Randomization and Reweighted $\ell_1$-Minimization for A-Optimal Design of Linear Inverse Problems

DOI10.1137/19M1267362zbMath1442.62175arXiv1906.03791MaRDI QIDQ3300853

Elizabeth Herman, Alen Alexanderian, Arvind K. Saibaba

Publication date: 30 July 2020

Published in: SIAM Journal on Scientific Computing (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1906.03791

zbMATH Keywords

uncertainty quantificationBayesian inversionlarge-scale ill-posed inverse problemsA-optimal experimental designrandomized matrix methodsreweighted \(\ell_1\) minimization

Mathematics Subject Classification ID

Computational methods for problems pertaining to statistics (62-08) Optimal statistical designs (62K05) Bayesian inference (62F15) Inverse problems for PDEs (35R30) Randomized algorithms (68W20) PDEs in connection with statistics (35Q62)

Related Items (7)

Learning physics-based models from data: perspectives from inverse problems and model reduction ⋮ Monte Carlo estimators for the Schatten \(p\)-norm of symmetric positive semidefinite matrices ⋮ Optimal Experimental Design for Inverse Problems in the Presence of Observation Correlations ⋮ Weighted sparsity regularization for source identification for elliptic PDEs ⋮ Randomized Low-Rank Approximation of Monotone Matrix Functions ⋮ Optimal Design of Large-scale Bayesian Linear Inverse Problems Under Reducible Model Uncertainty: Good to Know What You Don't Know ⋮ Optimal experimental design for infinite-dimensional Bayesian inverse problems governed by PDEs: a review

Cites Work

• Unnamed Item
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• Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions
• On Bayesian A- and D-optimal experimental designs in infinite dimensions
• Extension of Rotfel'd Theorem
• Numerical methods for \(A\)-optimal designs with a sparsity constraint for ill-posed inverse problems
• Enhancing sparsity by reweighted \(\ell _{1}\) minimization
• Bayesian experimental design: A review
• Randomized matrix-free trace and log-determinant estimators
• MM Optimization Algorithms
• Inverse problems: A Bayesian perspective
• A-Optimal Design of Experiments for Infinite-Dimensional Bayesian Linear Inverse Problems with Regularized $\ell_0$-Sparsification
• Adaptive A-Optimal Experimental Design for Linear Dynamical Systems
• Numerical methods for experimental design of large-scale linear ill-posed inverse problems
• Optimal Measurement Methods for Distributed Parameter System Identification
• Goal-oriented optimal design of experiments for large-scale Bayesian linear inverse problems
• Efficient D-Optimal Design of Experiments for Infinite-Dimensional Bayesian Linear Inverse Problems
• Numerical methods for the design of large-scale nonlinear discrete ill-posed inverse problems
• A Computational Framework for Infinite-Dimensional Bayesian Inverse Problems Part I: The Linearized Case, with Application to Global Seismic Inversion

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