Left and right preconditioning for electrical impedance tomography with structural information

DOI10.1088/0266-5611/28/5/055015zbMath1243.65133OpenAlexW2091173487MaRDI QIDQ2888766

Debra McGivney, Erkki Somersalo, Daniela Calvetti

Publication date: 4 June 2012

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

Full work available at URL: https://doi.org/10.1088/0266-5611/28/5/055015

zbMATH Keywords

algorithminverse problemfinite difference methodBayesian analysisnumerical examplespreconditioningiterative methodcomputational efficiencyKrylov subspace methodcovarianceelectrical impedance tomographylarge-scale problemleast-squares problemsx-ray imaging

Mathematics Subject Classification ID

Boundary value problems for second-order elliptic equations (35J25) Biomedical imaging and signal processing (92C55) Inverse problems for PDEs (35R30) Finite difference methods applied to problems in optics and electromagnetic theory (78M20) Iterative numerical methods for linear systems (65F10) Finite difference methods for boundary value problems involving PDEs (65N06) Complexity and performance of numerical algorithms (65Y20) Numerical methods for inverse problems for boundary value problems involving PDEs (65N21) Inverse problems (including inverse scattering) in optics and electromagnetic theory (78A46) Preconditioners for iterative methods (65F08)

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Optimal Low-rank Approximations of Bayesian Linear Inverse Problems ⋮ Efficient Inclusion of Total Variation Type Priors in Quantitative Photoacoustic Tomography ⋮ Preconditioners for Krylov subspace methods: An overview ⋮ Bayes Meets Krylov: Statistically Inspired Preconditioners for CGLS ⋮ Edge-promoting reconstruction of absorption and diffusivity in optical tomography ⋮ Edge-Enhancing Reconstruction Algorithm for Three-Dimensional Electrical Impedance Tomography ⋮ Approximation error method for imaging the human head by electrical impedance tomography* ⋮ Artificial boundary conditions and domain truncation in electrical impedance tomography. I: Theory and preliminary results

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