Hostname: page-component-cd9895bd7-dk4vv Total loading time: 0 Render date: 2024-12-29T04:15:43.675Z Has data issue: false hasContentIssue false
  • English
  • Français

Identification of multipoles via boundary measurements

Published online by Cambridge University Press:  21 November 2011

Y.-S. CHUNG ,
J. E. KIM  and
S.-Y. CHUNG
Y.-S. CHUNG
Affiliation:
Department of Mathematics, Yonsei University, Seoul, 120-749, Korea email: ysjung93@hanmail.net
J. E. KIM
Affiliation:
Department of Mathematics, The Ohio State University, Columbus, Ohio, USA email: jkim@math.ohio-state.edu
S.-Y. CHUNG
Affiliation:
Department of Mathematics and Program of Integrated Biotechnology, Sogang University, Seoul 121-742, Korea email: sychung@sogang.ac.kr
Get access Rights & Permissions [Opens in a new window]

Abstract

This paper provides an algorithm for identifying the multipoles of a meromorphic function from the boundary measurements, which can be applied to inverse source problems for a Poisson equation to reconstruct its source such as linear combination of mono and dipolar point sources. After establishing an algorithm that allows to identify the number, the locations and the moments of poles, we provide a stability estimate of the algorithm under the measurement error.

Keywords

Inverse source problemsEEGGeneralized Vandermende Matrices
Type
Papers
Information
European Journal of Applied Mathematics , Volume 23 , Issue 2 , April 2012 , pp. 289 - 313
Copyright
Copyright © Cambridge University Press 2011

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

[1]El Badia, A. & Ha-Duong, T. (2000) An inverse source problem in potential analysis. Inverse Probl. 16, 651–663.CrossRefGoogle Scholar
[2]Hämäläinen, M., Hari, R., Ilmoniemi, R. J., Knuutila, J. & Lounasmaa, O. V. (1993) Magnetoencephalography – theory, instrumentation and applications to noninvasive studies of the working human brain. Rev. Mod. Phys. 65, 413–497.CrossRefGoogle Scholar
[3]Jerbi, K., Mosher, J. C., Baillet, S. & Leahy, R. M. (2002) On MEG forward modelling using multipolar expansions. Phys. Med. Biol. 47, 523–555.CrossRefGoogle ScholarPubMed
[4]Kang, H. & Lee, H. (2004) Identification of simple poles via boundary measurements and an application of EIT. Inverse Probl. 20, 1853–1863.CrossRefGoogle Scholar
[5]Nara, T. & Ando, S. (2003) A projective method for an inverse source problem of the Poisson equation. Inverse Probl. 19, 355–369.CrossRefGoogle Scholar
[6]Nara, T., Oohama, J., Hashomoto, M., Takeda, T. & Ando, S. (2007) Direct reconstruction algorithm of current dipoles for vector magnetoencephalography and electroencephalography. Phys. Med. Biol. 52, 3859–3879.CrossRefGoogle ScholarPubMed
[7]Nolte, G. & Curio, G. (1997) On the calculation of magnetic fields based on multipole modeling of focal biological current sources. Biophys. J. 73, 1253–1262.CrossRefGoogle ScholarPubMed
[8]Stoer, J. & Bulirsch, R. (1992) Introduction to Numerical Analysis. Springer, Berlin.Google Scholar