Comparisons of parameter choice methods for regularization with discrete noisy data

Inverse Problems

Volumn 14, Issue 1, 1998, Pages 161-184

  Lukas, Mark A ^a  

^a MURDOCH UNIVERSITY   (Australia)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0001595602     PISSN: 02665611     EISSN: None     Source Type: Journal    
DOI: 10.1088/0266-5611/14/1/014     Document Type: Article

References (29)

1. Cox D D 1988 Approximation of method of regularization estimators Ann. Stat. 16 694-712
2. Craven P and Wahba G 1979 Smoothing noisy data with spline functions Numer. Math. 31 377-403
3. Davies A R and Anderssen R S 1986 Improved estimates of statistical regularization parameters in Fourier differentiation and smoothing Numer. Math. 48 671-97
4. Davies A R and Anderssen R S 1986 Optimization in the regularization of ill-posed problems J. Austral. Math. Soc. Ser. B 28 114-33
5. Engl H W and Gfrerer H 1988 A posteriori parameter choice for general regularization methods for solving linear ill-posed problems Appl. Numer. Math. 4 395-417
6. Gfrerer H 1987 An a posteriori parameter choice for ordinary and iterated Tikhonov regularization of ill-posed problems leading to optimal convergence rates Math. Comput. 49 507-22
7. Gradshteyn I S and Ryzhek I M 1994 Tables of Integrals, Series, and Products (London: Academic)
8. Groetsch C W 1984 The Theory of Tikhonov Regularization for Fredholm Equations of the First Kind (London: Pitman)
9. Hansen P C 1990 The discrete Picard condition for discrete ill-posed problems BIT 30 658-72
10. L and generalized cross-validation in ridge regression with application to spline smoothing Ann. Stat. 14 1101-12
11. Lukas M A 1981 Regularization of linear operator equations, PhD Thesis Australian National University, Canberra
12. Lukas M A 1988 Convergence rates for regularized solutions Math. Comput. 51 107-31
13. Lukas M A 1992 Methods for choosing the regularization parameter Inverse Problems in Partial Differential Equations (Proc. the Centre for Mathematical Analysis) ed R S Anderssen and A K Pani (Canberra: Australian National University)
14. Lukas M A 1993 Asymptotic optimality of generalized cross-validation for choosing the regularization parameter Numer. Math. 66 41-66
15. Lukas M A 1995 On the discrepancy principle and generalized maximum likelihood for regularization Bull. Austral. Math. Soc. 52 399-424
16. Lukas M A 1995 Convergence rates for moment collocation solutions of linear operator equations Numer. Funct. Anal. Opt. 16 743-50
17. Lukas M A 1998 Asymptotic behaviour of the minimum bound method for choosing the regularization parameter Inverse Problems 14 149-59
18. Morozov V A 1966 On the solution of functional equations by the method of regularization Sov. Math. Dokl. 7414-17
19. Morozov V A 1993 Regularization Methods for Ill-posed Problems (Boca Raton, FL: Chemical Rubber Company)
20. Raus T 1984 On the discrepancy principle for the solution of ill-posed problems Uch. Zap. Tartu Gos. Univ. 672 16-26 (in Russian)
21. Raus T 1984 On the residue principle for the solution of ill-posed problems with non-selfadjoint operator Uch. Zap. Tartu Gos. Univ. 715 12-20 (in Russian)
22. Speckman P 1985 Spline smoothing and optimal rates of convergence in nonparametric regression Ann. Stat. 13 970-83
23. Utreras F 1987 On generalized cross-validation for multivariate smoothing spline functions SIAM J. Sci. Stat. Comput. 8 630-43
24. Wahba G 1973 Convergence rates of certain approximate solutions to linear operator equations of the first kind J. Approx. Theory 7 167-85
25. Wahba G 1975 Smoothing noisy data by spline functions Numer. Math. 24 383-93
26. Wahba G 1977 Practical approximate solutions to linear operator equations when the data are noisy SIAM J. Numer. Anal. 14 651-67
27. Wahba G 1982 Constrained regularization for ill-posed linear operator equations, with applications in meteorology and medicine Statistical Decision Theory and Related Topics vol III, ed S S Gupta and J O Berger (New York: Academic)
28. Wahba G 1985 A comparison of GCV and GML for choosing the smoothing parameter in the generalized spline smoothing problem Ann. Stat. 13 1378-402
29. Wahba G 1990 Spline Models for Observational Data (Philadelphia, PA: SIAM)