l1Penalty for Ill-Posed Inverse Problems

DOI10.1080/03610920701826013zbMath1196.62035arXiv0709.2606OpenAlexW2056442178MaRDI QIDQ3634545

Jean-Michel Loubes

Publication date: 25 June 2009

Published in: Communications in Statistics - Theory and Methods (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0709.2606

zbMATH Keywords

inverse problemssparsityasymptotic statisticspenalized M-estimation

Mathematics Subject Classification ID

Asymptotic properties of nonparametric inference (62G20) Nonparametric estimation (62G05) Numerical solution to inverse problems in abstract spaces (65J22)

Related Items (2)

Adaptive complexity regularization for linear inverse problems ⋮ Multidimensional hazard estimation under generalized censoring

Cites Work

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• Wavelets, approximation, and statistical applications
• Oracle inequalities for inverse problems
• Adaptive estimation with soft thresholding penalties
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• An iterative thresholding algorithm for linear inverse problems with a sparsity constraint
• Statistical Inverse Estimation in Hilbert Scales
• Tikhonov regularization anda posteriorirules for solving nonlinear ill posed problems
• Nonparametric Instrumental Regression
• Consistency and rates of convergence of nonlinear Tikhonov regularization with random noise

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