Journal article
The imaging of small perturbations in an anisotropic media
Computers & mathematics with applications (1987), v 74(11), pp 2769-2783
01 Dec 2017
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Abstract
In this paper, we employ asymptotic analysis to determine information about small volume defects in a known anisotropic scattering medium from far field scattering data. The location of the defects is reconstructed via the MUSIC algorithm from the range of the multi static response matrix derived from the asymptotic expansion of the far field pattern in the presence of small defects. Since the same data determines the transmission eigenvalues corresponding to the perturbed media, we investigate how the presence of the defects changes the transmission eigenvalues and use this information to recover the strength of the small defects. We provide convergence results on transmission eigenvalues as the size of the defects tends to zero as well as derive the first correction term in the asymptotic expansion of the simple transmission eigenvalues. Numerical examples are presented to show the viability of our imaging method. (C) 2017 Elsevier Ltd. All rights reserved.
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Details
- Title
- The imaging of small perturbations in an anisotropic media
- Creators
- Fioralba Cakoni - Rutgers, The State University of New JerseyIsaac Harris - Texas A&M UniversityShari Moskow - Drexel University
- Publication Details
- Computers & mathematics with applications (1987), v 74(11), pp 2769-2783
- Publisher
- Elsevier
- Number of pages
- 15
- Grant note
- FA9550-17-1-0147 / AFOSR; United States Department of Defense; Air Force Office of Scientific Research (AFOSR) 392261 / Simons Foundation DMS-1602802; DMS-1411721 / NSF; National Science Foundation (NSF)
- Resource Type
- Journal article
- Language
- English
- Academic Unit
- Mathematics
- Web of Science ID
- WOS:000418980800011
- Scopus ID
- 2-s2.0-85026843273
- Other Identifier
- 991019168082104721
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- Collaboration types
- Domestic collaboration
- Web of Science research areas
- Mathematics, Applied