Geodesic
A rainbow inverse problem
A. Blasselle1 ; V. Calvez2 ; A. Moussa3
1 Laboratoire Jacques-Louis Lions, 175 rue du Chevaleret, 75013 Paris, France
2 UMPA, ENS Lyon, 46, allée d’Italie 69364 Lyon Cedex 07, France
3 CMLA, Cachan, 61 Avenue du Président Wilson, 94235 Cachan Cedex, France
ESAIM. Proceedings, Tome 30 (2010), pp. 142-152 Cet article a éte moissonné depuis la source EDP Sciences

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We consider the radiative transfer equation (RTE) with reflection in a three-dimensional domain, infinite in two dimensions, and prove an existence result. Then, we study the inverse problem of retrieving the optical parameters from boundary measurements, with help of existing results by Choulli and Stefanov. This theoretical analysis is the framework of an attempt to model the color of the skin. For this purpose, a code has been developed to solve the RTE and to study the sensitivity of the measurements made by biophysicists with respect to the physiological parameters responsible for the optical properties of this complex, multi-layered material.
DOI : 10.1051/proc/2010011

A. Blasselle 1 ; V. Calvez 2 ; A. Moussa 3

1 Laboratoire Jacques-Louis Lions, 175 rue du Chevaleret, 75013 Paris, France
2 UMPA, ENS Lyon, 46, allée d’Italie 69364 Lyon Cedex 07, France
3 CMLA, Cachan, 61 Avenue du Président Wilson, 94235 Cachan Cedex, France 
@article{EP_2010_30_a10,
     author = {A. Blasselle and V. Calvez and A. Moussa},
     title = {A rainbow inverse problem},
     journal = {ESAIM. Proceedings},
     pages = {142--152},
     year = {2010},
     volume = {30},
     doi = {10.1051/proc/2010011},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/proc/2010011/}
}
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A. Blasselle; V. Calvez; A. Moussa. A rainbow inverse problem. ESAIM. Proceedings, Tome 30 (2010), pp. 142-152. doi: 10.1051/proc/2010011

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