A unified approach to convergence rates for \(\ell^{1}\)-regularization and lacking sparsity

DOI10.1515/JIIP-2015-0058zbMath1336.65104arXiv1506.01582OpenAlexW2210196945MaRDI QIDQ278020

Bernd Hofmann, Jens Flemming, Ivan Veselić

Publication date: 2 May 2016

Published in: Journal of Inverse and Ill-Posed Problems (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1506.01582

zbMATH Keywords

convergence ratesvariational inequalitieslinear ill-posed problemsrestricted isometry propertysparsity constraintsTikhonov-type regularization

Mathematics Subject Classification ID

Inverse problems for PDEs (35R30) Numerical solutions of ill-posed problems in abstract spaces; regularization (65J20)

Related Items (7)

Oversmoothing regularization with \(\ell^1\)-penalty term ⋮ On ℓ 1 -Regularization Under Continuity of the Forward Operator in Weaker Topologies ⋮ Characterizations of Variational Source Conditions, Converse Results, and Maxisets of Spectral Regularization Methods ⋮ Elastic-net regularization versus ℓ ¹ -regularization for linear inverse problems with quasi-sparse solutions ⋮ Injectivity and \(\text{weak}^\star\)-to-weak continuity suffice for convergence rates in \(\ell^{1}\)-regularization ⋮ Maximal spaces for approximation rates in \(\ell^1\)-regularization ⋮ Modern regularization methods for inverse problems

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