A Taste of Inverse Problems

DOI10.1137/1.9781611974942zbMath1381.65042OpenAlexW4233305895MaRDI QIDQ4977164

Martin Hanke

Publication date: 3 August 2017

Full work available at URL: https://doi.org/10.1137/1.9781611974942

zbMATH Keywords

Hilbert spaceinverse problemstextbookconjugate gradient methodnumerical differentiationiterative regularizationTikhonov regularizationdiscrepancy principleill-posed problemsLandweber iteration

Mathematics Subject Classification ID

Numerical solutions to equations with linear operators (65J10) Mathematics for nonmathematicians (engineering, social sciences, etc.) (00A06) Numerical solutions of ill-posed problems in abstract spaces; regularization (65J20) Numerical methods for inverse problems for initial value and initial-boundary value problems involving PDEs (65M32) Numerical methods for inverse problems for integral equations (65R32) Numerical methods for inverse problems for boundary value problems involving PDEs (65N21) Linear operators and ill-posed problems, regularization (47A52) Numerical solution to inverse problems in abstract spaces (65J22) Numerical solution of inverse problems involving ordinary differential equations (65L09) Introductory exposition (textbooks, tutorial papers, etc.) pertaining to numerical analysis (65-01)

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Learning physics-based models from data: perspectives from inverse problems and model reduction ⋮ Uniqueness and numerical reconstruction for inverse problems dealing with interval size search ⋮ Solution of an acoustic transmission inverse problem by extended inversion ⋮ On the rate of convergence for the autocorrelation operator in functional autoregression ⋮ Inverse medium scattering problems with Kalman filter techniques ⋮ Noise Level Free Regularization of General Linear Inverse Problems under Unconstrained White Noise ⋮ On and Beyond Total Variation Regularization in Imaging: The Role of Space Variance ⋮ Global Uniqueness and Lipschitz-Stability for the Inverse Robin Transmission Problem ⋮ Uniqueness, Lipschitz Stability, and Reconstruction for the Inverse Optical Tomography Problem ⋮ A note on the uniqueness result for the inverse Henderson problem ⋮ Some inverse problems for the Burgers equation and related systems

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