Adaptive complexity regularization for linear inverse problems

DOI10.1214/07-EJS115zbMath1320.62075arXiv0807.4859MaRDI QIDQ1951768

Carenne Ludeña, Jean-Michel Loubes

Publication date: 24 May 2013

Published in: Electronic Journal of Statistics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0807.4859

zbMATH Keywords

regularizationinverse problemsadaptive estimation

Mathematics Subject Classification ID

Nonparametric estimation (62G05) Inverse problems for functional-differential equations (34K29)

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Cites Work

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• Risk hull method and regularization by projections of ill-posed inverse problems
• A statistical perspective on ill-posed inverse problems (with discussion)
• Risk bounds for model selection via penalization
• Thresholding estimators for linear inverse problems and deconvolutions
• Model selection for regression on a fixed design
• Oracle inequalities for inverse problems
• Sharp adaptation for inverse problems with random noise
• Nonlinear solution of linear inverse problems by wavelet-vaguelette decomposition
• Needlet algorithms for estimation in inverse problems
• l¹Penalty for Ill-Posed Inverse Problems
• Adaptive estimation with soft thresholding penalties
• Regularization by projection with a posteriori discretization level choice for linear and nonlinear ill-posed problems
• Adaptive Wavelet Galerkin Methods for Linear Inverse Problems
• Statistical Inverse Estimation in Hilbert Scales
• Generalized Inverses in Reproducing Kernel Spaces: An Approach to Regularization of Linear Operator Equations
• Convergence Rates of General Regularization Methods for Statistical Inverse Problems and Applications