Theory and examples of variational regularization with non-metric fitting functionals

DOI10.1515/jiip.2010.031zbMath1280.47062OpenAlexW2056982603MaRDI QIDQ2874468

Jens Flemming

Publication date: 30 January 2014

Published in: jiip (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1515/jiip.2010.031

zbMATH Keywords

convergence ratesvariational inequalitiesPoisson noisevariational regularization

Mathematics Subject Classification ID

Variational and other types of inequalities involving nonlinear operators (general) (47J20) Nonlinear ill-posed problems (47J06) Numerical solutions of ill-posed problems in abstract spaces; regularization (65J20) Linear operators and ill-posed problems, regularization (47A52)

Related Items (14)

Quasi-solution of linear inverse problems in non-reflexive Banach spaces ⋮ On the existence and stability of minimizers for generalized Tikhonov functionals with general similarity data ⋮ Stochastic Convergence of Regularized Solutions and Their Finite Element Approximations to Inverse Source Problems ⋮ Characterizations of Variational Source Conditions, Converse Results, and Maxisets of Spectral Regularization Methods ⋮ Error Estimates for Doubly-Generalized Tikhonov-Phillips Regularization ⋮ Convergence rates for regularization functionals with polyconvex integrands ⋮ Iteratively regularized Newton-type methods for general data misfit functionals and applications to Poisson data ⋮ Convergence rates of Tikhonov regularizations for elliptic and parabolic inverse radiativity problems ⋮ Convergence rates of Tikhonov regularization for recovering growth rates in a Lotka-Volterra competition model with diffusion ⋮ An MM algorithm for estimation of a two component semiparametric density mixture with a known component ⋮ Variational source condition for ill-posed backward nonlinear Maxwell’s equations ⋮ Variational Source Conditions in $L^p$-spaces ⋮ Variational source conditions for inverse Robin and flux problems by partial measurements ⋮ Convergence of a spectral regularization of a time-reversed reaction-diffusion problem with high-order Sobolev-Gevrey smoothness

Cites Work

• An extension of the variational inequality approach for obtaining convergence rates in regularization of nonlinear ill-posed problems
• On the interplay of source conditions and variational inequalities for nonlinear ill-posed problems
• Improved and extended results for enhanced convergence rates of Tikhonov regularization in Banach spaces
• Regularization with non-convex separable constraints
• Convergence rates for Tikhonov regularisation of non-linear ill-posed problems
• A New Approach to Source Conditions in Regularization with General Residual Term
• Joint additive Kullback–Leibler residual minimization and regularization for linear inverse problems
• Approximate source conditions for nonlinear ill-posed problems—chances and limitations
• Maximum Entropy Regularization for Fredholm Integral Equations of the First Kind
• A convergence rates result for Tikhonov regularization in Banach spaces with non-smooth operators
• Regularization of ill-posed problems in Banach spaces: convergence rates

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