Linearization of the forward map of electrical impedance tomography

Erfang Ma

doi:10.1088/1402-4896/ae32c9

Linearization of the forward map of electrical impedance tomography

Erfang Ma^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

Abstract

We analyze the nonlinear forward map of electrical impedance tomography (EIT) with the implicit function theorem. We show that the forward map is infinitely differentiable and use its Taylor expansion to quantify the error of this local linearization. We prove that the error of the linearization of second order could be halved with the popular log-transformation of conductivity in some cases. Simulations on a 3D EIT model also justify this theoretical finding.

Original language	English
Article number	035206
Journal	Physica Scripta
Volume	101
Issue number	3
DOIs	https://doi.org/10.1088/1402-4896/ae32c9
Publication status	Published - 23 Jan 2026

Keywords

electrical impedance tomography
forward map
linearization error
nonlinear analysis

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10.1088/1402-4896/ae32c9

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title = "Linearization of the forward map of electrical impedance tomography",

abstract = "We analyze the nonlinear forward map of electrical impedance tomography (EIT) with the implicit function theorem. We show that the forward map is infinitely differentiable and use its Taylor expansion to quantify the error of this local linearization. We prove that the error of the linearization of second order could be halved with the popular log-transformation of conductivity in some cases. Simulations on a 3D EIT model also justify this theoretical finding.",

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AB - We analyze the nonlinear forward map of electrical impedance tomography (EIT) with the implicit function theorem. We show that the forward map is infinitely differentiable and use its Taylor expansion to quantify the error of this local linearization. We prove that the error of the linearization of second order could be halved with the popular log-transformation of conductivity in some cases. Simulations on a 3D EIT model also justify this theoretical finding.

KW - electrical impedance tomography

KW - forward map

KW - linearization error

KW - nonlinear analysis

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DO - 10.1088/1402-4896/ae32c9

M3 - Article

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Linearization of the forward map of electrical impedance tomography

Abstract

Keywords

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