Error estimates for variational regularization of inverse problems with general noise models for data and operator

DOI10.1553/etna_vol57s127zbMath1498.65081OpenAlexW4292062060MaRDI QIDQ2100868

Frank Werner, Thorsten Hohage

Publication date: 25 November 2022

Published in: ETNA. Electronic Transactions on Numerical Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1553/etna_vol57s127

zbMATH Keywords

inverse problemerror boundsrandom noisevariational regularizationoperator noise

Mathematics Subject Classification ID

Applications of stochastic analysis (to PDEs, etc.) (60H30) White noise theory (60H40) Numerical solutions of ill-posed problems in abstract spaces; regularization (65J20)

Related Items (2)

On uniqueness and ill-posedness for the deautoconvolution problem in the multi-dimensional case ⋮ On a Dynamic Variant of the Iteratively Regularized Gauss–Newton Method with Sequential Data

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Regularization methods in Banach spaces.
• Variational source conditions and stability estimates for inverse electromagnetic medium scattering problems
• Iterative regularization methods for nonlinear ill-posed problems
• Minimization of Tikhonov functionals in Banach spaces
• Variational methods in imaging
• Partial differential equations. II: Qualitative studies of linear equations
• Characteristic inequalities of uniformly convex and uniformly smooth Banach spaces
• Weak convergence and empirical processes. With applications to statistics
• Upper and lower bounds for the Bregman divergence
• Sharp and simple bounds for the raw moments of the binomial and Poisson distributions
• Kullback-Leibler residual and regularization for inverse problems with noisy data and noisy operator
• Nonlinear estimation for linear inverse problems with error in the operator
• Convergence Rates for Exponentially Ill-Posed Inverse Problems with Impulsive Noise
• A Semismooth Newton Method for Nonlinear Parameter Identification Problems with Impulsive Noise
• Finite-dimensional approximation of tikhonov regularized solutions of non-linear ill-posed problems
• Discretization of variational regularization in Banach spaces
• Generalized Bregman distances and convergence rates for non-convex regularization methods
• Regularity of Gaussian white noise on the d-dimensional torus
• Convergence rate analysis of Tikhonov regularization for nonlinear ill-posed problems with noisy operators
• Convergence rates in expectation for Tikhonov-type regularization of inverse problems with Poisson data
• Mathematical Foundations of Infinite-Dimensional Statistical Models
• Tikhonov regularisation for non-linear ill-posed problems: optimal convergence rates and finite-dimensional approximation
• Iterative methods for nonlinear ill-posed problems in Banach spaces: convergence and applications to parameter identification problems
• Interpolation of Besov Spaces
• Discretization strategy for linear ill-posed problems in variable Hilbert scales
• Regularization of exponentially ill-posed problems
• Convergence rates and structure of solutions of inverse problems with imperfect forward models
• MODULI OF CONTINUITY FOR OPERATOR VALUED FUNCTIONS
• Variational regularisation for inverse problems with imperfect forward operators and general noise models
• Convergence analysis of (statistical) inverse problems under conditional stability estimates
• Optimal Convergence Rates for Tikhonov Regularization in Besov Spaces
• Variational Source Conditions and Conditional Stability Estimates for Inverse Problems in PDEs
• Convergence Rates for Inverse Problems with Impulsive Noise
• A convergence rates result for Tikhonov regularization in Banach spaces with non-smooth operators
• Convergence Rates of General Regularization Methods for Statistical Inverse Problems and Applications
• Characterizations of Variational Source Conditions, Converse Results, and Maxisets of Spectral Regularization Methods
• Optimal convergence rates for sparsity promoting wavelet-regularization in Besov spaces

This page was built for publication: Error estimates for variational regularization of inverse problems with general noise models for data and operator