Complexity of linear ill-posed problems in Hilbert space

DOI10.1016/j.jco.2016.10.003zbMath1354.65106OpenAlexW2535845662MaRDI QIDQ346297

Peter Mathé, Sergei V. Pereverzyev

Publication date: 5 December 2016

Published in: Journal of Complexity (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jco.2016.10.003

zbMATH Keywords

ill-posed probleminformation complexitybounded noiseadaptationstatistical inverse problem

Mathematics Subject Classification ID

Numerical solutions to equations with linear operators (65J10) Numerical solutions of ill-posed problems in abstract spaces; regularization (65J20) Linear operators and ill-posed problems, regularization (47A52) Numerical solution to inverse problems in abstract spaces (65J22)

Related Items (7)

A probabilistic oracle inequality and quantification of uncertainty of a modified discrepancy principle for statistical inverse problems ⋮ Optimal Convergence of the Discrepancy Principle for Polynomially and Exponentially Ill-Posed Operators under White Noise ⋮ Noise Level Free Regularization of General Linear Inverse Problems under Unconstrained White Noise ⋮ Randomized matrix approximation to enhance regularized projection schemes in inverse problems ⋮ Weak-norm posterior contraction rate of the 4DVAR method for linear severely ill-posed problems ⋮ Optimal indirect estimation for linear inverse problems with discretely sampled functional data ⋮ COMPLEXITY ESTIMATES FOR SEVERELY ILL-POSED PROBLEMS UNDER A POSTERIORI SELECTION OF REGULARIZATION PARAMETER

Cites Work

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• A mathematical introduction to compressive sensing
• Regularization theory for ill-posed problems. Selected topics
• Regularizability of ill-posed problems and the modulus of continuity
• What do we learn from the discrepancy principle?
• An information-based approach to ill-posed problems
• Optimal filtering of square-integrable signals in Gaussian noise
• Optimal Discretization of Inverse Problems in Hilbert Scales. Regularization and Self-Regularization of Projection Methods
• Regularization of some linear ill-posed problems with discretized random noisy data
• On a characteristic property of conditionally well-posed problems
• Modulus of continuity for conditionally stable ill-posed problems in Hilbert space
• What is the complexity of ill-posed problems?
• Optimal Estimation of Linear Operators in Hilbert Spaces from Inaccurate Data
• Geometry of linear ill-posed problems in variable Hilbert scales
• Statistical Inverse Estimation in Hilbert Scales
• Variable hilbert scales and their interpolation inequalities with applications to tikhonov regularization
• How general are general source conditions?

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