Identification of dipole sources in an elliptic equation from boundary measurements: application to the inverse EEG problem

DOI10.1515/156939406777571012zbMath1110.35102OpenAlexW2030551191MaRDI QIDQ3418639

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Publication date: 5 February 2007

Published in: Journal of Inverse and Ill-posed Problems (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1515/156939406777571012

zbMATH Keywords

optimizationMaxwell equationscost functionPoisson equationelectroencephalographyinverse source problemhuman brainlocal Lipshitz stability

Mathematics Subject Classification ID

Boundary value problems for second-order elliptic equations (35J25) Biomedical imaging and signal processing (92C55) Inverse problems for PDEs (35R30)

Related Items (9)

A finite element model for the data completion problem: analysis and assessment ⋮ Optimal design for parameter estimation in EEG problems in a 3D multilayered domain ⋮ An inverse dipole source problem in inhomogeneous media: application to the EEG source localization in neonates ⋮ On inertial iterated Tikhonov methods for solving ill-posed problems ⋮ EEG in neonates: forward modeling and sensitivity analysis with respect to variations of the conductivity ⋮ Review on mathematical modelling of electroencephalography (EEG) ⋮ Level-set approaches of L₂-type for recovering shape and contrast in ill-posed problems ⋮ A range-relaxed criteria for choosing the Lagrange multipliers in the iterated Tikhonov Kaczmarz method for solving systems of linear ill-posed equations ⋮ An efficient and robust algorithm for source reconstruction in the Helmholtz equation

Uses Software

• L-BFGS

Cites Work

• On the limited memory BFGS method for large scale optimization
• A reliable estimation method of a dipole for three-dimensional Poisson equation
• An estimation method for the number of point masses in an inverse logarithmic potential problem using discrete Fourier transform
• Relaxation of a variational method for impedance computed tomography
• Updating Quasi-Newton Matrices with Limited Storage
• Locations and strengths of point sources: stability estimates
• A projective method for an inverse source problem of the Poisson equation
• An inverse source problem in potential analysis
• Identification of Robin coefficients by the means of boundary measurements
• Inverse source problem in an anisotropic medium by boundary measurements
• Numerical implementation of a variational method for electrical impedance tomography
• Inverse problems for partial differential equations

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