JOINT INVERSE PROBLEMS AND DIFFERENTIAL GEOMETRY/PDE SEMINAR

Tuesday, August 3, 2004 Padelford C-36 1:30 pm Clear layer modeling and reconstructions in optical tomography

Guillaume Bal (Columbia University)

Transport solutions in highly scattering media are known to be well approximated by solutions to diffusion equations. As several numerical studies show, the presence of non-scattering areas, such as clear layers in optical tomography, hampers the use of classical diffusion. I will show that “generalized” diffusion equations can be derived to model the transport solution accurately in the small mean free path limit. I will then show that such clear layers (as well as any inhomogeneities inside the clear layer) can be uniquely determined by boundary measurements. This is based on adaptations of Kirsch’ factorization method.

For more information about this seminar, visit the DG/PDE Seminar Web page (from the Math Department home page, www.math.washington.edu, follow the link Seminars, Colloquia, and Conferences).

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