Convergence rates for regularization with sparsity constraints

zbMath1206.47016MaRDI QIDQ625554

Ronny Ramlau, Elena Resmerita

Publication date: 17 February 2011

Published in: ETNA. Electronic Transactions on Numerical Analysis (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/231073

zbMATH Keywords

ill-posed problemregularisationsparsityBregman distance

Mathematics Subject Classification ID

Numerical solutions of ill-posed problems in abstract spaces; regularization (65J20) Linear operators and ill-posed problems, regularization (47A52)

Related Items (13)

On ℓ 1 -Regularization Under Continuity of the Forward Operator in Weaker Topologies ⋮ Nonconvex flexible sparsity regularization: theory and monotone numerical schemes ⋮ Modified Tikhonov regularization for nonlinear ill-posed problems in Banach spaces ⋮ A projected homotopy perturbation method for nonlinear inverse problems in Banach spaces ⋮ Flexible sparse regularization ⋮ Elastic-net regularization versus ℓ ¹ -regularization for linear inverse problems with quasi-sparse solutions ⋮ A note on the minimization of a Tikhonov functional with ℓ¹-penalty ⋮ Necessary and sufficient conditions for linear convergence of ℓ1-regularization ⋮ Optimal Convergence Rates for Tikhonov Regularization in Besov Spaces ⋮ Unnamed Item ⋮ Tikhonov regularization with \({\ell^{0}}\)-term complementing a convex penalty: \({\ell^{1}}\)-convergence under sparsity constraints ⋮ Variational regularization theory based on image space approximation rates ⋮ The two-point gradient methods for nonlinear inverse problems based on Bregman projections

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