Well-posedness and convergence rates for sparse regularization with sublinear \(l^q\) penalty term
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Publication:2268306
DOI10.3934/IPI.2009.3.383zbMath1189.65112OpenAlexW2115266937MaRDI QIDQ2268306
Publication date: 10 March 2010
Published in: Inverse Problems and Imaging (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.3934/ipi.2009.3.383
Nonlinear ill-posed problems (47J06) Numerical solutions to equations with nonlinear operators (65J15) Numerical solutions of ill-posed problems in abstract spaces; regularization (65J20)
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Sparse optimization problems in fractional order Sobolev spaces ⋮ Non-convex sparse regularisation ⋮ On ℓ 1 -Regularization Under Continuity of the Forward Operator in Weaker Topologies ⋮ Nonconvex flexible sparsity regularization: theory and monotone numerical schemes ⋮ Multiscale hierarchical decomposition methods for ill-posed problems ⋮ The residual method for regularizing ill-posed problems ⋮ Flexible sparse regularization ⋮ Morozov's discrepancy principle for \(\alpha\ell_1-\beta\ell_2\) sparsity regularization ⋮ Injectivity and \(\text{weak}^\star\)-to-weak continuity suffice for convergence rates in \(\ell^{1}\)-regularization ⋮ Regularization Methods for Ill-Posed Problems ⋮ $ \newcommand{\e}{{\rm e}} {\alpha\ell_{1}-\beta\ell_{2}}$ regularization for sparse recovery ⋮ Convergence rates inℓ1-regularization when the basis is not smooth enough ⋮ Tikhonov regularization with \({\ell^{0}}\)-term complementing a convex penalty: \({\ell^{1}}\)-convergence under sparsity constraints ⋮ Regularization properties of the sequential discrepancy principle for Tikhonov regularization in Banach spaces
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