Hierachical Bayesian models and sparsity: ℓ 2 -magic

DOI10.1088/1361-6420/aaf5abzbMath1490.62078OpenAlexW2910526316MaRDI QIDQ4625206

Erkki Somersalo, Alexander Strang, Daniela Calvetti

Publication date: 22 February 2019

Published in: Inverse Problems (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1088/1361-6420/aaf5ab

Mathematics Subject Classification ID

Bayesian inference (62F15) Ill-posedness and regularization problems in numerical linear algebra (65F22) Numerical optimization and variational techniques (65K10)

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Cites Work

• Unnamed Item
• Conditionally Gaussian Hypermodels for Cerebral Source Localization
• A Gaussian hypermodel to recover blocky objects
• A hierarchical Krylov–Bayes iterative inverse solver for MEG with physiological preconditioning
• Decoding by Linear Programming
• Stable recovery of sparse overcomplete representations in the presence of noise
• From Sparse Solutions of Systems of Equations to Sparse Modeling of Signals and Images
• Iteratively reweighted least squares minimization for sparse recovery
• Introduction to Bayesian Scientific Computing
• For most large underdetermined systems of equations, the minimal 𝓁₁‐norm near‐solution approximates the sparsest near‐solution
• Stable signal recovery from incomplete and inaccurate measurements

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