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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Uniqueness and non-uniqueness in inverse radiative transfer


Authors: Plamen Stefanov and Alexandru Tamasan
Journal: Proc. Amer. Math. Soc. 137 (2009), 2335-2344
MSC (2000): Primary 35R30, 78A46
Published electronically: February 17, 2009
MathSciNet review: 2495267
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Abstract: We characterize the non-uniqueness in the inverse problem for the stationary transport model, in which the absorption $ a$ and the scattering coefficient $ k$ of the media are to be recovered from the albedo operator. We show that ``gauge equivalent'' pairs $ (a,k)$ yield the same albedo operator, and that we can recover uniquely the class of the gauge equivalent pairs. We apply this result to show unique determination of the media when the absorption $ a$ depends on the line of travel through each point while the scattering $ k$ obeys a symmetry property. Previously known results concerned the directional independent absorption $ a$.


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Additional Information

Plamen Stefanov
Affiliation: Department of Mathematics, Purdue University, 150 N. University Street, West Lafayette, Indiana 47907-2067
Email: stefanov@math.purdue.edu

Alexandru Tamasan
Affiliation: Department of Mathematics, University of Central Florida, 4000 Central Florida Boulevard, Orlando, Florida 32816
Email: tamasan@math.ucf.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-09-09839-6
PII: S 0002-9939(09)09839-6
Received by editor(s): September 15, 2008
Published electronically: February 17, 2009
Additional Notes: The first author was partly supported by NSF FRG Grant No. 0554065
Communicated by: Walter Craig
Article copyright: © Copyright 2009 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.