. Phys. , vol.24 , Issue.4 , pp. 181-182
    • Bakushinskii, A.B.1
  • 2
    • 44449090402 scopus 로고    scopus 로고
    • The quasi-optimality criterion for classical inverse problems
    • 035002
    • Bauer, F., Kindermann, S.: The quasi-optimality criterion for classical inverse problems. Inverse Probl. 24, 035002 (2008).
    • (2008) Inverse Probl. , vol.24
    • Bauer, F.1    Kindermann, S.2
  • 3
    • 59449104380 scopus 로고    scopus 로고
    • Recent results on the quasi-optimality principle
    • Bauer, F., Kindermann, S.: Recent results on the quasi-optimality principle. J. Inverse Ill-Posed Probl. 17(1), 5-18 (2009).
    • (2009) J. Inverse Ill-Posed Probl. , vol.17 , Issue.1 , pp. 5-18
    • Bauer, F.1    Kindermann, S.2
  • 5
    • 0039530583 scopus 로고    scopus 로고
    • Extrapolation techniques for ill-conditioned linear systems
    • Brezinski, C., Redivo-Zaglia, M., Rodriguez, G., Seatzu, S.: Extrapolation techniques for ill-conditioned linear systems. Numer. Math. 81(1), 1-29 (1998).
    • (1998) Numer. Math. , vol.81 , Issue.1 , pp. 1-29
    • Brezinski, C.1    Redivo-Zaglia, M.2    Rodriguez, G.3    Seatzu, S.4
  • 6
    • 0142023207 scopus 로고    scopus 로고
    • Multi-parameter regularization techniques for ill-conditioned linear systems
    • Brezinski, C., Redivo-Zaglia, M., Rodriguez, G., Seatzu, S.: Multi-parameter regularization techniques for ill-conditioned linear systems. Numer. Math. 94(2), 203-228 (2003).
    • (2003) Numer. Math. , vol.94 , Issue.2 , pp. 203-228
    • Brezinski, C.1    Redivo-Zaglia, M.2    Rodriguez, G.3    Seatzu, S.4
  • 7
    • 55349117124 scopus 로고    scopus 로고
    • Error estimates for linear systems with applications to regularization
    • Brezinski, C., Rodriguez, G., Seatzu, S.: Error estimates for linear systems with applications to regularization. Numer. Algorithms 49(14), 85-104 (2008).
    • (2008) Numer. Algorithms , vol.49 , Issue.14 , pp. 85-104
    • Brezinski, C.1    Rodriguez, G.2    Seatzu, S.3
  • 9
    • 44449103413 scopus 로고
    • On the quasioptimality principle for linear ill-posed problems in Hilbert space
    • In Russian
    • Glasko, V., Kriksin, Y.: On the quasioptimality principle for linear ill-posed problems in Hilbert space. Zh. Vychisl. Mat. Mat. Fiz. 24(11), 1603-1613 (1984) In Russian.
    • (1984) Zh. Vychisl. Mat. Mat. Fiz. , vol.24 , Issue.11 , pp. 1603-1613
    • Glasko, V.1    Kriksin, Y.2
  • 10
    • 33947697784 scopus 로고    scopus 로고
    • On rules for stopping the conjugate gradient type methods in ill-posed problems
    • Hämarik, U., Palm, R.: On rules for stopping the conjugate gradient type methods in ill-posed problems. Math. Model. Anal. 12(1), 61-70 (2007).
    • (2007) Math. Model. Anal. , vol.12 , Issue.1 , pp. 61-70
    • Hämarik, U.1    Palm, R.2
  • 11
    • 34547285727 scopus 로고    scopus 로고
    • Use of extrapolation in regularization methods
    • Hämarik, U., Palm, R., Raus, T.: Use of extrapolation in regularization methods. J. Inverse Ill-Posed Probl. 15(3), 277-294 (2007).
    • (2007) J. Inverse Ill-Posed Probl. , vol.15 , Issue.3 , pp. 277-294
    • Hämarik, U.1    Palm, R.2    Raus, T.3
  • 12
    • 73449093887 scopus 로고    scopus 로고
    • On minimization strategies for choice of the regularization parameter in ill-posed problems
    • Hämarik, U., Palm, R., Raus, T.: On minimization strategies for choice of the regularization parameter in ill-posed problems. Numer. Funct. Anal. Optim. 30(9-10), 924-950 (2009).
    • (2009) Numer. Funct. Anal. Optim. , vol.30 , Issue.9-10 , pp. 924-950
    • Hämarik, U.1    Palm, R.2    Raus, T.3
  • 13
    • 77951703736 scopus 로고    scopus 로고
    • Extrapolation of Tikhonov regularization method
    • Hämarik, U., Palm, R., Raus, T.: Extrapolation of Tikhonov regularization method. Math. Model. Anal. 15(1), 55-68 (2010).
    • (2010) Math. Model. Anal. , vol.15 , Issue.1 , pp. 55-68
    • Hämarik, U.1    Palm, R.2    Raus, T.3
  • 14
    • 21944449591 scopus 로고    scopus 로고
    • Choice of the regularization parameter in ill-posed problems with rough estimate of the noise level of data
    • Hämarik, U., Raus, T.: Choice of the regularization parameter in ill-posed problems with rough estimate of the noise level of data. WSEAS Trans. Math. 4(2), 76-81 (2005).
    • (2005) WSEAS Trans. Math. , vol.4 , Issue.2 , pp. 76-81
    • Hämarik, U.1    Raus, T.2
  • 15
    • 33745766913 scopus 로고    scopus 로고
    • On the choice of the regularization parameter in ill-posed problems with approximately given noise level of data
    • Hämarik, U., Raus, T.: On the choice of the regularization parameter in ill-posed problems with approximately given noise level of data. J. Inverse Ill-Posed Probl. 14(3), 251-266 (2006).
    • (2006) J. Inverse Ill-Posed Probl. , vol.14 , Issue.3 , pp. 251-266
    • Hämarik, U.1    Raus, T.2
  • 16
    • 21944442815 scopus 로고    scopus 로고
    • On the monotone error rule for parameter choice in iterative and continuous regularization methods
    • Hämarik, U., Tautenhahn, U.: On the monotone error rule for parameter choice in iterative and continuous regularization methods. BIT Numer. Math. 41(5), 1029-1038 (2001).
    • (2001) BIT Numer. Math. , vol.41 , Issue.5 , pp. 1029-1038
    • Hämarik, U.1    Tautenhahn, U.2
  • 17
    • 0032400284 scopus 로고    scopus 로고
    • Nonstationary iterated Tikhonov regularization
    • Hanke, M., Groetsch, C. W.: Nonstationary iterated Tikhonov regularization. J. Optim. Theory Appl. 98(1), 37-53 (1998).
    • (1998) J. Optim. Theory Appl. , vol.98 , Issue.1 , pp. 37-53
    • Hanke, M.1    Groetsch, C.W.2
  • 18
    • 0042208667 scopus 로고    scopus 로고
    • A general heuristic for choosing the regularization parameter in ill-posed problems
    • Hanke, M., Raus, T.: A general heuristic for choosing the regularization parameter in ill-posed problems. SIAM J. Sci. Comput. 17(4), 956-972 (1996).
    • (1996) SIAM J. Sci. Comput. , vol.17 , Issue.4 , pp. 956-972
    • Hanke, M.1    Raus, T.2
  • 19
    • 0000570697 scopus 로고
    • Analysis of discrete ill-posed problems by means of the L-curve
    • Hansen, P. C.: Analysis of discrete ill-posed problems by means of the L-curve. SIAM Rev. 34(4), 561-580 (1992).
    • (1992) SIAM Rev. , vol.34 , Issue.4 , pp. 561-580
    • Hansen, P.C.1
  • 20
    • 13344267706 scopus 로고
    • Regularization tools: A Matlab package for analysis and solution of discrete ill-posed problems
    • Hansen, P. C.: Regularization tools: A Matlab package for analysis and solution of discrete ill-posed problems. Numer. Algorithms 6(1), 1-35 (1994).
    • (1994) Numer. Algorithms , vol.6 , Issue.1 , pp. 1-35
    • Hansen, P.C.1
  • 21
    • 77956038243 scopus 로고    scopus 로고
    • Heuristic parameter-choice rules for convex variational regularization based on error estimates
    • Jin, B., Lorenz, D. A.: Heuristic parameter-choice rules for convex variational regularization based on error estimates. SIAM J. Numer. Anal. 48(3), 1208-1229 (2010).
    • (2010) SIAM J. Numer. Anal. , vol.48 , Issue.3 , pp. 1208-1229
    • Jin, B.1    Lorenz, D.A.2
  • 22
    • 54749153001 scopus 로고    scopus 로고
    • On the convergence of the quasioptimality criterion for (iterated) Tikhonov regularization
    • Kindermann, S., Neubauer, A.: On the convergence of the quasioptimality criterion for (iterated) Tikhonov regularization. Inverse Probl. Imaging 2(2), 291-299 (2008).
    • (2008) Inverse Probl. Imaging , vol.2 , Issue.2 , pp. 291-299
    • Kindermann, S.1    Neubauer, A.2
  • 23
    • 0000739264 scopus 로고
    • On the solution of functional equations by the method of regularization
    • Morozov, V. A.: On the solution of functional equations by the method of regularization. Sov. Math. Dokl. 7, 414-417 (1966).
    • (1966) Sov. Math. Dokl. , vol.7 , pp. 414-417
    • Morozov, V.A.1
  • 24
    • 54749127344 scopus 로고    scopus 로고
    • The convergence of a new heuristic parameter selection criterion for general regularization methods
    • 055005
    • Neubauer, A.: The convergence of a new heuristic parameter selection criterion for general regularization methods. Inverse Probl. 24, 055005 (2008).
    • (2008) Inverse Probl. , vol.24
    • Neubauer, A.1
  • 26
    • 73449089367 scopus 로고    scopus 로고
    • New rule for choice of the regularization parameter in (iterated) Tikhonov method
    • Raus, T., Hämarik, U.: New rule for choice of the regularization parameter in (iterated) Tikhonov method. Math. Model. Anal. 14(2), 187-198 (2009).
    • (2009) Math. Model. Anal. , vol.14 , Issue.2 , pp. 187-198
    • Raus, T.1    Hämarik, U.2
  • 27
    • 0013298158 scopus 로고    scopus 로고
    • The use of monotonicity for choosing the regularization parameter in ill-posed problems
    • Tautenhahn, U., Hämarik, U.: The use of monotonicity for choosing the regularization parameter in ill-posed problems. Inverse Probl. 15(6), 1487-1505 (1999).
    • (1999) Inverse Probl. , vol.15 , Issue.6 , pp. 1487-1505
    • Tautenhahn, U.1    Hämarik, U.2
  • 29
    • 6544255866 scopus 로고
    • On the question of quasioptimal choice of a regularized approximation
    • Tikhonov, A. N., Glasko, V. B., Kriksin, Y.: On the question of quasioptimal choice of a regularized approximation. Sov. Math. Dokl. 20, 1036-1040 (1979).
    • (1979) Sov. Math. Dokl. , vol.20 , pp. 1036-1040
    • Tikhonov, A.N.1    Glasko, V.B.2    Kriksin, Y.3
  • 31
    • 0011481293 scopus 로고
    • The discrepancy principle for a class of regularization methods
    • Vainikko, G. M.: The discrepancy principle for a class of regularization methods. USSR Comput. Math. Math. Phys. 22(3), 1-19 (1982).
    • (1982) USSR Comput. Math. Math. Phys. , vol.22 , Issue.3 , pp. 1-19
    • Vainikko, G.M.1
  • 33
    • 0000544453 scopus 로고
    • Practical approximate solutions to linear operator equations when the data are noisy
    • Wahba, G.: Practical approximate solutions to linear operator equations when the data are noisy. SIAM J. Numer. Anal. 14(4), 651-657 (1977).
    • (1977) SIAM J. Numer. Anal. , vol.14 , Issue.4 , pp. 651-657
    • Wahba, G.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.