Free Access
| Issue |
ESAIM: PS
Volume 14, 2010
|
|
|---|---|---|
| Page(s) | 173 - 191 | |
| DOI | https://doi.org/10.1051/ps:2008024 | |
| Published online | 29 July 2010 | |
- Y. Baraud, Model selection for regression on a fixed design. Probab. Theory Relat. Fields 117 (2000) 467–493. [Google Scholar]
- L. Birgé and P. Massart, Minimal penalties for Gaussian model selection. Probab. Theory Relat. Fields. 138 (2007) 33–73. [Google Scholar]
- 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. [Google Scholar]
- 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. [Google Scholar]
- O. Bousquet, Concentration inequalities for sub-additive functions using the entropy method. Stoch. Inequalities Appl. 56 (2003) 213–247. [Google Scholar]
- 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] [Google Scholar]
- P. Chow and R. Khasminskii, Statistical approach to dynamical inverse problems. Commun. Math. Phys. 189 (1997) 521–531. [CrossRef] [Google Scholar]
- D. Donoho, Nonlinear solution of linear inverse problems by wavelet-vaguelette decomposition. Appl. Comput. Harmon. Anal. 2 (1995) 101–126. [Google Scholar]
- H. Engl, Regularization methods for solving inverse problems, in ICIAM 99 (Edinburgh), pp. 47–62. Oxford Univ. Press, Oxford (2000). [Google Scholar]
- H. Engl, M. Hanke and A. Neubauer, Regularization of inverse problems. Math. Appl. 375. Kluwer Academic Publishers Group, Dordrecht (1996). [Google Scholar]
- F. Gamboa, New Bayesian methods for ill posed problems. Statist. Decisions 17 (1999) 315–337. [MathSciNet] [Google Scholar]
- 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] [Google Scholar]
- J. Kalifa and S. Mallat, Thresholding estimators for linear inverse problems and deconvolutions. Ann. Statist. 31 (2003) 58–109. [Google Scholar]
- 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] [Google Scholar]
- J.-M. Loubes and C. Ludena, Adaptive complexity regularization for inverse problems. Electron. J. Statist. 2 (2008) 661–677. [Google Scholar]
- B. Mair and F. Ruymgaart, Statistical inverse estimation in Hilbert scales. SIAM J. Appl. Math. 56 (1996) 1424–1444. [Google Scholar]
- A. Neubauer, Tikhonov regularization of nonlinear ill-posed problems in Hilbert scales. Appl. Anal. 46 (1992) 59–72. [CrossRef] [MathSciNet] [Google Scholar]
- F. O'Sullivan, Convergence characteristics of methods of regularization estimators for nonlinear operator equations. SIAM J. Numer. Anal. 27 (1990) 1635–1649. [CrossRef] [MathSciNet] [Google Scholar]
- R. Snieder, An extension of Backus-Gilbert theory to nonlinear inverse problems. Inv. Prob. 7 (1991) 409–433. [CrossRef] [Google Scholar]
- 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] [Google Scholar]
- 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. [Google Scholar]
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.