Tue, 21 July, 2009, 17:15-18:15, Foyer
Optical Diffusion Tomography (ODT) is a medical imaging technique based on absorption and scattering of near infrared light in biological tissue. The propagation of light in dense media is usually modelled by the Boltzmann equation, in which the scattering and absorption properties of the tissue under investigation enter as coefficients.
For solving the inverse problem of determining the tissue properties from
transmission measurements, the so-called diffusion approximation of the
Boltzmann equation is most widely used. The inverse problem then reduces
to a parameter estimation problem in an elliptic respectively parabolic pde.
While on the one hand, the diffusion approximation facilitates the solution
of the inverse problem, it also introduces a substantial modeling error on the other hand. As a result only qualitative reconstruction can be obtained.
In order to obtain quantitative results, we investigate better approximations
of the Boltzmann equation by higher order moment methods and other Galerkin
methods in the velocity space, and compare to results obtained by the
Presentation slides (pdf, 2.1 MB)
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