A shape optimization approach for electrical impedance tomography with point measurements
Abstract
Working within the class of piecewise constant conductivities, the inverse problem of electrical impedance tomography can be recast as a shape optimization problem where the discontinuity interface is the unknown. Using Gr\"oger's -estimates for mixed boundary value problems, the averaged adjoint method is extended to the case of Banach spaces, which allows to compute the derivative of shape functionals involving point evaluations. We compute the corresponding distributed expression of the shape derivative and show that it may contain Dirac measures in addition to the usual domain integrals. We use this distributed shape derivative to devise a numerical algorithm, show various numerical results supporting the method, and based on these results we discuss the influence of the point measurements patterns on the quality of the reconstructions.
Keywords
Cite
@article{arxiv.1911.06074,
title = {A shape optimization approach for electrical impedance tomography with point measurements},
author = {Yuri Flores Albuquerque and Antoine Laurain and Kevin Sturm},
journal= {arXiv preprint arXiv:1911.06074},
year = {2022}
}
Comments
24 pages, the reference "Bolsa de Produtividade em Pesquisa - PQ 2018, process: 304258/2018-0" was corrected in the Acknowledgements