Shuai Lu et al 2007 Inverse Problems 23 217 doi:10.1088/0266-5611/23/1/011
An analysis of Tikhonov regularization for nonlinear ill-posed problems under a general smoothness assumption
Shuai Lu, Sergei V Pereverzev and Ronny Ramlau
Show affiliationsIn this paper we introduce an adaptive regularization scheme based on algorithms for minimization of the Tikhonov functional to reconstruct the solution x† of nonlinear ill-posed problem F(x) = y, where the right-hand side is replaced by noisy data yδ 
Y with ||y − yδ|| ≤ δ, and F : D(F) ⊂ X → Y is a nonlinear operator between Hilbert spaces X and Y. Under the assumption that Fréchet derivative F' is Lipschitz continuous, a choice of the regularization parameter and the stopping criteria for minimization algorithms are presented. We prove that under a general source condition given in terms of a nonlinear operator F the error ||x† − xk|| between the regularized approximation xk and the solution x† is of optimal order.
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Issue 1 (February 2007)
Received 7 August 2006, in final form 21 November 2006
Published 11 December 2006
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An analysis of Tikhonov regularization for nonlinear ill-posed problems under a general smoothness assumption
Shuai Lu et al 2007 Inverse Problems 23 217
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