2018年7月
円形電気回路におけるディリクレ-ノイマン写像による導電率の再構成
同志社大学ハリス理化学研究報告
- ,
- ,
- 巻
- 59
- 号
- 2
- 開始ページ
- 69
- 終了ページ
- 74
- 記述言語
- 日本語
- 掲載種別
- 記事・総説・解説・論説等(大学・研究所紀要)
- DOI
- 10.14988/pa.2018.0000000166
The theory of inverse boundary value problems has been used in fields of engineering and physics such as non-destructive testing, medical imaging. <br />
Calder\'{o}n's inverse problem for an elliptic partial differential equation appears in electrical impedance tomography (EIT).<br />
EIT is one of techniques for medical imaging.<br />
One can infer inside of human body by the surface electrode measurements. <br />
Mathematically, this technique corresponds to the reconstruction of the electrical conductivity from boundary measurements.<br />
One of theoretical models of boundary measurements is the Dirichlet-to-Neumann map.<br />
In the present paper, we consider a discrete analogue of Calder\'{o}n's inverse problem.<br />
Namely, we derive a reconstruction procedure of conductivity on circular resistor networks from the Dirichlet-to-Neumann map.<br />
A numerical example of perturbation of the Dirichlet-to-Neumann map is also given in this paper.
Calder\'{o}n's inverse problem for an elliptic partial differential equation appears in electrical impedance tomography (EIT).<br />
EIT is one of techniques for medical imaging.<br />
One can infer inside of human body by the surface electrode measurements. <br />
Mathematically, this technique corresponds to the reconstruction of the electrical conductivity from boundary measurements.<br />
One of theoretical models of boundary measurements is the Dirichlet-to-Neumann map.<br />
In the present paper, we consider a discrete analogue of Calder\'{o}n's inverse problem.<br />
Namely, we derive a reconstruction procedure of conductivity on circular resistor networks from the Dirichlet-to-Neumann map.<br />
A numerical example of perturbation of the Dirichlet-to-Neumann map is also given in this paper.
- リンク情報
- ID情報
-
- DOI : 10.14988/pa.2018.0000000166
- ISSN : 2189-5937