On an inverse boundary problem arising in brain imaging

Youjun Deng; Hongyu Liu; Gunther Uhlmann

doi:10.1016/j.jde.2019.03.019

On an inverse boundary problem arising in brain imaging

Youjun Deng^*, Hongyu Liu^*, Gunther Uhlmann^*

^*Corresponding author for this work

Research output: Journal Publications and Reviews › RGC 21 - Publication in refereed journal › peer-review

31 Citations (Scopus)

Abstract

We consider the inverse problem of recovering both an unknown electric current and the surrounding electromagnetic parameters of a medium from boundary measurements. This inverse problem arises in brain imaging. We show that under generic conditions one can recover both the source and the electromagnetic parameters if these are piecewise constant and the source current is invariant in a fixed direction or a harmonic function, respectively.

Original language	English
Pages (from-to)	2471-2502
Journal	Journal of Differential Equations
Volume	267
Issue number	4
Online published	1 Apr 2019
DOIs	https://doi.org/10.1016/j.jde.2019.03.019
Publication status	Published - 5 Aug 2019
Externally published	Yes

Research Keywords

Electroencephalography and magnetoencephalography
Identifiability and uniqueness
Inverse boundary problem
Maxwell system

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title = "On an inverse boundary problem arising in brain imaging",

abstract = "We consider the inverse problem of recovering both an unknown electric current and the surrounding electromagnetic parameters of a medium from boundary measurements. This inverse problem arises in brain imaging. We show that under generic conditions one can recover both the source and the electromagnetic parameters if these are piecewise constant and the source current is invariant in a fixed direction or a harmonic function, respectively.",

keywords = "Electroencephalography and magnetoencephalography, Identifiability and uniqueness, Inverse boundary problem, Maxwell system",

author = "Youjun Deng and Hongyu Liu and Gunther Uhlmann",

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T1 - On an inverse boundary problem arising in brain imaging

AU - Deng, Youjun

AU - Liu, Hongyu

AU - Uhlmann, Gunther

PY - 2019/8/5

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N2 - We consider the inverse problem of recovering both an unknown electric current and the surrounding electromagnetic parameters of a medium from boundary measurements. This inverse problem arises in brain imaging. We show that under generic conditions one can recover both the source and the electromagnetic parameters if these are piecewise constant and the source current is invariant in a fixed direction or a harmonic function, respectively.

AB - We consider the inverse problem of recovering both an unknown electric current and the surrounding electromagnetic parameters of a medium from boundary measurements. This inverse problem arises in brain imaging. We show that under generic conditions one can recover both the source and the electromagnetic parameters if these are piecewise constant and the source current is invariant in a fixed direction or a harmonic function, respectively.

KW - Electroencephalography and magnetoencephalography

KW - Identifiability and uniqueness

KW - Inverse boundary problem

KW - Maxwell system

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U2 - 10.1016/j.jde.2019.03.019

DO - 10.1016/j.jde.2019.03.019

M3 - RGC 21 - Publication in refereed journal

SN - 0022-0396

VL - 267

SP - 2471

EP - 2502

JO - Journal of Differential Equations

JF - Journal of Differential Equations

IS - 4

ER -

On an inverse boundary problem arising in brain imaging

Abstract

Research Keywords

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