Regularization properties of Tikhonov regularization with sparsity constraints

zbMath1171.65042MaRDI QIDQ836752

Ronny Ramlau

Publication date: 8 September 2009

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

Full work available at URL: https://eudml.org/doc/130630

zbMATH Keywords

convergencenumerical resultsinverse problemsTikhonov regularizationnonlinear operator equationssparsitya posteriori parameter choicenonlinear Hammerstein equation

Mathematics Subject Classification ID

Numerical methods for integral equations (65R20) Other nonlinear integral equations (45G10) Particular nonlinear operators (superposition, Hammerstein, Nemytski?, Uryson, etc.) (47H30) Nonlinear ill-posed problems (47J06) Numerical solutions to equations with nonlinear operators (65J15) Numerical solutions of ill-posed problems in abstract spaces; regularization (65J20) Numerical solution to inverse problems in abstract spaces (65J22)

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Oversmoothing regularization with \(\ell^1\)-penalty term ⋮ On ℓ 1 -Regularization Under Continuity of the Forward Operator in Weaker Topologies ⋮ On the parameter estimation problem of magnetic resonance advection imaging ⋮ A projected homotopy perturbation method for nonlinear inverse problems in Banach spaces ⋮ Characterizations of adjoint Sobolev embedding operators with applications in inverse problems ⋮ Representation of operators using fusion frames ⋮ Projected gradient iteration for nonlinear operator equation ⋮ Mathematical Imbalance Determination from Vibrational Measurements and Industrial Applications ⋮ Image reconstruction for diffuse optical tomography based on radiative transfer equation ⋮ Tikhonov regularization with \({\ell^{0}}\)-term complementing a convex penalty: \({\ell^{1}}\)-convergence under sparsity constraints ⋮ The two-point gradient methods for nonlinear inverse problems based on Bregman projections

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