FEM-based scalp-to-cortex EEG data mapping via the solution of the Cauchy problem

DOI10.1515/jiip-2019-0065zbMath1446.65147arXiv1907.01504OpenAlexW3025493577MaRDI QIDQ2194640

Mikhail Malovichko, M. V. Fedorov, Ekaterina Skidchenko, Nikolay Yavich, Nikolay Koshev

Publication date: 4 September 2020

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

Full work available at URL: https://arxiv.org/abs/1907.01504

zbMATH Keywords

Cauchy problemill-posed problemsource localizationsuper resolutiondata mapping

Mathematics Subject Classification ID

Biological applications of optics and electromagnetic theory (78A70) Biomedical imaging and signal processing (92C55) PDEs in connection with biology, chemistry and other natural sciences (35Q92) Ill-posed problems for PDEs (35R25) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Harmonic, subharmonic, superharmonic functions in higher dimensions (31B05) Iterative numerical methods for linear systems (65F10) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Elliptic equations and elliptic systems (35J99) Boundary value and inverse problems for harmonic functions in higher dimensions (31B20) Numerical methods for ill-posed problems for boundary value problems involving PDEs (65N20)

Related Items (2)

Uniqueness' failure for the finite element Cauchy-Poisson's problem ⋮ Full Discretization of Cauchy's Problem by Lavrentiev--Finite Element Method

Uses Software

• iso2mesh

Cites Work

• Unnamed Item
• Carleman weight functions for a globally convergent numerical method for ill-posed Cauchy problems for some quasilinear PDEs
• Localization of the activity source in the inverse problem of magnetoencephalography
• Numerical solution of an ill-posed Cauchy problem for a quasilinear parabolic equation using a Carleman weight function
• Numerical solution of a Cauchy problem for the Laplace equation
• A MANN ITERATIVE REGULARIZATION METHOD FOR ELLIPTIC CAUCHY PROBLEMS
• An $H_\mathsf{div}$-Based Mixed Quasi-reversibility Method for Solving Elliptic Cauchy Problems
• A Carleman estimate and the balancing principle in the quasi-reversibility method for solving the Cauchy problem for the Laplace equation
• A Numerical Method to Solve a Phaseless Coefficient Inverse Problem from a Single Measurement of Experimental Data
• Convergence rates for the quasi-reversibility method to solve the Cauchy problem for Laplace's equation
• Numerical analysis of a two-level preconditioner for the diffusion equation with an anisotropic diffusion tensor
• The balancing principle for the regularization of elliptic Cauchy problems
• Cortical mapping by Laplace–Cauchy transmission using a boundary element method
• A mixed formulation of quasi-reversibility to solve the Cauchy problem for Laplace's equation

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