Uniqueness and Nonuniqueness in Inverse Problems for Elliptic Partial Differential Equations and Related Medical Imaging
Author
Source
Advances in Mathematical Physics
Issue
Vol. 2015, Issue 2015 (31 Dec. 2015), pp.1-8, 8 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2015-01-31
Country of Publication
Egypt
No. of Pages
8
Main Subjects
Abstract EN
Unique determination issues about inverse problems for elliptic partial differential equations in divergence form are summarized and discussed.
The inverse problems include medical imaging problems including electrical impedancetomography (EIT), diffuse optical tomography (DOT), and inverse scattering problem (ISP) which is an elliptic inverse problem closely related with DOT and EIT.
If the coefficient inside the divergence is isotropic, many uniqueness results are known.
However, it is known that inverse problem with anisotropic coefficients has many possible coefficients giving the samemeasured data for the inverse problem.
For anisotropic coefficient with anomaly with or without jumps from known or unknown background, nonuniqueness of the inverse problems is discussed and the relation to cloaking or illusion of the anomaly is explained.
The uniqueness and nonuniqueness issues are discussed firstly for EIT and secondly for ISP in similar arguments.
Arguing the relation between source-to-detector map and Dirichlet-to-Neumann map in DOT and the uniqueness and nonuniqueness of DOT are also explained.
American Psychological Association (APA)
Kwon, Kiwoon. 2015. Uniqueness and Nonuniqueness in Inverse Problems for Elliptic Partial Differential Equations and Related Medical Imaging. Advances in Mathematical Physics،Vol. 2015, no. 2015, pp.1-8.
https://search.emarefa.net/detail/BIM-1053043
Modern Language Association (MLA)
Kwon, Kiwoon. Uniqueness and Nonuniqueness in Inverse Problems for Elliptic Partial Differential Equations and Related Medical Imaging. Advances in Mathematical Physics No. 2015 (2015), pp.1-8.
https://search.emarefa.net/detail/BIM-1053043
American Medical Association (AMA)
Kwon, Kiwoon. Uniqueness and Nonuniqueness in Inverse Problems for Elliptic Partial Differential Equations and Related Medical Imaging. Advances in Mathematical Physics. 2015. Vol. 2015, no. 2015, pp.1-8.
https://search.emarefa.net/detail/BIM-1053043
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1053043