Sparse regularization with l q penalty term
From MaRDI portal
Publication:3537476
DOI10.1088/0266-5611/24/5/055020zbMath1157.65033arXiv0806.3222OpenAlexW2950042078MaRDI QIDQ3537476
Markus Grasmair, Markus Haltmeier, Otmar Scherzer
Publication date: 6 November 2008
Published in: Inverse Problems (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/0806.3222
Nonlinear ill-posed problems (47J06) Numerical solutions to equations with nonlinear operators (65J15) Numerical solutions of ill-posed problems in abstract spaces; regularization (65J20)
Related Items
Sparse optimization problems in fractional order Sobolev spaces ⋮ Oversmoothing regularization with \(\ell^1\)-penalty term ⋮ Dilational interpolatory inequalities ⋮ Convergence and regularization results for optimal control problems with sparsity functional ⋮ Sparsity regularization of the diffusion coefficient identification problem: well-posedness and convergence rates ⋮ Reconstructing conductivity coefficients based on sparsity regularization and measured data in electrical impedance tomography ⋮ Convergence rates for the joint solution of inverse problems with compressed sensing data ⋮ Non-convex sparse regularisation ⋮ Parameter choices for sparse regularization with the ℓ1 norm * ⋮ On ℓ 1 -Regularization Under Continuity of the Forward Operator in Weaker Topologies ⋮ Lasso Granger Causal Models: Some Strategies and Their Efficiency for Gene Expression Regulatory Networks ⋮ Shearlet-based regularization in statistical inverse learning with an application to x-ray tomography ⋮ Nonconvex flexible sparsity regularization: theory and monotone numerical schemes ⋮ Regularization and numerical solution of the inverse scattering problem using shearlet frames ⋮ Inverse problems with nonnegative and sparse solutions: algorithms and application to the phase retrieval problem ⋮ Infinite dimensional compressed sensing from anisotropic measurements and applications to inverse problems in PDE ⋮ Modified Tikhonov regularization for nonlinear ill-posed problems in Banach spaces ⋮ An extension of the variational inequality approach for obtaining convergence rates in regularization of nonlinear ill-posed problems ⋮ Weighted sparsity regularization for source identification for elliptic PDEs ⋮ Translation invariant diagonal frame decomposition of inverse problems and their regularization ⋮ Stability of the elastic net estimator ⋮ Convex regularization of local volatility models from option prices: convergence analysis and rates ⋮ Inducing sparsity via the horseshoe prior in imaging problems ⋮ Convergence analysis of critical point regularization with non-convex regularizers ⋮ NETT: solving inverse problems with deep neural networks ⋮ The residual method for regularizing ill-posed problems ⋮ Source Conditions for Non-Quadratic Tikhonov Regularization ⋮ Tikhonov regularization with oversmoothing penalty for non-linear ill-posed problems in Hilbert scales ⋮ Efficient regularization with wavelet sparsity constraints in photoacoustic tomography ⋮ Sparsity and level set regularization for diffuse optical tomography using a transport model in 2D ⋮ Flexible sparse regularization ⋮ Elastic-net regularization versus ℓ 1 -regularization for linear inverse problems with quasi-sparse solutions ⋮ Morozov's discrepancy principle for \(\alpha\ell_1-\beta\ell_2\) sparsity regularization ⋮ Joint super-resolution image reconstruction and parameter identification in imaging operator: analysis of bilinear operator equations, numerical solution, and application to magnetic particle imaging ⋮ Deep synthesis network for regularizing inverse problems ⋮ Identification of alterations in the Jacobian of biochemical reaction networks from steady state covariance data at two conditions ⋮ A scalable algorithm for MAP estimators in Bayesian inverse problems with Besov priors ⋮ A New Approach to Source Conditions in Regularization with General Residual Term ⋮ On the interplay of source conditions and variational inequalities for nonlinear ill-posed problems ⋮ New regularization method and iteratively reweighted algorithm for sparse vector recovery ⋮ Far Field Splitting by Iteratively Reweighted $\ell^1$ Minimization ⋮ Necessary and sufficient conditions for linear convergence of ℓ1-regularization ⋮ Elastic-Net Regularization: Iterative Algorithms and Asymptotic Behavior of Solutions ⋮ $ \newcommand{\e}{{\rm e}} {\alpha\ell_{1}-\beta\ell_{2}}$ regularization for sparse recovery ⋮ Sparse Regularization of Inverse Problems by Operator-Adapted Frame Thresholding ⋮ Unnamed Item ⋮ Convergence rates inℓ1-regularization when the basis is not smooth enough ⋮ A global minimization algorithm for Tikhonov functionals with sparsity constraints ⋮ Solving inverse problems using data-driven models ⋮ Tikhonov regularization with \({\ell^{0}}\)-term complementing a convex penalty: \({\ell^{1}}\)-convergence under sparsity constraints ⋮ Multilevel preconditioning and adaptive sparse solution of inverse problems ⋮ \(l^1\)-weighted regularization for the problem of recovering sparse initial conditions in parabolic equations from final measurements ⋮ Regularity of the Parameter-to-State Map of a Parabolic Partial Differential Equation ⋮ Regularization of inverse problems by filtered diagonal frame decomposition ⋮ Regularization properties of the sequential discrepancy principle for Tikhonov regularization in Banach spaces