Inversion without Explicit Jacobian Calculations in Electrical Impedance Tomography

4th International Workshop on New Computational Methods for Inverse Problems

物理学;计算机科学

Fouchard, A.^1,2 ; Bonnet, S.^1 ; Hervé, L.^1 ; David, O.^2

CEA, Leti, MINATEC Campus, 17 rue des Martyrs, Grenoble, Cedex 9

F38054, France^1

Université Joseph Fourier, Grenoble Institute of Neuroscience, Bâtiment E.J. Safra, La Tronche

38700, France^2

关键词: Computational burden;    Conductivity distributions;    Efficient implementation;    Electrical impe dance tomography (EIT);    Electrical impedance tomography;    Electrical measurement;    Jacobian calculations;    Preconditioned conjugate gradient;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/542/1/012002/pdf
DOI  :  10.1088/1742-6596/542/1/012002

学科分类：计算机科学（综合）

来源: IOP

【 摘 要 】

Electrical impedance tomography (EIT) is the inverse problem of finding the internal conductivity distribution of a medium given boundary electrical measurements performed via an electrode array onto its surface. Conventional inversion schemes adopt Tikhonov regularized Newton-type methods. Following a transport back-transport approach, we develop in this work an adjoint approach which allows reducing computational burden in enabling inversion without explicit Jacobian calculation. Forward and back-projection operators are defined from potential gradients, along with their efficient implementation. These derivations allow the transparent use of inversion algorithms. We first check the implementation of operators. We then evaluate how reconstructions perform on simulated noisy data using a preconditioned conjugate gradient. We eventually practice our inversion framework on experimental data acquired in vitro from a saline phantom.