On ℓ 1 -Regularization Under Continuity of the Forward Operator in Weaker Topologies

DOI10.1007/978-3-319-70824-9_4OpenAlexW2768642448MaRDI QIDQ4554173

Bernd Hofmann, Daniel Gerth

Publication date: 13 November 2018

Published in: Trends in Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1711.08642

Mathematics Subject Classification ID

Linear operators and ill-posed problems, regularization (47A52)

Cites Work

• Unnamed Item
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• A unified approach to convergence rates for \(\ell^{1}\)-regularization and lacking sparsity
• Regularization methods in Banach spaces.
• Convergence rates for regularization with sparsity constraints
• Injectivity and \(\text{weak}^\star\)-to-weak continuity suffice for convergence rates in \(\ell^{1}\)-regularization
• Regularization properties of Tikhonov regularization with sparsity constraints
• Variational methods in imaging
• Well-posedness and convergence rates for sparse regularization with sublinear \(l^q\) penalty term
• Convergence rates for \(\ell^1\)-regularization without the help of a variational inequality
• On \(\ell^1\)-regularization in light of Nashed's ill-posedness concept
• Convergence rates for ${{\ell }}^{1}$-regularization without injectivity-type assumptions
• Regularization properties of the sequential discrepancy principle for Tikhonov regularization in Banach spaces
• Elastic-net regularization versus ℓ ¹ -regularization for linear inverse problems with quasi-sparse solutions
• Generalized Bregman distances and convergence rates for non-convex regularization methods
• Necessary and sufficient conditions for linear convergence of ℓ1-regularization
• Parameter choice in Banach space regularization under variational inequalities
• Regularization with non-convex separable constraints
• Convergence rates and source conditions for Tikhonov regularization with sparsity constraints
• Sparse regularization with l ^q penalty term
• An Introduction to Banach Space Theory
• One new strategy for a priori choice of regularizing parameters in Tikhonov's regularization
• An iterative thresholding algorithm for linear inverse problems with a sparsity constraint
• Convergence rates inℓ¹-regularization if the sparsity assumption fails
• Convergence rates inℓ¹-regularization when the basis is not smooth enough
• A convergence rates result for Tikhonov regularization in Banach spaces with non-smooth operators
• On the interplay of basis smoothness and specific range conditions occurring in sparsity regularization
• On Some Open Questions Concerning Strictly Singular Operators