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Resolution and stability analysis in full-aperture, linearized conductivity and wave imaging


Authors: Habib Ammari, Josselin Garnier and Knut Sølna
Journal: Proc. Amer. Math. Soc. 141 (2013), 3431-3446
MSC (2010): Primary 35R30, 35B30
DOI: https://doi.org/10.1090/S0002-9939-2013-11590-X
Published electronically: June 11, 2013
MathSciNet review: 3080166
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Abstract: In this paper we consider resolution estimates in both the linearized conductivity problem and the wave imaging problem. Our purpose is to provide explicit formulas for the resolving power of the measurements in the presence of measurement noise. We show that the low-frequency regime in wave imaging and the inverse conductivity problem are very sensitive to measurement noise, while high frequencies increase stability in wave imaging.


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Additional Information

Habib Ammari
Affiliation: Department of Mathematics and Applications, École Normale Supérieure, 45 Rue d’Ulm, 75005 Paris, France
Email: habib.ammari@ens.fr

Josselin Garnier
Affiliation: Laboratoire de Probabilités et Modèles Aléatoires and Laboratoire Jacques-Louis Lions, Université Paris VII, 75205 Paris Cedex 13, France
Email: garnier@math.jussieu.fr

Knut Sølna
Affiliation: Department of Mathematics, University of California, Irvine, California 92697
Email: ksolna@math.uci.edu

DOI: https://doi.org/10.1090/S0002-9939-2013-11590-X
Keywords: Inverse conductivity problem, wave imaging, resolution, stability
Received by editor(s): August 26, 2011
Received by editor(s) in revised form: December 6, 2011
Published electronically: June 11, 2013
Additional Notes: This work was supported by the ERC Advanced Grant Project MULTIMOD–267184.
Communicated by: Walter Craig
Article copyright: © Copyright 2013 American Mathematical Society