Convergence rates inℓ1-regularization when the basis is not smooth enough

DOI10.1080/00036811.2014.886106zbMath1325.65076arXiv1311.1923OpenAlexW2041478165WikidataQ58186317 ScholiaQ58186317MaRDI QIDQ4982025

Jens Flemming, Markus Hegland

Publication date: 23 March 2015

Published in: Applicable Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1311.1923

zbMATH Keywords

convergencevariational inequalitynumerical examplesTikhonov regularizationlinear ill-posed problemsparsity constraintsmoothing property\(\ell^{1}\)-regularizationnonsmooth basis

Mathematics Subject Classification ID

Variational inequalities (49J40) Numerical solutions to equations with linear operators (65J10) Numerical solutions of ill-posed problems in abstract spaces; regularization (65J20) Linear operators and ill-posed problems, regularization (47A52) Numerical methods for variational inequalities and related problems (65K15)

Related Items (6)

On ℓ 1 -Regularization Under Continuity of the Forward Operator in Weaker Topologies ⋮ Variational source conditions and stability estimates for inverse electromagnetic medium scattering problems ⋮ Injectivity and \(\text{weak}^\star\)-to-weak continuity suffice for convergence rates in \(\ell^{1}\)-regularization ⋮ Sparse signal inversion with impulsive noise by dual spectral projected gradient method ⋮ Maximal spaces for approximation rates in \(\ell^1\)-regularization ⋮ Tikhonov regularization with \({\ell^{0}}\)-term complementing a convex penalty: \({\ell^{1}}\)-convergence under sparsity constraints

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