Integral formulation of the complete electrode model of electrical impedance tomography

IF 1.5 4区数学 Q2 MATHEMATICS, APPLIED

Inverse Problems and Imaging Pub Date : 2020-01-01 DOI:10.3934/ipi.2020017

Erfang Ma

引用次数: 4

Abstract

We model electrical impedance tomography (EIT) based on the minimum energy principle. It results in a constrained minimization problem in terms of current density. The new formulation is proved to have a unique solution within appropriate function spaces. By characterizing its solution with the Lagrange multiplier method, we relate the new formulation to the so-called shunt model and the complete electrode model (CEM) of EIT. Based on the new formulation, we also propose a new numerical method to solve the forward problem of EIT. The new solver is formulated in terms of current. It was shown to give similar results to that of the traditional finite element method, with simulations on a 2D EIT model.

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电阻抗层析成像全电极模型的积分公式

基于最小能量原理，建立了电阻抗层析成像(EIT)模型。这就导致了电流密度的约束最小化问题。证明了新公式在适当的函数空间内具有唯一解。通过用拉格朗日乘子法表征其解，我们将新公式与所谓的分流模型和全电极模型(CEM)联系起来。在此基础上，提出了一种新的求解EIT正演问题的数值方法。新的求解器是用电流表示的。在二维EIT模型上进行了仿真，得到了与传统有限元方法相似的结果。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Inverse Problems and Imaging 数学-物理：数学物理

CiteScore

2.50

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Inverse Problems and Imaging publishes research articles of the highest quality that employ innovative mathematical and modeling techniques to study inverse and imaging problems arising in engineering and other sciences. Every published paper has a strong mathematical orientation employing methods from such areas as control theory, discrete mathematics, differential geometry, harmonic analysis, functional analysis, integral geometry, mathematical physics, numerical analysis, optimization, partial differential equations, and stochastic and statistical methods. The field of applications includes medical and other imaging, nondestructive testing, geophysical prospection and remote sensing as well as image analysis and image processing. This journal is committed to recording important new results in its field and will maintain the highest standards of innovation and quality. To be published in this journal, a paper must be correct, novel, nontrivial and of interest to a substantial number of researchers and readers.