A unified framework for constructing globally convergent algorithms for multidimensional coefficient inverse problems

DOI10.1080/00036810410001712844zbMath1064.35208OpenAlexW2069675674WikidataQ58162787 ScholiaQ58162787MaRDI QIDQ4656465

Michael V. Klibanov, Alexandre Timonov

Publication date: 11 March 2005

Published in: Applicable Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/00036810410001712844

zbMATH Keywords

computational experimentscoefficient inverse problemglobally convergent algorithmsconvexification approachoptical frequency sounding

Mathematics Subject Classification ID

Biomedical imaging and signal processing (92C55) Inverse problems for PDEs (35R30) Initial value problems for second-order hyperbolic equations (35L15) Inverse problems (including inverse scattering) in optics and electromagnetic theory (78A46) Optimization problems in optics and electromagnetic theory (78M50)

Related Items (9)

Comparative study of the least squares approximation of the modified Bessel function ⋮ Molecular seismology: an inverse problem in nanobiology ⋮ Imaging of land mines by the globally convergent convexification method using a simplified mathematical model ⋮ A globally convergent convexification algorithm for multidimensional coefficient inverse problems ⋮ A new iterative procedure for the numerical solution of coefficient inverse problems ⋮ Comparative studies of the globally convergent convexification algorithm with application to imaging of antipersonnel land mines ⋮ High speed imaging of antipersonnel land mines by the convexification algorithm for a simplified mathematical model in two dimensions ⋮ Biography of Michael V. Klibanov Professor, Ph.D. and Doctor of Science in Physics and Mathematics and an outstanding expert in inverse problems ⋮ Approximate Global Convergence in Imaging of Land Mines from Backscattered Data

Uses Software

• TIGRA

Cites Work

• A new slant on the inverse problems of electromagnetic frequency sounding: ‘convexification’ of a multiextremal objective function via the Carleman weight functions
• Layer stripping: a direct numerical method for impedance imaging
• Inverse scattering via skin effect
• A sequential minimization algorithm based on the convexification approach
• TIGRA an iterative algorithm for regularizing nonlinear ill-posed problems
• A steepest descent algorithm for the global minimization of the Tikhonov functional
• Inverse problems for partial differential equations

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