Reconstructing conductivity coefficients based on sparsity regularization and measured data in electrical impedance tomography

DOI10.1080/17415977.2015.1018678zbMath1326.92048OpenAlexW1974121761MaRDI QIDQ3456559

Quy Muoi Pham

Publication date: 9 December 2015

Published in: Inverse Problems in Science and Engineering (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/17415977.2015.1018678

zbMATH Keywords

well-posednessconvergence rateSobolev gradientgradient-type algorithmelectrical impedance tomographysparse regularization

Mathematics Subject Classification ID

Biomedical imaging and signal processing (92C55) Numerical methods for inverse problems for boundary value problems involving PDEs (65N21) Fractional partial differential equations (35R11)

Related Items (6)

Convergence of proximal algorithms with stepsize controls for non-linear inverse problems and application to sparse non-negative matrix factorization ⋮ Inverse problems with nonnegative and sparse solutions: algorithms and application to the phase retrieval problem ⋮ Descent gradient methods for nonsmooth minimization problems in ill-posed problems ⋮ Non-convex ℓ_p regularization for sparse reconstruction of electrical impedance tomography ⋮ Application of a class of iterative algorithms and their accelerations to Jacobian-based linearized EIT image reconstruction ⋮ \(l^1\)-weighted regularization for the problem of recovering sparse initial conditions in parabolic equations from final measurements

Cites Work

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• Proximal Minimization Methods with Generalized Bregman Functions
• An implementation of the reconstruction algorithm of A Nachman for the 2D inverse conductivity problem
• An iterative thresholding algorithm for linear inverse problems with a sparsity constraint
• Electrical impedance tomography
• An analysis of electrical impedance tomography with applications to Tikhonov regularization
• A convergence rates result for Tikhonov regularization in Banach spaces with non-smooth operators
• Open issues of stability for the inverse conductivity problem

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