Abstract

In this paper, we show that by using microwave measurements at different frequencies and ultrasound localized perturbations to create local changes in the medium it is possible to extend the method developed by Ammari et al. in [SIAM J. Appl. Math., 68 (2008), pp. 1557–1573] to problems of the form $\nabla\cdot(a\nabla u)+k^{2}qu=0$ in $\Omega$, $u=\varphi$ on $\partial\Omega$, and to reliably reconstruct both the real-valued functions a and q from the internal energies $a|\nabla u|^2$ and $q|u|^2$.

MSC codes

  1. 31B20
  2. 35B37
  3. 35L05

Keywords

  1. hybrid imaging
  2. expansion methods
  3. microwave imaging
  4. elastic perturbation
  5. resolution enhancement
  6. explicit inversion formula
  7. optimal control

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Information & Authors

Information

Published In

cover image SIAM Journal on Applied Mathematics
SIAM Journal on Applied Mathematics
Pages: 2112 - 2130
ISSN (online): 1095-712X

History

Submitted: 21 March 2011
Accepted: 21 September 2011
Published online: 8 December 2011

MSC codes

  1. 31B20
  2. 35B37
  3. 35L05

Keywords

  1. hybrid imaging
  2. expansion methods
  3. microwave imaging
  4. elastic perturbation
  5. resolution enhancement
  6. explicit inversion formula
  7. optimal control

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