Free Access
Issue
ESAIM: PS
Volume 14, 2010
Page(s) 409 - 434
DOI https://doi.org/10.1051/ps/2009011
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] [Google Scholar]
  2. F. Bauer and T. Hohage, A Lepskij-type stopping rule for regularized Newton methods. Inv. Probab. 21 (2005) 1975–1991. [CrossRef] [Google Scholar]
  3. L. Birgé and P. Massart, Gaussian model selection. J. Eur. Math. Soc. 3 (2001) 203–268. [CrossRef] [MathSciNet] [Google Scholar]
  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] [Google Scholar]
  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] [Google Scholar]
  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] [Google Scholar]
  7. Y. Cao and Y. Golubev, On oracle inequalities related to smoothing splines. Math. Meth. Stat. 15 (2006) 398–414. [Google Scholar]
  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] [Google Scholar]
  9. L. Cavalier and A.B. Tsybakov, Sharp adaptation for inverse problems with random noise. Probab. Theory Relat. Fields 123 (2002) 323–354. [CrossRef] [Google Scholar]
  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] [Google Scholar]
  11. D.L. Donoho, Nonlinear solutions of linear inverse problems by wavelet-vaguelette decomposition. Appl. Comput. Harmon. Anal. 2 (1995) 101–126. [CrossRef] [MathSciNet] [Google Scholar]
  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] [Google Scholar]
  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] [Google Scholar]
  14. H.W. Engl, M. Hanke and A. Neubauer, Regularization of Inverse Problems. Kluwer Academic Publishers Group, Dordrecht (1996). [Google Scholar]
  15. M.S Ermakov, Minimax estimation of the solution of an ill-posed convolution type problem. Probl. Inf. Transm. 25 (1989) 191–200. [Google Scholar]
  16. Yu. Golubev, The principle of penalized empirical risk in severely ill-posed problems. Theory Probab. Appl. 130 (2004) 18–38. [Google Scholar]
  17. M. Hanke, Accelerated Lanweber iterations for the solution of ill-posed equations. Numer. Math. 60 (1991) 341–373. [CrossRef] [MathSciNet] [Google Scholar]
  18. T. Hida, Brownian Motion. Springer-Verlag, New York-Berlin (1980). [Google Scholar]
  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] [Google Scholar]
  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] [Google Scholar]
  21. A. Kneip, Ordered linear smoother. Ann. Statist. 22 (1994) 835–866. [CrossRef] [MathSciNet] [Google Scholar]
  22. J.M Loubes and C. Ludena, Penalized estimators for non-linear inverse problems. ESAIM: PS 14 (2010) 173–191 [CrossRef] [EDP Sciences] [Google Scholar]
  23. C. Marteau, On the stability of the risk hull method for projection estimator. J. Stat. Plan. Inf. 139 (2009) 1821–1835. [CrossRef] [Google Scholar]
  24. P. Mathé, The Lepskij principle revisited. Inv. Probab. 22 (2006) L11–L15. [CrossRef] [Google Scholar]
  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] [Google Scholar]
  26. D.N.G. Roy and L.S. Couchman, Inverse problems and inverse scattering of plane waves. Academic Press, San Diego (2002). [Google Scholar]

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