A converse result for Banach space convergence rates in Tikhonov-type convex regularization of ill-posed linear equations
From MaRDI portal
Publication:1615427
DOI10.1515/JIIP-2017-0116OpenAlexW2964187539WikidataQ130038308 ScholiaQ130038308MaRDI QIDQ1615427
Publication date: 31 October 2018
Published in: Journal of Inverse and Ill-Posed Problems (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1712.01499
convergence ratesBanach spacelinear equationill-posed problemvariational source conditionconverse result
Linear operators and ill-posed problems, regularization (47A52) Numerical solution to inverse problems in abstract spaces (65J22)
Related Items (6)
A note on the approximate symmetry of Bregman distances ⋮ Estimating Solution Smoothness and Data Noise with Tikhonov Regularization ⋮ Penalty-based smoothness conditions in convex variational regularization ⋮ The Kurdyka–Łojasiewicz Inequality as Regularity Condition ⋮ Modern regularization methods for inverse problems ⋮ Variational regularization theory based on image space approximation rates
Cites Work
- Unnamed Item
- Unnamed Item
- Convex Tikhonov regularization in Banach spaces: new results on convergence rates
- Regularization methods in Banach spaces.
- An extension of the variational inequality approach for obtaining convergence rates in regularization of nonlinear ill-posed problems
- Injectivity and \(\text{weak}^\star\)-to-weak continuity suffice for convergence rates in \(\ell^{1}\)-regularization
- Variational methods in imaging
- Existence of variational source conditions for nonlinear inverse problems in Banach spaces
- Iteratively regularized Newton-type methods for general data misfit functionals and applications to Poisson data
- Convergence Rates for Exponentially Ill-Posed Inverse Problems with Impulsive Noise
- On complex-valued deautoconvolution of compactly supported functions with sparse Fourier representation
- Variational inequalities and higher order convergence rates for Tikhonov regularisation on Banach spaces
- Solution smoothness of ill-posed equations in Hilbert spaces: four concepts and their cross connections
- Generalized Bregman distances and convergence rates for non-convex regularization methods
- Sharp converse results for the regularization error using distance functions
- Parameter choice in Banach space regularization under variational inequalities
- Optimal Convergence Rates Results for Linear Inverse Problems in Hilbert Spaces
- On Converse and Saturation Results for Tikhonov Regularization of Linear Ill-Posed Problems
- Geometry of linear ill-posed problems in variable Hilbert scales
- Tikhonov regularization with oversmoothing penalty for non-linear ill-posed problems in Hilbert scales
- A convergence rates result for Tikhonov regularization in Banach spaces with non-smooth operators
- Characterizations of Variational Source Conditions, Converse Results, and Maxisets of Spectral Regularization Methods
- Verification of a variational source condition for acoustic inverse medium scattering problems
This page was built for publication: A converse result for Banach space convergence rates in Tikhonov-type convex regularization of ill-posed linear equations