On the lifting of deterministic convergence rates for inverse problems with stochastic noise
DOI10.3934/ipi.2017031zbMath1368.60073arXiv1604.07189OpenAlexW2963261054MaRDI QIDQ2360781
Ronny Ramlau, Andreas Hofinger, Daniel Gerth
Publication date: 12 July 2017
Published in: Inverse Problems and Imaging (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1604.07189
convergence ratesTikhonov regularizationill-posed problemBayesian approachstochastic inverse problem
Nonlinear ill-posed problems (47J06) Computational methods for stochastic equations (aspects of stochastic analysis) (60H35) Numerical methods for inverse problems for integral equations (65R32)
Related Items (1)
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Statistical and computational inverse problems.
- On the Lambert \(w\) function
- A convergence analysis of the Landweber iteration for nonlinear ill-posed problems
- Discretization-invariant Bayesian inversion and Besov space priors
- Entfernung zweier zufälliger Grössen und die Konvergenz nach Wahrscheinlichkeit
- Inverse problems: A Bayesian perspective
- Discrepancy principle for statistical inverse problems with application to conjugate gradient iteration
- Convergence rates in expectation for Tikhonov-type regularization of inverse problems with Poisson data
- Inverse problems as statistics
- Maximuma posterioriprobability estimates in infinite-dimensional Bayesian inverse problems
- Convergence results for the Bayesian inversion theory
- On the small balls problem for equivalent Gaussian measures
- On autoconvolution and regularization
- Monte Carlo analysis of inverse problems
- An iterative thresholding algorithm for linear inverse problems with a sparsity constraint
- Inverse Problem Theory and Methods for Model Parameter Estimation
- A stochastic convergence analysis for Tikhonov regularization with sparsity constraints
- Convergence Rates of General Regularization Methods for Statistical Inverse Problems and Applications
- Morozov's discrepancy principle for Tikhonov-type functionals with nonlinear operators
- Analysis of regularized inversion of data corrupted by white Gaussian noise
- Introduction to Bayesian Scientific Computing
- Convergence rate for the Bayesian approach to linear inverse problems
- Regularization of an autoconvolution problem in ultrashort laser pulse characterization
- Consistency and rates of convergence of nonlinear Tikhonov regularization with random noise
This page was built for publication: On the lifting of deterministic convergence rates for inverse problems with stochastic noise