Free Access
Volume 14, 2010
Page(s) 409 - 434
Published online 22 December 2010
  1. A. Barron, L. Birgé and P. Massart, Risk bounds for model selection via penalization. Probab. Theory Relat. Fields 113 (1999) 301–413. [CrossRef] [MathSciNet]
  2. F. Bauer and T. Hohage, A Lepskij-type stopping rule for regularized Newton methods. Inv. Probab. 21 (2005) 1975–1991. [CrossRef]
  3. L. Birgé and P. Massart, Gaussian model selection. J. Eur. Math. Soc. 3 (2001) 203–268. [CrossRef] [MathSciNet]
  4. N. Bissantz, T. Hohage and A. Munk, Consistency and rates of convergence of nonlinear Tikhonov regularization with random noise. Inv. Probab. 20 (2004) 1773–1789. [CrossRef]
  5. N. Bissantz, G. Claeskens, H. Holzmann and A. Munk, Testing for lack of fit in inverse regression – with applications to biophotonic imaging. J. R. Stat. Soc. Ser. B 71 (2009) 25–48. [CrossRef] [MathSciNet]
  6. N. Bissantz, T. Hohage, A. Munk and F. Ryumgaart, Convergence rates of general regularization methods for statistical inverse problems and applications. SIAM J. Numer. Anal. 45 (2007) 2610–2636. [CrossRef] [MathSciNet] [PubMed]
  7. Y. Cao and Y. Golubev, On oracle inequalities related to smoothing splines. Math. Meth. Stat. 15 (2006) 398–414.
  8. L. Cavalier and Y. Golubev, Risk hull method and regularization by projections of ill-posed inverse problems. Ann. Statist. 34 (2006) 1653–1677. [CrossRef] [MathSciNet]
  9. L. Cavalier and A.B. Tsybakov, Sharp adaptation for inverse problems with random noise. Probab. Theory Relat. Fields 123 (2002) 323–354. [CrossRef]
  10. L. Cavalier, G.K. Golubev, D. Picard and A.B. Tsybakov, Oracle inequalities for inverse problems. Ann. Statist. 30 (2002) 843–874. [CrossRef] [MathSciNet]
  11. D.L. Donoho, Nonlinear solutions of linear inverse problems by wavelet-vaguelette decomposition. Appl. Comput. Harmon. Anal. 2 (1995) 101–126. [CrossRef] [MathSciNet]
  12. S. Efromovich, Robust and efficient recovery of a signal passed trough a filter and then contaminated by non-gaussian noise. IEEE Trans. Inf. Theory 43 (1997) 1184–1191. [CrossRef]
  13. H.W. Engl, On the choice of the regularization parameter for iterated Tikhonov regularization of ill-posed problems. J. Approx. Theory 49 (1987) 55–63. [CrossRef] [MathSciNet]
  14. H.W. Engl, M. Hanke and A. Neubauer, Regularization of Inverse Problems. Kluwer Academic Publishers Group, Dordrecht (1996).
  15. M.S Ermakov, Minimax estimation of the solution of an ill-posed convolution type problem. Probl. Inf. Transm. 25 (1989) 191–200.
  16. Yu. Golubev, The principle of penalized empirical risk in severely ill-posed problems. Theory Probab. Appl. 130 (2004) 18–38.
  17. M. Hanke, Accelerated Lanweber iterations for the solution of ill-posed equations. Numer. Math. 60 (1991) 341–373. [CrossRef] [MathSciNet]
  18. T. Hida, Brownian Motion. Springer-Verlag, New York-Berlin (1980).
  19. I.M. Johnstone and B.W. Silverman, Speed of estimation in positron emission tomography and related inverse problems. Ann. Statist. 18 (1990) 251–280. [CrossRef] [MathSciNet]
  20. I.M. Johnstone, G. Kerkyacharian, D. Picard and M. Raimondo, Wavelet deconvolution in a periodic setting. J. R. Stat. Soc. B 66 (2004) 547–573. [CrossRef]
  21. A. Kneip, Ordered linear smoother. Ann. Statist. 22 (1994) 835–866. [CrossRef] [MathSciNet]
  22. J.M Loubes and C. Ludena, Penalized estimators for non-linear inverse problems. ESAIM: PS 14 (2010) 173–191 [CrossRef] [EDP Sciences]
  23. C. Marteau, On the stability of the risk hull method for projection estimator. J. Stat. Plan. Inf. 139 (2009) 1821–1835. [CrossRef]
  24. P. Mathé, The Lepskij principle revisited. Inv. Probab. 22 (2006) L11–L15. [CrossRef]
  25. P. Mathé and S.V. Pereverzev, Optimal discretization of inverse problems in Hilbert scales. Regularization and self-regularization of projection methods. SIAM J. Numer. Anal. 38 (2001) 1999–2021. [CrossRef] [MathSciNet]
  26. D.N.G. Roy and L.S. Couchman, Inverse problems and inverse scattering of plane waves. Academic Press, San Diego (2002).

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