Sparse Regularization of Inverse Problems by Operator-Adapted Frame Thresholding

DOI10.1007/978-3-030-47174-3_10OpenAlexW2995873372MaRDI QIDQ4964112

Jürgen Frikel, Markus Haltmeier

Publication date: 24 February 2021

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

Full work available at URL: https://arxiv.org/abs/1909.09364

zbMATH Keywords

convergenceconvergence ratesHilbert spaceslinear ill-posed problemssparse regularization\(\ell^1\)-regularizationdiagonal frame decompositionframe-based regularization

Mathematics Subject Classification ID

Computational methods for sparse matrices (65F50) Numerical solutions of ill-posed problems in abstract spaces; regularization (65J20) Linear operators and ill-posed problems, regularization (47A52)

Related Items (4)

On regularization via frame decompositions with applications in tomography ⋮ Translation invariant diagonal frame decomposition of inverse problems and their regularization ⋮ Deep synthesis network for regularizing inverse problems ⋮ Regularization of inverse problems by filtered diagonal frame decomposition

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Radon transform inversion using the shearlet representation
• A wavelet multilevel method for ill-posed problems stabilized by Tikhonov regularization
• Sparse regularization in limited angle tomography
• Recovering edges in ill-posed inverse problems: Optimality of curvelet frames.
• Nonlinear solution of linear inverse problems by wavelet-vaguelette decomposition
• A Tikhonov-based projection iteration for nonlinear ill-posed problems with sparsity con\-straints
• The Mathematics of Computerized Tomography
• On complex-valued deautoconvolution of compactly supported functions with sparse Fourier representation
• Necessary and sufficient conditions for linear convergence of ℓ1-regularization
• Convergence rates and source conditions for Tikhonov regularization with sparsity constraints
• Sparse regularization with l ^q penalty term
• Spherical means with centers on a hyperplane in even dimensions
• Stable Signal Reconstruction via $\ell^1$-Minimization in Redundant, Non-Tight Frames
• Efficient regularization with wavelet sparsity constraints in photoacoustic tomography
• An iterative thresholding algorithm for linear inverse problems with a sparsity constraint
• Wavelet-Galerkin methods for ill-posed problems
• Analysis versus synthesis in signal priors
• An introduction to frames and Riesz bases

This page was built for publication: Sparse Regularization of Inverse Problems by Operator-Adapted Frame Thresholding