Free Access
Volume 14, 2010
Page(s) 173 - 191
Published online 29 July 2010
  1. Y. Baraud, Model selection for regression on a fixed design. Probab. Theory Relat. Fields 117 (2000) 467–493. [CrossRef] [MathSciNet]
  2. L. Birgé and P. Massart, Minimal penalties for Gaussian model selection. Probab. Theory Relat. Fields. 138 (2007) 33–73.
  3. N. Bissantz, T. Hohage and A. Munk, Consistency and rates of convergence of nonlinear Tikhonov regularization with random noise. Inv. Prob. 20 (2004) 1773–1789.
  4. N. Bissantz, T. Hohage, A. Munk and F. Ruymgaart, Convergence rates of general regularization methods for statistical inverse problems and applications. SIAM J. Numer. Anal. 45 (2007) 2610–2636. [CrossRef] [MathSciNet] [PubMed]
  5. O. Bousquet, Concentration inequalities for sub-additive functions using the entropy method. Stoch. Inequalities Appl. 56 (2003) 213–247.
  6. L. Cavalier, G.K. Golubev, D. Picard and A.B. Tsybakov, Oracle inequalities for inverse problems. Ann. Statist. 30 (2002) 843–874. Dedicated to the memory of Lucien Le Cam. [CrossRef] [MathSciNet]
  7. P. Chow and R. Khasminskii, Statistical approach to dynamical inverse problems. Commun. Math. Phys. 189 (1997) 521–531. [CrossRef]
  8. D. Donoho, Nonlinear solution of linear inverse problems by wavelet-vaguelette decomposition. Appl. Comput. Harmon. Anal. 2 (1995) 101–126. [CrossRef] [MathSciNet]
  9. H. Engl, Regularization methods for solving inverse problems, in ICIAM 99 (Edinburgh), pp. 47–62. Oxford Univ. Press, Oxford (2000).
  10. H. Engl, M. Hanke and A. Neubauer, Regularization of inverse problems. Math. Appl. 375. Kluwer Academic Publishers Group, Dordrecht (1996).
  11. F. Gamboa, New Bayesian methods for ill posed problems. Statist. Decisions 17 (1999) 315–337. [MathSciNet]
  12. Q. Jin and U. Amato, A discrete scheme of Landweber iteration for solving nonlinear ill-posed problems. J. Math. Anal. Appl. 253 (2001) 187–203. [CrossRef] [MathSciNet]
  13. J. Kalifa and S. Mallat, Thresholding estimators for linear inverse problems and deconvolutions. Ann. Statist. 31 (2003) 58–109. [CrossRef] [MathSciNet]
  14. B. Kaltenbacher, Regularization by projection with a posteriori discretization level choice for linear and nonlinear ill-posed problems. Inv. Prob. 16 (2000) 1523–1539. [CrossRef]
  15. J.-M. Loubes and C. Ludena, Adaptive complexity regularization for inverse problems. Electron. J. Statist. 2 (2008) 661–677. [CrossRef]
  16. B. Mair and F. Ruymgaart, Statistical inverse estimation in Hilbert scales. SIAM J. Appl. Math. 56 (1996) 1424–1444. [CrossRef] [MathSciNet]
  17. A. Neubauer, Tikhonov regularization of nonlinear ill-posed problems in Hilbert scales. Appl. Anal. 46 (1992) 59–72. [CrossRef] [MathSciNet]
  18. F. O'Sullivan, Convergence characteristics of methods of regularization estimators for nonlinear operator equations. SIAM J. Numer. Anal. 27 (1990) 1635–1649. [CrossRef] [MathSciNet]
  19. R. Snieder, An extension of Backus-Gilbert theory to nonlinear inverse problems. Inv. Prob. 7 (1991) 409–433. [CrossRef]
  20. U. Tautenhahn and Qi-nian Jin, Tikhonov regularization and a posteriori rules for solving nonlinear ill posed problems. Inv. Prob. 19 (2003) 1–21. [CrossRef]
  21. A.N. Tikhonov, A.S. Leonov and A.G. Yagola, Nonlinear ill-posed problems, volumes 1 and 2. Appl. Math. Math. Comput. 14. Chapman & Hall, London (1998). Translated from the Russian.

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