Case Studies and a Pitfall for Nonlinear Variational Regularization Under Conditional Stability
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[1] G. Burton. Sobolev Spaces , 2013 .
[2] A. Louis. Inverse und schlecht gestellte Probleme , 1989 .
[3] Ulrich Tautenhahn,et al. On a general regularization scheme for nonlinear ill-posed problems: II. Regularization in Hilbert scales , 1998 .
[4] M. Grasmair. Generalized Bregman distances and convergence rates for non-convex regularization methods , 2010 .
[5] F. Natterer. Error bounds for tikhonov regularization in hilbert scales , 1984 .
[6] Rudolf Gorenflo,et al. Operator theoretic treatment of linear Abel integral equations of first kind , 1999 .
[7] Peter Mathé,et al. Enhancing linear regularization to treat large noise , 2011 .
[8] Bernd Hofmann,et al. Optimal rates for Lavrentiev regularization with adjoint source conditions , 2017, Math. Comput..
[9] S. Kindermann. Convex Tikhonov regularization in Banach spaces: New results on convergence rates , 2015 .
[10] B. Hofmann,et al. Tikhonov regularization in Hilbert scales under conditional stability assumptions , 2018, Inverse Problems.
[11] Barbara Kaltenbacher,et al. A note on logarithmic convergence rates for nonlinear Tikhonov regularization , 2008 .
[12] D. Lorenz,et al. Convergence rates and source conditions for Tikhonov regularization with sparsity constraints , 2008, 0801.1774.
[13] Shuai Lu,et al. The index function and Tikhonov regularization for ill-posed problems , 2014, J. Comput. Appl. Math..
[14] B. Hofmann,et al. Tikhonov regularization with oversmoothing penalty for non-linear ill-posed problems in Hilbert scales , 2017, 1705.03289.
[15] T. Hohage,et al. Variational source conditions and stability estimates for inverse electromagnetic medium scattering problems , 2015, 1512.06586.
[16] Andreas Neubauer,et al. When do Sobolev spaces form a Hilbert scale , 1988 .
[17] Thorsten Hohage,et al. Verification of a variational source condition for acoustic inverse medium scattering problems , 2015, 1503.05763.
[18] Bernd Hofmann,et al. An extension of the variational inequality approach for obtaining convergence rates in regularization of nonlinear ill-posed problems , 2010 .
[19] Bernd Hofmann,et al. On autoconvolution and regularization , 1994 .
[20] Thorsten Hohage,et al. Characterizations of Variational Source Conditions, Converse Results, and Maxisets of Spectral Regularization Methods , 2016, SIAM J. Numer. Anal..
[21] Martin Burger,et al. Convergence rates in $\mathbf{\ell^1}$-regularization if the sparsity assumption fails , 2012 .
[22] Masahiro Yamamoto,et al. LETTER TO THE EDITOR: One new strategy for a priori choice of regularizing parameters in Tikhonov's regularization , 2000 .
[23] B. Hofmann,et al. A Priori Parameter Choice in Tikhonov Regularization with Oversmoothing Penalty for Non-linear Ill-Posed Problems , 2018, Springer Proceedings in Mathematics & Statistics.
[24] Thorsten Hohage,et al. Convergence rates in expectation for Tikhonov-type regularization of inverse problems with Poisson data , 2012, 1204.1669.
[25] B. Hofmann,et al. Penalty-based smoothness conditions in convex variational regularization , 2018, Journal of Inverse and Ill-posed Problems.
[26] Andreas Neubauer,et al. On Landweber iteration for nonlinear ill-posed problems in Hilbert scales , 2000, Numerische Mathematik.
[27] C. W. Groetsch,et al. Inverse Problems in the Mathematical Sciences , 1993 .
[28] Andreas Neubauer,et al. Tikhonov regularization of nonlinear III-posed problems in hilbert scales , 1992 .
[29] Bernd Hofmann,et al. Parameter choice in Banach space regularization under variational inequalities , 2012 .
[31] Yu. I. Petunin,et al. SCALES OF BANACH SPACES , 1966 .
[32] Jens Flemming. Existence of variational source conditions for nonlinear inverse problems in Banach spaces , 2017 .
[33] U Tautenhahn,et al. Error estimates for regularized solutions of non-linear ill-posed problems , 1994 .
[35] A. Tikhonov,et al. Nonlinear Ill-Posed Problems , 1997 .
[36] Bernd Hofmann,et al. On ill-posedness concepts, stable solvability and saturation , 2017, 1709.01109.
[37] Lea Fleischer,et al. Regularization of Inverse Problems , 1996 .
[38] Bernd Hofmann,et al. About a deficit in low-order convergence rates on the example of autoconvolution , 2015 .
[39] Masahiro Yamamoto,et al. Time-fractional diffusion equation in the fractional Sobolev spaces , 2015 .
[40] M. Hanke,et al. A convergence analysis of the Landweber iteration for nonlinear ill-posed problems , 1995 .
[41] Otmar Scherzer,et al. Factors influencing the ill-posedness of nonlinear problems , 1994 .
[42] Bernd Hofmann,et al. Regularization properties of the sequential discrepancy principle for Tikhonov regularization in Banach spaces , 2014 .
[43] Thorsten Hohage,et al. Optimal Convergence Rates for Tikhonov Regularization in Besov Spaces , 2020, SIAM J. Numer. Anal..
[44] Oversmoothing regularization with $\ell^1$-penalty term , 2019, AIMS Mathematics.
[45] Bernd Hofmann,et al. On the interplay of source conditions and variational inequalities for nonlinear ill-posed problems , 2010 .
[46] Sergei V. Pereverzev,et al. Regularization in Hilbert scales under general smoothing conditions , 2005 .
[47] O. Scherzer,et al. A convergence rates result for Tikhonov regularization in Banach spaces with non-smooth operators , 2007 .
[48] Barbara Kaltenbacher,et al. Regularization Methods in Banach Spaces , 2012, Radon Series on Computational and Applied Mathematics.
[49] R. Ramlau,et al. Morozov's discrepancy principle for Tikhonov-type functionals with nonlinear operators , 2010 .
[50] R. Ramlau,et al. An analysis of Tikhonov regularization for nonlinear ill-posed problems under a general smoothness assumption , 2007 .
[51] P. Mathé. The Lepskii principle revisited , 2006 .