"Regularization of Nonlinear Inverse Problems - From Functional Analysis to Data-Driven Approaches"Otmar ScherzerThe starting point of this talk is the paper of Engl, Kunisch, Neubauer ``Convergence rates for Tikhonov Regularization of Nonlinear Ill--Posed Problems'', Inverse Problems, 5.3 (1989), 523-540. The analysis of this paper is based on functional analysis. We use their fundamental techniques to analyze Tikhonov regularization which is based on data-driven approaches. In order to do so we consider discretization of Tikhonov regularization, as it has been analyzed by Neubauer and S., Num. Funct. Anal. Opt. 11, 1-2 (1990), 85-99 ``Finite--dimensional approximation of Tikhonov regularized solutions of non-linear ill-posed problems''. |
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