A stable recovering of dipole sources from partial boundary measurements

El-Badia, A; Farah, Maha

doi:10.1088/0266-5611/26/11/115006

Cited by 9 publications

(10 citation statements)

References 30 publications

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“…The analysis of the EEG forward model is an essential preliminary step to the resolution of the corresponding inverse source problem. In the head model of adults, theoretical and numerical results exist [9,13,14,16,29,10,4]. For the neonatal head model, identifiability and stability results for the inverse EEG source problem have been obtained in parallel to the present work [11].…”

Section: Mesh Nodes Tetrahedramentioning

confidence: 85%

EEG in neonates: Forward modeling and sensitivity analysis with respect to variations of the conductivity

Azizollahi

Darbas²,

Diallo³

et al. 2018

Mathematical Biosciences &Amp; Engineering

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The paper is devoted to the analysis of electroencephalography (EEG) in neonates. The goal is to investigate the impact of fontanels on EEG measurements, i.e. on the values of the electric potential on the scalp. In order to answer this clinical issue, a complete mathematical study (modeling, existence and uniqueness result, realistic simulations) is carried out. A model for the forward problem in EEG source localization is proposed. The model is able to take into account the presence and ossification process of fontanels which are characterized by a variable conductivity. From a mathematical point of view, the model consists in solving an elliptic problem with a singular source term in an inhomogeneous medium. A subtraction approach is used to deal with the singularity in the source term, and existence and uniqueness results are proved for the continuous problem. Discretization is performed with 3D Finite Elements of type P1 and error estimates are proved in the energy norm (H 1-norm). Numerical simulations for a three-layer spherical model as well as for a realistic neonatal head model including or not the fontanels have been

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Section: Mesh Nodes Tetrahedramentioning

confidence: 85%

EEG in neonates: Forward modeling and sensitivity analysis with respect to variations of the conductivity

Azizollahi

Darbas²,

Diallo³

et al. 2018

Mathematical Biosciences &Amp; Engineering

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“…However, before solving the algebraic equations in (14), we must determine the final state u(x, T * ) in order to obtain R(v) as defined by (13). More precisely, we only need to determine the quantities…”

Section: Application Of Algebraic Methodsmentioning

confidence: 99%

“…More incite, and a means of determining the correct value of m, may be obtained by studying the singular values of the complete M × M matrix H as was done for dipole source applications. [13] These values are shown in Unfortunately, the singular values shown in Figure 3 are not helpful. In fact, the reason the algorithm identified m = 3 as the rank of (μ 0 , μ 1 , .…”

Section: Relative Intensity Methodsmentioning

confidence: 99%

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On an inverse source problem for the heat equation. Application to a pollution detection problem, II

Andrle

Badia

2014

Inverse Problems in Science and Engineering

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This work considers the inverse problem of localizing and characterizing multiple stationary pollution sources in surface waters or atmospheric media. This particular problem has been studied before and a uniqueness result was shown. In this paper, we revisit this work with the objective of providing a more complete study. In particular, an alternative uniqueness proof is conducted which is valid for more general pollution source structures. Additionally, a practical numerical identification method is developed and implemented. Finally, several numerical studies are performed which illustrate practical considerations as well as the effectiveness of the approach.

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“…For example, Cimetiére et al [11], who were concerned with a line-segment crack identification from incomplete over-specified boundary data, use an iterated Tikhonov regularization method for solving the Cauchy problem. Whereas Elbadia et al [16] recover the boundary data for an electroencephalography application by a Koslov's algorithm. Ben Abda et al [9] identify epilepsy focus from over-determined electrical measurements (potential and current flux) on the scalp using complex analysis techniques.…”

Section: Introductionmentioning

confidence: 99%

Recovering data in groundwater: boundary conditions and Wells’ positions and fluxes

Tlatli-Hariga

Bouhlila²,

Abda

2011

Comput Geosci

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In this paper, we present an original methodology for recovering boundary conditions and hydraulic parameters in an aquifer domain. Boundary data are identified from the knowledge of over-specified boundary data on another part of the boundary. Then parameters, here wells' positions and fluxes, are recovered by the use of the reciprocity principle (Andrieux and Ben Abda, Mech Res Commun 20:415-420, 1993; Andrieux and Ben Abda, Inverse Probl 12:553-564, 1996). The boundary recovering method is based on the minimization of an energy-like error functional (Andrieux et al., Inverse Probl 22:115-133;Baranger and Andrieux, 2010).

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A stable recovering of dipole sources from partial boundary measurements

Cited by 9 publications

References 30 publications

EEG in neonates: Forward modeling and sensitivity analysis with respect to variations of the conductivity

EEG in neonates: Forward modeling and sensitivity analysis with respect to variations of the conductivity

On an inverse source problem for the heat equation. Application to a pollution detection problem, II

Recovering data in groundwater: boundary conditions and Wells’ positions and fluxes

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