Risk estimators for choosing regularization parameters in ill-posed problems -- properties and limitations

DOI10.3934/ipi.2018047OpenAlexW2580509819MaRDI QIDQ1785032

Nicolai Bissantz, Felix Lucka, Martin Burger, Frank Wübbeling, Christoph Brune, Katharina Proksch, Dette, Holger

Publication date: 27 September 2018

Published in: Inverse Problems and Imaging (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1701.04970

zbMATH Keywords

Stein's methoddiscrepancy principleill-posed problemsregularization parameter choicerisk estimators

Mathematics Subject Classification ID

Asymptotic properties of parametric estimators (62F12) Ill-posedness and regularization problems in numerical linear algebra (65F22) Inverse problems in optimal control (49N45)

Related Items (11)

Early stopping for statistical inverse problems via truncated SVD estimation ⋮ A probabilistic oracle inequality and quantification of uncertainty of a modified discrepancy principle for statistical inverse problems ⋮ Convergence of regularization methods with filter functions for a regularization parameter chosen with GSURE and mildly ill-posed inverse problems ⋮ Empirical risk minimization as parameter choice rule for general linear regularization methods ⋮ Tomographic reconstruction from Poisson distributed data: a fast and convergent EM-TV dual approach ⋮ Semi-discrete Tikhonov regularization in RKHS with large randomly distributed noise ⋮ Noise Level Free Regularization of General Linear Inverse Problems under Unconstrained White Noise ⋮ A parameter choice rule for Tikhonov regularization based on predictive risk ⋮ Maximum Likelihood Estimation of Regularization Parameters in High-Dimensional Inverse Problems: An Empirical Bayesian Approach Part I: Methodology and Experiments ⋮ Beyond the Bakushinkii veto: regularising linear inverse problems without knowing the noise distribution ⋮ Predictive risk estimation for the expectation maximization algorithm with Poisson data

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